Total Posts:44|Showing Posts:1-30|Last Page
Jump to topic:

Negative Numbers

anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/16/2015 2:10:27 AM
Posted: 1 year ago
I would like to discuss whether Negative Numbers have any relevance to the physical Universe. I believe Negative Numbers to be a Philosophy rather than having any true value to Mathematics. I believe that as a set, Negative Numbers contradict real Positive Numbers, and therefore should be considered a logical fallacy.

I will start by explaining why I believe Negative Numbers are a Philosophy. Negative Numbers are a relatively new idea. There are several Historical records that indicate Negative Numbers were used in some way to describe Debt in certain ancient cultures. Debt is the only purpose mankind has ever had any need of Negative Numbers until the late 18th century. Philosophical mathematicians such as John Wallis, Casper Wessel, and William Hamilton changed this when they developed a set of rules to deal with Negative Numbers.

Which brings me to my next concern with Negative Numbers. The reason mankind was so reluctant to accept them was because of it's square root. A negative times a negative equals a positive, so there is no square root of -1. Because of this, most Mathematicians throughout History denied Negative Numbers, and Diophantus called such an idea "absurd".

That was until the 1500's, when Bombelli developed rules for working with what he called "Imaginary Numbers". Therefore, because the square root of a negative does not exist, we now "imagine" that such a number exists, and continue working out the problem based on Uncertain premises (Uncertainty Principle).

However, to do such a thing defies the Laws of Logic. Consider the following.

i^2=

(sq. rt. -1)^2=

(sq. rt. -1^2)=

sq. rt. 1=

1

This is a contradiction, and therefore it is Logically acceptable to deny any assertions based on the premises of Negative Numbers. Their acceptance has led to much Philosophical nonsense, and they are merely a figment of our imagination.

I hope we can have a fun discussion about this. Thank you all and God bless you.
dee-em
Posts: 6,481
Add as Friend
Challenge to a Debate
Send a Message
6/16/2015 7:00:14 AM
Posted: 1 year ago
At 6/16/2015 2:10:27 AM, anonymouswho wrote:
I would like to discuss whether Negative Numbers have any relevance to the physical Universe. I believe Negative Numbers to be a Philosophy rather than having any true value to Mathematics. I believe that as a set, Negative Numbers contradict real Positive Numbers, and therefore should be considered a logical fallacy.

I will start by explaining why I believe Negative Numbers are a Philosophy. Negative Numbers are a relatively new idea. There are several Historical records that indicate Negative Numbers were used in some way to describe Debt in certain ancient cultures. Debt is the only purpose mankind has ever had any need of Negative Numbers until the late 18th century. Philosophical mathematicians such as John Wallis, Casper Wessel, and William Hamilton changed this when they developed a set of rules to deal with Negative Numbers.

Which brings me to my next concern with Negative Numbers. The reason mankind was so reluctant to accept them was because of it's square root. A negative times a negative equals a positive, so there is no square root of -1. Because of this, most Mathematicians throughout History denied Negative Numbers, and Diophantus called such an idea "absurd".

That was until the 1500's, when Bombelli developed rules for working with what he called "Imaginary Numbers". Therefore, because the square root of a negative does not exist, we now "imagine" that such a number exists, and continue working out the problem based on Uncertain premises (Uncertainty Principle).

However, to do such a thing defies the Laws of Logic. Consider the following.

i^2=

(sq. rt. -1)^2=

(sq. rt. -1^2)=

sq. rt. 1=

1

This is a contradiction, and therefore it is Logically acceptable to deny any assertions based on the premises of Negative Numbers. Their acceptance has led to much Philosophical nonsense, and they are merely a figment of our imagination.

I hope we can have a fun discussion about this. Thank you all and God bless you.

The last equality is in error. There are two possible values for sq. rt 1, namely 1 and -1. You chose the first and ignored the second, which you had obfuscated by squaring.

Using index notation illustrates where you went wrong.

i^2=
((-1)^1/2)^2=
(-1)^1=
-1

Or

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1
Saint_of_Me
Posts: 2,402
Add as Friend
Challenge to a Debate
Send a Message
6/16/2015 1:57:22 PM
Posted: 1 year ago
One thing that can help is to realize that mathematics is a world of
its own that can be used to MODEL things in the real world, but, like
any model, is not IDENTICAL to that real world. Negative numbers are
part of the "model world", but the real world--nor so much.

But.....there are some situations where negative numbers make sense (and a negative answer to a problem might be valid) and others where they do not--so that a
negative answer just means there is no solution to the original
problem).

But real world apps? Yeah..a few I reckon. How bout the weather? LOL

In the case of temperatures, the 0 point (except in
absolute temperature) is arbitrary, so that SOME negative values are
possible, but others are not.

Finance? Well...In the case of money, a negative answer may or may not be valid. If
you are just spending money from a basic checking account, a negative
balance
means that you are overdrawn--but it DOES still have meaning,
because you now owe that much money to the bank. .

So.....how to interpret the negative result depends on the situation; often
positive and negative are just two sides of the same coin, each with
its own interpretation.

In physics.......I am not aware of any usage of negative numbers. (Hmm..I wonder if they would be used in equation regarding anti-matter? LOL)

Ah...another field they could be used is in geometry--or navigation. Like on a graph with an x, y axis and you are mapping coordinates.

Because it's helpful to assign numbers to locations in space, called coordinates, in order to measure distances. For these coordinates to make sense, we need to choose a reference point from which distances will be measured in order to assign coordinates. (This reference point can be assigned the value of zero in each of the three spatial dimensions. )

So...consider one direction, or axis, in relation to the reference point, like the north-south direction. We might decide to give a location a positive coordinate on the north-south axis if it lies north of the reference point.

But If it lies south of the reference point, we would then give it a negative value. Setting up a coordinate system like this allows to easily calculate distances between two locations using the ordinary laws of math applied to the coordinates--including the laws of negative numbers.

For example, if there is one location that is assigned a coordinate of 3 units north, and another that is assigned a coordinate of 2 units south, then the distance between them is .......3 - (-2) = 5 units.
Science Flies Us to the Moon. Religion Flies us Into Skyscrapers.
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/16/2015 11:45:45 PM
Posted: 1 year ago
At 6/16/2015 7:00:14 AM, dee-em wrote:
At 6/16/2015 2:10:27 AM, anonymouswho wrote:
I would like to discuss whether Negative Numbers have any relevance to the physical Universe. I believe Negative Numbers to be a Philosophy rather than having any true value to Mathematics. I believe that as a set, Negative Numbers contradict real Positive Numbers, and therefore should be considered a logical fallacy.

I will start by explaining why I believe Negative Numbers are a Philosophy. Negative Numbers are a relatively new idea. There are several Historical records that indicate Negative Numbers were used in some way to describe Debt in certain ancient cultures. Debt is the only purpose mankind has ever had any need of Negative Numbers until the late 18th century. Philosophical mathematicians such as John Wallis, Casper Wessel, and William Hamilton changed this when they developed a set of rules to deal with Negative Numbers.

Which brings me to my next concern with Negative Numbers. The reason mankind was so reluctant to accept them was because of it's square root. A negative times a negative equals a positive, so there is no square root of -1. Because of this, most Mathematicians throughout History denied Negative Numbers, and Diophantus called such an idea "absurd".

That was until the 1500's, when Bombelli developed rules for working with what he called "Imaginary Numbers". Therefore, because the square root of a negative does not exist, we now "imagine" that such a number exists, and continue working out the problem based on Uncertain premises (Uncertainty Principle).

However, to do such a thing defies the Laws of Logic. Consider the following.

i^2=

(sq. rt. -1)^2=

(sq. rt. -1^2)=

sq. rt. 1=

1

This is a contradiction, and therefore it is Logically acceptable to deny any assertions based on the premises of Negative Numbers. Their acceptance has led to much Philosophical nonsense, and they are merely a figment of our imagination.

I hope we can have a fun discussion about this. Thank you all and God bless you.

The last equality is in error. There are two possible values for sq. rt 1, namely 1 and -1. You chose the first and ignored the second, which you had obfuscated by squaring.

Using index notation illustrates where you went wrong.

i^2=
((-1)^1/2)^2=
(-1)^1=
-1

Or

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1

Dee-em! Hello my friend. I hope you enjoy this topic, I thought it would be interesting.

I have a few problems with your math. I don't really understand how you are getting -1. Why does:

((-1)^1/2)^2=

(-1)^1

I'm pretty sure the only logical outcomes for ((-1)^1/2)^2 is either 1 or i, and it can't be 1 because 1^2 will never be negative. I assume you are saying the square root of -1 is "supposed" to be "equivalent" to (-1)^1, but since the square root of -1 is nonexistent, I deny this assertion. Let me see if I can make this contradiction clearer.

1=

1^1/2=

((-1)-1)^1/2=

((-1)^1/2)x((-1)^1/2)=

i x i=

-1

This means that 1 is equal to -1. That is a contradiction and makes absolutely no sense.

2x3=6

It will always equal 6. Even if we invert the numbers:

3x2=6

However, I'm supposed to believe that i^2 is equal to both 1 as well as -1. If I have 1 apple, I might also have -1 apple? What is "negative one" anyways? If Zero is nothing, how might one have less than nothing, other than the imaginary scenario of debt? If there is 1 bird on a limb, might there also be -1 bird on -1 limb? To whom does the bird owe?

This is my other problem with Negative Numbers. How is it that one can HAVE a negative of something? Let's take temperature for example. Based on the Celsius scale, 0.01 is freezing, 100 is boiling, and -273.15 is the lowest possible temperature. That is why we have the Kelvin scale, which recognizes -273.15 as Absolute Zero. Therefore, there is no fundamental need for Negative Numbers.

If I have 1 apple, how might I give you 2 apples, so that I will have -1? If there is 1 bird on a limb, how might two birds fly off of the limb so that there is -1 bird?

Thank you my friend.
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/17/2015 12:48:10 AM
Posted: 1 year ago
At 6/16/2015 1:57:22 PM, Saint_of_Me wrote:
One thing that can help is to realize that mathematics is a world of
its own that can be used to MODEL things in the real world, but, like
any model, is not IDENTICAL to that real world. Negative numbers are
part of the "model world", but the real world--nor so much.

But.....there are some situations where negative numbers make sense (and a negative answer to a problem might be valid) and others where they do not--so that a
negative answer just means there is no solution to the original
problem).

But real world apps? Yeah..a few I reckon. How bout the weather? LOL

In the case of temperatures, the 0 point (except in
absolute temperature) is arbitrary, so that SOME negative values are
possible, but others are not.

Finance? Well...In the case of money, a negative answer may or may not be valid. If
you are just spending money from a basic checking account, a negative
balance
means that you are overdrawn--but it DOES still have meaning,
because you now owe that much money to the bank. .

So.....how to interpret the negative result depends on the situation; often
positive and negative are just two sides of the same coin, each with
its own interpretation.

In physics.......I am not aware of any usage of negative numbers. (Hmm..I wonder if they would be used in equation regarding anti-matter? LOL)

Ah...another field they could be used is in geometry--or navigation. Like on a graph with an x, y axis and you are mapping coordinates.

Because it's helpful to assign numbers to locations in space, called coordinates, in order to measure distances. For these coordinates to make sense, we need to choose a reference point from which distances will be measured in order to assign coordinates. (This reference point can be assigned the value of zero in each of the three spatial dimensions. )

So...consider one direction, or axis, in relation to the reference point, like the north-south direction. We might decide to give a location a positive coordinate on the north-south axis if it lies north of the reference point.

But If it lies south of the reference point, we would then give it a negative value. Setting up a coordinate system like this allows to easily calculate distances between two locations using the ordinary laws of math applied to the coordinates--including the laws of negative numbers.

For example, if there is one location that is assigned a coordinate of 3 units north, and another that is assigned a coordinate of 2 units south, then the distance between them is .......3 - (-2) = 5 units.

Hello my friend. Thanks for joining the discussion. If you read what I wrote to dee-em, I already addressed the temperature situation, as well as the debt since I believe debt to be an imaginary scenario. Since nothing physical is involved. The coordinate situation is strange to me. Why not make both West and East positive numbers? We could call it 2W+3E=5?

If I take a line graph, and wish to make a square with an area of 16 cubits, then of the top right side of my line I can square 2, which will give me an area of 4 cubits. If I then multiply the left top side, I can multiple -2x2 and I will get an area of -4 cubits. The same can be done on the right bottom side. However, when I get to the bottom left side, I must multiply -2(-2), and that is going to put my corner in the same position as the top right corner. I will then have a 90" angle, and nothing physically solid.

If I do the same thing, using positive numbers going in all directions, I get a perfect square with the middle point being Zero. As long as I understand the direction I wish to go, there is no need to bring Negative Numbers into the equation.

Does that make any sense? Thank you friend and God bless you.
Enji
Posts: 1,022
Add as Friend
Challenge to a Debate
Send a Message
6/17/2015 2:08:06 AM
Posted: 1 year ago
I honestly can't tell if this thread and most of the comments in it are serious. Negative numbers are or should be considered to be logically fallacious? WTF did I just read?
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/17/2015 3:15:11 AM
Posted: 1 year ago
At 6/17/2015 2:08:06 AM, Enji wrote:
I honestly can't tell if this thread and most of the comments in it are serious. Negative numbers are or should be considered to be logically fallacious? WTF did I just read?

Hello friend, it is good to meet you. Thank you for joining us. Yes I'm serious. Do you have any concerns with anything I've said?
dee-em
Posts: 6,481
Add as Friend
Challenge to a Debate
Send a Message
6/17/2015 3:48:15 AM
Posted: 1 year ago
At 6/16/2015 11:45:45 PM, anonymouswho wrote:
At 6/16/2015 7:00:14 AM, dee-em wrote:
At 6/16/2015 2:10:27 AM, anonymouswho wrote:
I would like to discuss whether Negative Numbers have any relevance to the physical Universe. I believe Negative Numbers to be a Philosophy rather than having any true value to Mathematics. I believe that as a set, Negative Numbers contradict real Positive Numbers, and therefore should be considered a logical fallacy.

I will start by explaining why I believe Negative Numbers are a Philosophy. Negative Numbers are a relatively new idea. There are several Historical records that indicate Negative Numbers were used in some way to describe Debt in certain ancient cultures. Debt is the only purpose mankind has ever had any need of Negative Numbers until the late 18th century. Philosophical mathematicians such as John Wallis, Casper Wessel, and William Hamilton changed this when they developed a set of rules to deal with Negative Numbers.

Which brings me to my next concern with Negative Numbers. The reason mankind was so reluctant to accept them was because of it's square root. A negative times a negative equals a positive, so there is no square root of -1. Because of this, most Mathematicians throughout History denied Negative Numbers, and Diophantus called such an idea "absurd".

That was until the 1500's, when Bombelli developed rules for working with what he called "Imaginary Numbers". Therefore, because the square root of a negative does not exist, we now "imagine" that such a number exists, and continue working out the problem based on Uncertain premises (Uncertainty Principle).

However, to do such a thing defies the Laws of Logic. Consider the following.

i^2=

(sq. rt. -1)^2=

(sq. rt. -1^2)=

sq. rt. 1=

1

This is a contradiction, and therefore it is Logically acceptable to deny any assertions based on the premises of Negative Numbers. Their acceptance has led to much Philosophical nonsense, and they are merely a figment of our imagination.

I hope we can have a fun discussion about this. Thank you all and God bless you.

The last equality is in error. There are two possible values for sq. rt 1, namely 1 and -1. You chose the first and ignored the second, which you had obfuscated by squaring.

Using index notation illustrates where you went wrong.

i^2=
((-1)^1/2)^2=
(-1)^1=
-1

Or

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1

Dee-em! Hello my friend. I hope you enjoy this topic, I thought it would be interesting.

I have a few problems with your math. I don't really understand how you are getting -1. Why does:

((-1)^1/2)^2=

(-1)^1

When you have a power to a power, you multiply the indices. 1/2 x 2 = 1. This is high school level mathematics.

I'm pretty sure the only logical outcomes for ((-1)^1/2)^2 is either 1 or i, and it can't be 1 because 1^2 will never be negative. I assume you are saying the square root of -1 is "supposed" to be "equivalent" to (-1)^1, but since the square root of -1 is nonexistent, I deny this assertion. Let me see if I can make this contradiction clearer.

I have absolutely no idea what you are getting at. Look up the rules for indices in any secondary school maths textbook.

1=

1^1/2=

((-1)-1)^1/2=

((-1)^1/2)x((-1)^1/2)=

i x i=

-1

This means that 1 is equal to -1. That is a contradiction and makes absolutely no sense.

No. You are arbitrarily choosing -1 x -1 = 1 in line 3. But 1 x 1 = 1. So you are obfuscating again. What's more you are now agreeing that i^2 = -1 in line 5 which directly contradicts your earlier 'proof'. In other words, you are accepting what you are trying to disprove!

2x3=6

It will always equal 6. Even if we invert the numbers:

3x2=6

However, I'm supposed to believe that i^2 is equal to both 1 as well as -1.

When you are doing algebra and square both sides in order to simplify, you must have been taught of the danger - that two solutions are possible for the unknown because the sign is lost. See here:

http://math.stackexchange.com...

You are falling for a simple mathematical fallacy when squaring - the sign (information) is lost.

If I have 1 apple, I might also have -1 apple? What is "negative one" anyways? If Zero is nothing, how might one have less than nothing, other than the imaginary scenario of debt? If there is 1 bird on a limb, might there also be -1 bird on -1 limb? To whom does the bird owe?

This is my other problem with Negative Numbers. How is it that one can HAVE a negative of something? Let's take temperature for example. Based on the Celsius scale, 0.01 is freezing, 100 is boiling, and -273.15 is the lowest possible temperature. That is why we have the Kelvin scale, which recognizes -273.15 as Absolute Zero. Therefore, there is no fundamental need for Negative Numbers.

If I have 1 apple, how might I give you 2 apples, so that I will have -1? If there is 1 bird on a limb, how might two birds fly off of the limb so that there is -1 bird?

Thank you my friend.

Um, debt is real. Trust me.
slo1
Posts: 4,354
Add as Friend
Challenge to a Debate
Send a Message
6/17/2015 8:50:30 AM
Posted: 1 year ago
At 6/16/2015 2:10:27 AM, anonymouswho wrote:
I would like to discuss whether Negative Numbers have any relevance to the physical Universe. I believe Negative Numbers to be a Philosophy rather than having any true value to Mathematics. I believe that as a set, Negative Numbers contradict real Positive Numbers, and therefore should be considered a logical fallacy.

I will start by explaining why I believe Negative Numbers are a Philosophy. Negative Numbers are a relatively new idea. There are several Historical records that indicate Negative Numbers were used in some way to describe Debt in certain ancient cultures. Debt is the only purpose mankind has ever had any need of Negative Numbers until the late 18th century. Philosophical mathematicians such as John Wallis, Casper Wessel, and William Hamilton changed this when they developed a set of rules to deal with Negative Numbers.

Which brings me to my next concern with Negative Numbers. The reason mankind was so reluctant to accept them was because of it's square root. A negative times a negative equals a positive, so there is no square root of -1. Because of this, most Mathematicians throughout History denied Negative Numbers, and Diophantus called such an idea "absurd".

That was until the 1500's, when Bombelli developed rules for working with what he called "Imaginary Numbers". Therefore, because the square root of a negative does not exist, we now "imagine" that such a number exists, and continue working out the problem based on Uncertain premises (Uncertainty Principle).

However, to do such a thing defies the Laws of Logic. Consider the following.

i^2=

(sq. rt. -1)^2=

(sq. rt. -1^2)=

sq. rt. 1=

1

This is a contradiction, and therefore it is Logically acceptable to deny any assertions based on the premises of Negative Numbers. Their acceptance has led to much Philosophical nonsense, and they are merely a figment of our imagination.

I hope we can have a fun discussion about this. Thank you all and God bless you.

Of course negative numbers have associations to real world properties. Numbers are just descriptions of real word properties.

1. Negative cash flow. It means you are spending more money than what you are taking in, a very real situation, which would be award having both money out and money in being positive. You could not represent the final net position without a negative number and would always have to represent with two positive numbers which would represent a negative position anyway.

2. Cartesian plane, a negative indicates a direction. Since direction can go for infinity if a starting point (0,0)and negative direction (left & down) was not used it would be very impractical to use.

3. Vectors become worthless without negatives. How would I ever calculate the net force when dealing with many forces in different directions?

I think you are getting the point. Summary and net calculations are worthless without negative numbers.
Floid
Posts: 751
Add as Friend
Challenge to a Debate
Send a Message
6/17/2015 10:06:43 AM
Posted: 1 year ago
At 6/16/2015 2:10:27 AM, anonymouswho wrote:
I would like to discuss whether Negative Numbers have any relevance to the physical Universe. I believe Negative Numbers to be a Philosophy rather than having any true value to Mathematics. I believe that as a set, Negative Numbers contradict real Positive Numbers, and therefore should be considered a logical fallacy.

1.) Positive numbers don't have any relevance to the physical universe either. We use math to try to model the physical universe. But the physical universe is what it is without our concepts of numbers or how they may relate to modeling the universe.

2.) Mathematics in general falls in the domain of abstraction and logic (call this philosophy if you want). Negative numbers are just as valid in that domain as are positive numbers.

3.) Negative numbers do contradict positive numbers in that if you add an equally negative number to an equally positive number you get 0. Perfect contradiction. No logical fallacy there though.
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/17/2015 6:38:34 PM
Posted: 1 year ago
At 6/17/2015 3:48:15 AM, dee-em wrote:
At 6/16/2015 11:45:45 PM, anonymouswho wrote:
At 6/16/2015 7:00:14 AM, dee-em wrote:
At 6/16/2015 2:10:27 AM, anonymouswho wrote:

The last equality is in error. There are two possible values for sq. rt 1, namely 1 and -1. You chose the first and ignored the second, which you had obfuscated by squaring.

Using index notation illustrates where you went wrong.

i^2=
((-1)^1/2)^2=
(-1)^1=
-1

Or

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1

Dee-em! Hello my friend. I hope you enjoy this topic, I thought it would be interesting.

I have a few problems with your math. I don't really understand how you are getting -1. Why does:

((-1)^1/2)^2=

(-1)^1

When you have a power to a power, you multiply the indices. 1/2 x 2 = 1. This is high school level mathematics.

Ah, now I see the problem. I'm afraid you are forgetting PEMAS. Parenthesis are always worked out first. You worked the exponents first, which does not work. Here's an example:

(6+(3^2))^3=

If we do the exponents first, we get

(6^3)+(3^6)=

216+729=

945

That is incorrect. The correct answer is

(6+(3^2))^3=

(6+9)^3=

15^3=

3375

Therefore,

((-1)^1/2)^2=

(-1^1/2)^2=

Since (-1^1/2) doesn't exist, then the answer is either

i^2 (because it's imaginary)

Or

(-1^1/2)x(-1^1/2)=

i x i=

(An imaginary nonexistent number) x (An imaginary nonexistent number)=

I can only imagine a nonexistent number


I'm pretty sure the only logical outcomes for ((-1)^1/2)^2 is either 1 or i, and it can't be 1 because 1^2 will never be negative. I assume you are saying the square root of -1 is "supposed" to be "equivalent" to (-1)^1, but since the square root of -1 is nonexistent, I deny this assertion. Let me see if I can make this contradiction clearer.

I have absolutely no idea what you are getting at. Look up the rules for indices in any secondary school maths textbook.

I did, but only because you fooled me with your clever trick.

1=

1^1/2=

((-1)-1)^1/2=

((-1)^1/2)x((-1)^1/2)=

i x i=

-1

This means that 1 is equal to -1. That is a contradiction and makes absolutely no sense.

No. You are arbitrarily choosing -1 x -1 = 1 in line 3. But 1 x 1 = 1. So you are obfuscating again. What's more you are now agreeing that i^2 = -1 in line 5 which directly contradicts your earlier 'proof'. In other words, you are accepting what you are trying to disprove!

No, I'm not accepting what I'm trying to disprove. I'm showing why this whole equation is nonsense, because the whole premises of negative numbers is nonsense.

2x3=6

It will always equal 6. Even if we invert the numbers:

3x2=6

However, I'm supposed to believe that i^2 is equal to both 1 as well as -1.

When you are doing algebra and square both sides in order to simplify, you must have been taught of the danger - that two solutions are possible for the unknown because the sign is lost. See here:

http://math.stackexchange.com...

You are falling for a simple mathematical fallacy when squaring - the sign (information) is lost.

Thank you for that link. I really liked what one person in particular said:

"Start with a false proposition

e.g.: W22;2=+2

square both sides

(W22;2)^2=(+2)^2

and it becomes true (!?)

+4=+4

So the operation turns (some) false statements into true statements."

This is fun. The rest of it was a bunch of nonsense about Negative Numbers, which I deny.

If I have 1 apple, I might also have -1 apple? What is "negative one" anyways? If Zero is nothing, how might one have less than nothing, other than the imaginary scenario of debt? If there is 1 bird on a limb, might there also be -1 bird on -1 limb? To whom does the bird owe?

This is my other problem with Negative Numbers. How is it that one can HAVE a negative of something? Let's take temperature for example. Based on the Celsius scale, 0.01 is freezing, 100 is boiling, and -273.15 is the lowest possible temperature. That is why we have the Kelvin scale, which recognizes -273.15 as Absolute Zero. Therefore, there is no fundamental need for Negative Numbers.

If I have 1 apple, how might I give you 2 apples, so that I will have -1? If there is 1 bird on a limb, how might two birds fly off of the limb so that there is -1 bird?

Thank you my friend.

Um, debt is real. Trust me.

How is debt real? There may be real consequences for debt, but debt itself is a figment of our imagination. Consider the following:

I go to a bank and take a loan for $500. I am now under a contractual agreement that I will pay the back back $500 (this bank doesn't change interest because they're awesome). So I have $500 and I also "have" -$500. This means I have $0.

I then take my $0 and buy a $500 guitar. Now I have no $500, and all I have left is -$500.

I get my paycheck a week later. It's $300. So I now have -$200. Unfortunately, my car breaks down and I have to take it to a mechanic. He charges me $200. So now I take my -$200 and pay him $200. I now have -$400, and I put $100 of it in a sock. A week later I die a very lonely man with no immediate family. A new family purchases my home. They find the sock. Inside the sock is $100 that they now physically hold. Where is the -$400? It is now $0 because it never existed to begin with.

So we have:

(-500)+500=

0

0-500=

-500

(-500)+300=

-200

(-200)-200=

-400=

$100 in a sock and $400 in debt=

$100 to the new family and $0 to the bank

So you see, the math works, but it doesn't actually "mean" anything. All negative numbers either equal a positive number to someone else or zero.

You're from Australia, correct? I assumed all Australians were familiar with Economics and the evils of Capitalist America, since you have one of the best Economic systems in the world. We have the Federal Reserve that prints this imaginary money out of nothing every day. It's really just a number on a computer screen. In fact, I find it interesting that the Federal Reserve was initiated not too long after the acceptance of Negative Numbers. Seems to be a deceitful correlation there. Anyways, thank you friend. I look forward to hearing from you soon.
dee-em
Posts: 6,481
Add as Friend
Challenge to a Debate
Send a Message
6/17/2015 8:36:52 PM
Posted: 1 year ago
At 6/17/2015 6:38:34 PM, anonymouswho wrote:
At 6/17/2015 3:48:15 AM, dee-em wrote:
At 6/16/2015 11:45:45 PM, anonymouswho wrote:
At 6/16/2015 7:00:14 AM, dee-em wrote:
At 6/16/2015 2:10:27 AM, anonymouswho wrote:

The last equality is in error. There are two possible values for sq. rt 1, namely 1 and -1. You chose the first and ignored the second, which you had obfuscated by squaring.

Using index notation illustrates where you went wrong.

i^2=
((-1)^1/2)^2=
(-1)^1=
-1

Or

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1

Dee-em! Hello my friend. I hope you enjoy this topic, I thought it would be interesting.

I have a few problems with your math. I don't really understand how you are getting -1. Why does:

((-1)^1/2)^2=

(-1)^1

When you have a power to a power, you multiply the indices. 1/2 x 2 = 1. This is high school level mathematics.

Ah, now I see the problem. I'm afraid you are forgetting PEMAS. Parenthesis are always worked out first. You worked the exponents first, which does not work. Here's an example:

(6+(3^2))^3=

If we do the exponents first, we get

(6^3)+(3^6)=

216+729=

945

That is incorrect. The correct answer is

(6+(3^2))^3=

(6+9)^3=

15^3=

3375

Goal-post moving and irrelevant. We've been down this path before. There was no addition in any example I gave you.

Therefore,

((-1)^1/2)^2=

(-1^1/2)^2=

Since (-1^1/2) doesn't exist, then the answer is either

i^2 (because it's imaginary)

Or

(-1^1/2)x(-1^1/2)=

i x i=

(An imaginary nonexistent number) x (An imaginary nonexistent number)=

I can only imagine a nonexistent number

i^2 is what you started out with. Well done. Lol.

I'm pretty sure the only logical outcomes for ((-1)^1/2)^2 is either 1 or i, and it can't be 1 because 1^2 will never be negative. I assume you are saying the square root of -1 is "supposed" to be "equivalent" to (-1)^1, but since the square root of -1 is nonexistent, I deny this assertion. Let me see if I can make this contradiction clearer.

I have absolutely no idea what you are getting at. Look up the rules for indices in any secondary school maths textbook.

I did, but only because you fooled me with your clever trick.

There was no trick.

1=

1^1/2=

((-1)-1)^1/2=

((-1)^1/2)x((-1)^1/2)=

i x i=

-1

This means that 1 is equal to -1. That is a contradiction and makes absolutely no sense.

No. You are arbitrarily choosing -1 x -1 = 1 in line 3. But 1 x 1 = 1. So you are obfuscating again. What's more you are now agreeing that i^2 = -1 in line 5 which directly contradicts your earlier 'proof'. In other words, you are accepting what you are trying to disprove!

No, I'm not accepting what I'm trying to disprove. I'm showing why this whole equation is nonsense, because the whole premises of negative numbers is nonsense.

Denying what you did in the face of the black and white evidence just makes you look foolish.

2x3=6

It will always equal 6. Even if we invert the numbers:

3x2=6

However, I'm supposed to believe that i^2 is equal to both 1 as well as -1.

When you are doing algebra and square both sides in order to simplify, you must have been taught of the danger - that two solutions are possible for the unknown because the sign is lost. See here:

http://math.stackexchange.com...

You are falling for a simple mathematical fallacy when squaring - the sign (information) is lost.

Thank you for that link. I really liked what one person in particular said:

"Start with a false proposition

e.g.: W22;2=+2

square both sides

(W22;2)^2=(+2)^2

and it becomes true (!?)

+4=+4

So the operation turns (some) false statements into true statements."

Because squaring both sides of an equation is fraught with danger as information is lost. I keep telling you that. If you had paid attention in maths class at school, you might even remember your teacher carefully explaining this to you. When you have an equation you must do exactly the same operation to both sides. Squaring violates this rule. In your example you multiplied the LHS by -2 and the RHS by +2. That is a different operation on each side. Enough said.

This is fun. The rest of it was a bunch of nonsense about Negative Numbers, which I deny.

Yes, denial is best when argument fails. Lol.

If I have 1 apple, I might also have -1 apple? What is "negative one" anyways? If Zero is nothing, how might one have less than nothing, other than the imaginary scenario of debt? If there is 1 bird on a limb, might there also be -1 bird on -1 limb? To whom does the bird owe?

This is my other problem with Negative Numbers. How is it that one can HAVE a negative of something? Let's take temperature for example. Based on the Celsius scale, 0.01 is freezing, 100 is boiling, and -273.15 is the lowest possible temperature. That is why we have the Kelvin scale, which recognizes -273.15 as Absolute Zero. Therefore, there is no fundamental need for Negative Numbers.

If I have 1 apple, how might I give you 2 apples, so that I will have -1? If there is 1 bird on a limb, how might two birds fly off of the limb so that there is -1 bird?

Thank you my friend.

Um, debt is real. Trust me.

How is debt real? There may be real consequences for debt, but debt itself is a figment of our imagination. Consider the following:
< snipped nonsense >
You're from Australia, correct? I assumed all Australians were familiar with Economics and the evils of Capitalist America, since you have one of the best Economic systems in the world. We have the Federal Reserve that prints this imaginary money out of nothing every day. It's really just a number on a computer screen. In fact, I find it interesting that the Federal Reserve was initiated not too long after the acceptance of Negative Numbers. Seems to be a deceitful correlation there. Anyways, thank you friend. I look forward to hearing from you soon.

Gish gallop. We have travelled this path before. I have neither the patience nor the inclination to correct your numerous misconceptions about credit and debit and basic accounting principles. Please carry on with your ignorant and blinkered views on any subject you think you are an expert in at any given time. I will watch on with wry amusement.
Enji
Posts: 1,022
Add as Friend
Challenge to a Debate
Send a Message
6/17/2015 11:23:13 PM
Posted: 1 year ago
Floid hits the nail on the head. Negative numbers are no more or less valid/fallacious than positive numbers. You are essentially arguing against subtraction.
Sidewalker
Posts: 3,713
Add as Friend
Challenge to a Debate
Send a Message
6/18/2015 6:10:56 AM
Posted: 1 year ago
At 6/16/2015 2:10:27 AM, anonymouswho wrote:
I would like to discuss whether Negative Numbers have any relevance to the physical Universe. I believe Negative Numbers to be a Philosophy rather than having any true value to Mathematics.

Mathematics is an abstraction, just a logical human construct, simply a tool which is valid when it is useful, Negative Numbers are valid because they are useful.

I believe that as a set, Negative Numbers contradict real Positive Numbers, and therefore should be considered a logical fallacy.

Nonsense, do you think left contradicts right, up contradicts down? Negative Numbers don"t "contradict real Positive Numbers", they simply represent the opposite of real Positive Numbers. If a positive number is used to represent a specific direction in a coordinate system, the negative number simply represents the opposite direction. Negative numbers can represent measurements below zero on a scale, on a temperature scale for instance, positive numbers represent degrees above zero, negative numbers represent degrees below zero, these negative numbers correspond to real measurements, which make them useful and valid.

I will start by explaining why I believe Negative Numbers are a Philosophy. Negative Numbers are a relatively new idea. There are several Historical records that indicate Negative Numbers were used in some way to describe Debt in certain ancient cultures. Debt is the only purpose mankind has ever had any need of Negative Numbers until the late 18th century. Philosophical mathematicians such as John Wallis, Casper Wessel, and William Hamilton changed this when they developed a set of rules to deal with Negative Numbers.

More nonsense, first of all, there have almost always been calculations that would entail negative numbers, negative numbers are simply a matter of subtraction which is as old as mathematics itself. The Chinese were notating and working with negative numbers by around 200 BCE (which is a negative number on the Julian Calendar), the rules for dealing with negative numbers were included in Jiuzhang Suanshu"s "The Nine Chapters on the Mathematical Art by around 100 CE, and the Indian mathematician Brahmagupta had laid out explicit rules for dealing with negative numbers by around 620 C.E.

Which brings me to my next concern with Negative Numbers. The reason mankind was so reluctant to accept them was because of it's square root. A negative times a negative equals a positive, so there is no square root of -1. Because of this, most Mathematicians throughout History denied Negative Numbers, and Diophantus called such an idea "absurd".

That was until the 1500's, when Bombelli developed rules for working with what he called "Imaginary Numbers". Therefore, because the square root of a negative does not exist, we now "imagine" that such a number exists, and continue working out the problem based on Uncertain premises (Uncertainty Principle).

However, to do such a thing defies the Laws of Logic. Consider the following.

i^2=

(sq. rt. -1)^2=

(sq. rt. -1^2)=

sq. rt. 1=

1

This is a contradiction, and therefore it is Logically acceptable to deny any assertions based on the premises of Negative Numbers. Their acceptance has led to much Philosophical nonsense, and they are merely a figment of our imagination.

Nonsense, it doesn"t logically follow that just because there is no square root of a negative number, that it is "logically acceptable to deny any assertions based on the premises of Negative Numbers", that is pure nonsense. The simple fact that a negative number times a negative number is a positive number doesn"t invalidate subtraction; it doesn"t invalidate scales and coordinate systems.

Mathematics is a pure abstraction, simply a human construct that is useful, when positive numbers are useful they are valid, when negative numbers are useful they are valid, I it isn"t useful to try to find the square root of a negative number then just don"t do it, there is certainly no reason to get all bunged up about it and deny the basic foundational principles of the useful abstraction we call mathematics.


I hope we can have a fun discussion about this. Thank you all and God bless you.

That depends, if you are some kind of intellectual masochist that enjoys being logically spanked, then yeah, you could have fun with it.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/18/2015 10:52:41 AM
Posted: 1 year ago
At 6/17/2015 8:36:52 PM, dee-em wrote:


Goal-post moving and irrelevant. We've been down this path before. There was no addition in any example I gave you.

Yes there was.

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1

You see, you added the two square roots of -1 and got 1. You can't do that because you have to work the (-1) first because it's the inner most parenthesis. Actually, -1 shouldn't be in parenthesis by its self anyways. It should be:

-(1^((1/2)^2))

That would give you -1, but it's hardly the square root of -1 after you add all the parentheses. Anyways, when it comes to actually finding the square root of -1, we'd have to write

(-1^(1/2))

So if we square that, we get

(-1^(1/2))^2=

(-1^(1/2))"(-1^(1/2))=

There is no square root of -1, so this equation becomes

i x i

And then we must assume that because we've given i the definition of the square root of -1, then i x i is equal to -1. The problem is, we are taking two nonexistent numbers and "assuming" they equal -1.


Therefore,

((-)1^(1/2)))^2)=

(-1^1/2)^2=

Since (-1^1/2) doesn't exist, then the answer is either

i^2 (because it's imaginary)

Or

(-1^1/2)x(-1^1/2)=

i x i=

(An imaginary nonexistent number) x (An imaginary nonexistent number)=

I can only imagine a nonexistent number

i^2 is what you started out with. Well done. Lol.

Yes because that's the only thing that can be done. See here:

http://www.friesian.com... (I will come back to this article often. It doesn't agree with what I'm presenting, but it does show the philosophical implications of imaginary numbers)

"That is what I find the most exasperating about a particular attitude. If the expression sqrt. -1 has a solution that is not a real number, what is that? Well, it is i. OK. But what then is i? It is sqrt. -1. So we are back where we started. This is a circular and question-begging procedure. We should listen to the logicians quietly snorting in the background. The expression "i" consists of a variable for an unknown. The unknown in this case will be a constant, and it will be the number that solves the expression "sqrt. -1." Since the expression is a square root, for which there are algorithms, and the root to be taken is of sqrt. -1, we might think that some algorithm will get us the answer. It doesn't"

I'm pretty sure the only logical outcomes for ((-1)^1/2)^2 is either 1 or i, and it can't be 1 because 1^2 will never be negative. I assume you are saying the square root of -1 is "supposed" to be "equivalent" to (-1)^1, but since the square root of -1 is nonexistent, I deny this assertion. Let me see if I can make this contradiction clearer.

I have absolutely no idea what you are getting at. Look up the rules for indices in any secondary school maths textbook.

I did, but only because you fooled me with your clever trick.

There was no trick.

I'm sorry for accusing you of tricking me.

1=

1^1/2=

((-1)-1)^1/2=

((-1)^1/2)x((-1)^1/2)=

i x i=

-1

This means that 1 is equal to -1. That is a contradiction and makes absolutely no sense.

No. You are arbitrarily choosing -1 x -1 = 1 in line 3. But 1 x 1 = 1. So you are obfuscating again. What's more you are now agreeing that i^2 = -1 in line 5 which directly contradicts your earlier 'proof'. In other words, you are accepting what you are trying to disprove!

No, I'm not accepting what I'm trying to disprove. I'm showing why this whole equation is nonsense, because the whole premises of negative numbers is nonsense.

Denying what you did in the face of the black and white evidence just makes you look foolish.

I don't agree that i^2 equals -1. Obviously I wrote this to show how ridiculous it is to say that i^2 equals -1, because that means 1=-1



Thank you for that link. I really liked what one person in particular said:

"Start with a false proposition

e.g.: W22;2=+2

square both sides

(W22;2)^2=(+2)^2

and it becomes true (!?)

+4=+4

So the operation turns (some) false statements into true statements."

Because squaring both sides of an equation is fraught with danger as information is lost. I keep telling you that. If you had paid attention in maths class at school, you might even remember your teacher carefully explaining this to you. When you have an equation you must do exactly the same operation to both sides. Squaring violates this rule. In your example you multiplied the LHS by -2 and the RHS by +2. That is a different operation on each side. Enough said.

It looks like when I copied and pasted, some of the characters messed up.

In that equation, the number -2 is squared by +2, and the number +2 is squared by +2. Thus, the same operation was done for both sides. They both equal 4.


This is fun. The rest of it was a bunch of nonsense about Negative Numbers, which I deny.

Yes, denial is best when argument fails. Lol.

Denial is best when we're talking about something impossible to exist.

If I have 1 apple, I might also have -1 apple? What is "negative one" anyways? If Zero is nothing, how might one have less than nothing, other than the imaginary scenario of debt? If there is 1 bird on a limb, might there also be -1 bird on -1 limb? To whom does the bird owe?

This is my other problem with Negative Numbers. How is it that one can HAVE a negative of something? Let's take temperature for example. Based on the Celsius scale, 0.01 is freezing, 100 is boiling, and -273.15 is the lowest possible temperature. That is why we have the Kelvin scale, which recognizes -273.15 as Absolute Zero. Therefore, there is no fundamental need for Negative Numbers.

If I have 1 apple, how might I give you 2 apples, so that I will have -1? If there is 1 bird on a limb, how might two birds fly off of the limb so that there is -1 bird?

Thank you my friend.

Um, debt is real. Trust me.

How is debt real? There may be real consequences for debt, but debt itself is a figment of our imagination. Consider the following:
< snipped nonsense >
You're from Australia, correct? I assumed all Australians were familiar with Economics and the evils of Capitalist America, since you have one of the best Economic systems in the world. We have the Federal Reserve that prints this imaginary money out of nothing every day. It's really just a number on a computer screen. In fact, I find it interesting that the Federal Reserve was initiated not too long after the acceptance of Negative Numbers. Seems to be a deceitful correlation there. Anyways, thank you friend. I look forward to hearing from you soon.

Gish gallop. We have travelled this path before. I have neither the patience nor the inclination to correct your numerous misconceptions about credit and debit and basic accounting principles. Please carry on with your ignorant and blinkered views on any subject you think you are an expert in at any given time. I will watch on with wry amusement.

Gish gallop? Did you just learn that one because you've used it a lot this go around. Okay, we don't have to talk about debt unless it strictly has to do with Negative Numbers; because without debt, there isn't too much of an argument for them.

Remember, my main argument is that Negative Numbers should have no relevance to physical reality. If you have any free time, I'd really like to know what you think of my example stories. Thank you dee-em.
Floid
Posts: 751
Add as Friend
Challenge to a Debate
Send a Message
6/18/2015 12:57:39 PM
Posted: 1 year ago
Remember, my main argument is that Negative Numbers should have no relevance to phys

Describe to me mathematically the acceleration of a ball thrown into the air without using negative numbers.
Enji
Posts: 1,022
Add as Friend
Challenge to a Debate
Send a Message
6/18/2015 3:51:14 PM
Posted: 1 year ago
At 6/18/2015 10:52:41 AM, anonymouswho wrote:
Remember, my main argument is that Negative Numbers should have no relevance to physical reality.
CP symmetry was postulated in the late 1950's. Scientists proposed that if you reversed the charges of particles (e.g. replace an electron with a positron) and reversed spatial parity (i.e. flip the sign of all 3 spatial coordinates), the laws of physics and behaviour of physical systems would remain unchanged. However, experimental discovery of CP-violations prove this is not the case. If CP symmetry held, maybe you'd have an argument that negative numbers have no relevance to physical reality because you could just flip-flop signs and everything would remain the same. CP-violation, however, proves that the sign of charges and parity is relevant to physical reality.
dee-em
Posts: 6,481
Add as Friend
Challenge to a Debate
Send a Message
6/18/2015 9:46:07 PM
Posted: 1 year ago
At 6/18/2015 10:52:41 AM, anonymouswho wrote:
At 6/17/2015 8:36:52 PM, dee-em wrote:

Goal-post moving and irrelevant. We've been down this path before. There was no addition in any example I gave you.

Yes there was.

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1

You see, you added the two square roots of -1 and got 1. You can't do that because you have to work the (-1) first because it's the inner most parenthesis.

That addition is completely unrelated to the example you gave. It's one of the standard laws for indices. See rule #3:

http://mathematics.laerd.com...

This is all high-school level mathematics.

Actually, -1 shouldn't be in parenthesis by its self anyways. It should be:

-(1^((1/2)^2))

Why? You're just making up your own rules as you go along. i = (-1)^1/2. i<> -(1^1/2). By definition.

That would give you -1, but it's hardly the square root of -1 after you add all the parentheses. Anyways, when it comes to actually finding the square root of -1, we'd have to write

(-1^(1/2))

So if we square that, we get

(-1^(1/2))^2=

(-1^(1/2))"(-1^(1/2))=

There is no square root of -1, so this equation becomes

i x i

And then we must assume that because we've given i the definition of the square root of -1, then i x i is equal to -1. The problem is, we are taking two nonexistent numbers and "assuming" they equal -1.

You are lost in confusion. I don't know where to begin correcting you. You set out aiming to prove i^2 = 1. I showed you your error, in that squaring can only be done with an awareness of the loss of information about the sign. I also showed you the correct way to do it, giving the result of -1 as you would expect. You haven't identified any problem with my maths. I can't help you further.

i^2 is what you started out with. Well done. Lol.

Yes because that's the only thing that can be done.

If you set out to prove i^2 = i^2, then you succeeded.

See here:

http://www.friesian.com... (I will come back to this article often. It doesn't agree with what I'm presenting, but it does show the philosophical implications of imaginary numbers)

"That is what I find the most exasperating about a particular attitude. If the expression sqrt. -1 has a solution that is not a real number, what is that? Well, it is i. OK. But what then is i? It is sqrt. -1. So we are back where we started. This is a circular and question-begging procedure. We should listen to the logicians quietly snorting in the background. The expression "i" consists of a variable for an unknown. The unknown in this case will be a constant, and it will be the number that solves the expression "sqrt. -1." Since the expression is a square root, for which there are algorithms, and the root to be taken is of sqrt. -1, we might think that some algorithm will get us the answer. It doesn't"

More gish gallop.

I have absolutely no idea what you are getting at. Look up the rules for indices in any secondary school maths textbook.

I did, but only because you fooled me with your clever trick.

There was no trick.

I'm sorry for accusing you of tricking me.

Contrition. Good. There is hope for you yet.

No. You are arbitrarily choosing -1 x -1 = 1 in line 3. But 1 x 1 = 1. So you are obfuscating again. What's more you are now agreeing that i^2 = -1 in line 5 which directly contradicts your earlier 'proof'. In other words, you are accepting what you are trying to disprove!

No, I'm not accepting what I'm trying to disprove. I'm showing why this whole equation is nonsense, because the whole premises of negative numbers is nonsense.

Denying what you did in the face of the black and white evidence just makes you look foolish.

I don't agree that i^2 equals -1. Obviously I wrote this to show how ridiculous it is to say that i^2 equals -1, because that means 1=-1

And I clearly identified your error. Not once have you acknowledged the problem with squaring.

Thank you for that link. I really liked what one person in particular said:

"Start with a false proposition

e.g.: W22;2=+2

square both sides

(W22;2)^2=(+2)^2

and it becomes true (!?)

+4=+4

So the operation turns (some) false statements into true statements."

Because squaring both sides of an equation is fraught with danger as information is lost. I keep telling you that. If you had paid attention in maths class at school, you might even remember your teacher carefully explaining this to you. When you have an equation you must do exactly the same operation to both sides. Squaring violates this rule. In your example you multiplied the LHS by -2 and the RHS by +2. That is a different operation on each side. Enough said.

It looks like when I copied and pasted, some of the characters messed up.

In that equation, the number -2 is squared by +2, and the number +2 is squared by +2. Thus, the same operation was done for both sides. They both equal 4.

What does squaring by +2 mean? Squaring is the operation of multiplying a number by itself. The notation of a^2 is just shorthand for a x a. The LHS is -2 so it is multiplied by -2. The RHS is +2 so it is multiplied by +2. Different operations on each side. I'm not sure that this could be any clearer.

This is fun. The rest of it was a bunch of nonsense about Negative Numbers, which I deny.

Yes, denial is best when argument fails. Lol.

Denial is best when we're talking about something impossible to exist.

We're talking about mathematical constructs. Positive numbers don't have any more existence than negative numbers. Why are you a bigot against negative numbers?
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/19/2015 7:07:23 AM
Posted: 1 year ago
At 6/17/2015 10:06:43 AM, Floid wrote:
At 6/16/2015 2:10:27 AM, anonymouswho wrote:
I would like to discuss whether Negative Numbers have any relevance to the physical Universe. I believe Negative Numbers to be a Philosophy rather than having any true value to Mathematics. I believe that as a set, Negative Numbers contradict real Positive Numbers, and therefore should be considered a logical fallacy.

1.) Positive numbers don't have any relevance to the physical universe either. We use math to try to model the physical universe. But the physical universe is what it is without our concepts of numbers or how they may relate to modeling the universe.

Hello Floid, thank you for joining this conversation. I'm sorry it's taken so long to reply.

Your interpretation of mathematics is perfectly acceptable, and in such a case, I wouldn't care if someone wants to play math tricks and make up imaginary scenarios. But when we try to use Negative Numbers to "model" the physical Universe, then I deny the whole proposition. To answer dee-em's last question, the reason I'm against Negative Numbers is because Philosophers try to use them as excuses for their flawed Science. I'll give a few examples:

My first concern is that Negative and Imaginary Numbers are used to model the physical Universe. Whether it be temperature or time, there is always a beginning. I also don't believe this beginning is ever absolutely zero, because that would be something out of nothing. Regardless, there will never be and has never been negative temperature or negative time. I believe time began Plank Time after the "Big Bang", and it has continued forward but never backward. So for simplicity sake, that would be zero, rather than the present being zero, past negative, and future positive.

Which brings me to my next concern. The only justification for Negative Numbers is an excuse that I have heard for everything from the Origin of the Universe to Free Will; the Uncertainty Principle of Quantum Mechanics. I deny the Uncertainty Principle because it defies Logic. I feel that if there should be a contradiction in any of our beliefs, then we must either reevaluate what we're seeing until we find a coherent answer, or we must deny the whole proposition. Here's a quote from my article that mentions the Uncertainty Principle:

http://www.friesian.com...

"The second is suggested by quantum mechanics, where reality, while "really" being out there, is at the same time conditioned by the observation of subjects. Observation collapses the sum of possibilities into discrete actualities. This gives to subjects a role in the constitution of reality that was always objectionable to a four-square Realist like Albert Einstein."

Complex numbers are supposedly essential to understanding Quantum Mechanics, and yet nobody really understands Quantum Mechanics because there is always the delusion of Uncertainty.

Besides Free Will, my biggest problem with Complex Numbers is Imaginary Time. It is believed that before Plank Time after the Big Bang, an infinite amount of matter and an infinite amount of energy was infinitely condensed into the Singularity. There have been no valid rebuttals to this until Stephen Hawking introduced what he calls "Imaginary Time". Basically, because there is an infinite amount of Positive Numbers, there is likewise an infinite amount of Negative Numbers. Therefore, Hawking's "imagines" that there was infinite time before the Big Bang, as well as infinite Imaginary Time. He basically says "hey, we call imaginary numbers real, so imaginary time can be real too". No it can't, because it is a figment of his imagination. This all has to do with the Uncertainty Principle, which can't work without Complex Numbers; and Complex Numbers likewise fall apart without the Uncertainty Principle.

2.) Mathematics in general falls in the domain of abstraction and logic (call this philosophy if you want). Negative numbers are just as valid in that domain as are positive numbers.

I believe mathematics falls into the domain of Logic, and when it comes to modeling the Universe, I believe that Negative Numbers give us nothing but nonsense. I believe Positive Numbers are the only mathematics that model reality. For example: if I have 3 apples, and I give you 2, then I have 1 apple and you have 2. The 1 apple that I have exists, and the 2 apples you have still exist, even though I no longer posses them. This is because 3-2=1 and that is True. There is no other possible outcome, and this tells us that Truth does exist.

Now I have 1 apple. I some how give you 3 apples. I now have -2 apples? Where? Under what circumstance is something this absurd acceptable?

3.) Negative numbers do contradict positive numbers in that if you add an equally negative number to an equally positive number you get 0. Perfect contradiction. No logical fallacy there though.

A perfect contradiction is still a contradiction. Sometimes something appears correct until we work on it a little further and find the whole thing is nonsense. Such as the square root of -1.

Describe to me mathematically the acceleration of a ball thrown into the air without using negative numbers.

Okay.

Let d= deceleration (whereas we understand that for deceleration, the final velocity will always be less than the initial velocity)

Initial velocity vi= 20
Final velocity vf= 0
Time taken t= 5

So deceleration is (vi-vf)/t, or

(20-0)/5=

d4 m/s^2

So, let a= acceleration (whereas we understand that for acceleration, the final velocity will always be greater than the initial velocity)

Initial velocity vi= 10
final velocity vf= 20
time taken t= 5

So acceleration is (vf-vi)/t (simply reverse the order of the velocities)

(20-10)/5=

a2 m/s^2

Thank you my friend. I hope to hear from you soon.
Floid
Posts: 751
Add as Friend
Challenge to a Debate
Send a Message
6/19/2015 8:10:11 AM
Posted: 1 year ago
At 6/19/2015 7:07:23 AM, anonymouswho wrote:
At 6/17/2015 10:06:43 AM, Floid wrote:
Describe to me mathematically the acceleration of a ball thrown into the air without using negative numbers.

Okay.

Let d= deceleration (whereas we understand that for deceleration, the final velocity will always be less than the initial velocity)

So deceleration is (vi-vf)/t, or

So, let a= acceleration (whereas we understand that for acceleration, the final velocity will always be greater than the initial velocity)

So acceleration is (vf-vi)/t (simply reverse the order of the velocities)

Now see if you can come up with a mathematical relationship between deceleration and acceleration.
Floid
Posts: 751
Add as Friend
Challenge to a Debate
Send a Message
6/19/2015 8:27:38 AM
Posted: 1 year ago
At 6/19/2015 8:10:11 AM, Floid wrote:
At 6/19/2015 7:07:23 AM, anonymouswho wrote:
At 6/17/2015 10:06:43 AM, Floid wrote:
Describe to me mathematically the acceleration of a ball thrown into the air without using negative numbers.

Okay.

Let d= deceleration (whereas we understand that for deceleration, the final velocity will always be less than the initial velocity)

So deceleration is (vi-vf)/t, or

So, let a= acceleration (whereas we understand that for acceleration, the final velocity will always be greater than the initial velocity)

So acceleration is (vf-vi)/t (simply reverse the order of the velocities)

And after you discover the mathematical relationship between acceleration and deceleration readdress my original question: mathematically describe the acceleration of a ball thrown in the air . To help you along assume the acceleration due to gravity is a uniform 9.8 m/s^2. I would suggest using coordinate system aligned with gravity so you don't have to bother with multiple axes.
Greyparrot
Posts: 14,313
Add as Friend
Challenge to a Debate
Send a Message
6/19/2015 9:48:48 AM
Posted: 1 year ago
I suppose you could always redefine negative numbers as a positive value in an opposite direction.
Then just use subtraction for computing.
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/19/2015 10:24:10 AM
Posted: 1 year ago
At 6/19/2015 8:27:38 AM, Floid wrote:
At 6/19/2015 8:10:11 AM, Floid wrote:
At 6/19/2015 7:07:23 AM, anonymouswho wrote:
At 6/17/2015 10:06:43 AM, Floid wrote:
Describe to me mathematically the acceleration of a ball thrown into the air without using negative numbers.

Okay.

Let d= deceleration (whereas we understand that for deceleration, the final velocity will always be less than the initial velocity)

So deceleration is (vi-vf)/t, or

So, let a= acceleration (whereas we understand that for acceleration, the final velocity will always be greater than the initial velocity)

So acceleration is (vf-vi)/t (simply reverse the order of the velocities)

And after you discover the mathematical relationship between acceleration and deceleration readdress my original question: mathematically describe the acceleration of a ball thrown in the air . To help you along assume the acceleration due to gravity is a uniform 9.8 m/s^2. I would suggest using coordinate system aligned with gravity so you don't have to bother with multiple axes.

I had originally used gravity to explain deceleration and acceleration, but I decided to keep it simple and use an easy example. I have to go to bed now, so I will try to work on this tonight. I still have a few people that I haven't replied to, and I have to reply to dee-em also. All of this math is not easy to do with the limited characters I can use. Plus I write everything from my phone, so please bear with me. Thank you very much for continuing this discussion with me. God bless you friend.
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/20/2015 5:05:41 AM
Posted: 1 year ago
At 6/18/2015 3:51:14 PM, Enji wrote:
At 6/18/2015 10:52:41 AM, anonymouswho wrote:
Remember, my main argument is that Negative Numbers should have no relevance to physical reality.
CP symmetry was postulated in the late 1950's. Scientists proposed that if you reversed the charges of particles (e.g. replace an electron with a positron) and reversed spatial parity (i.e. flip the sign of all 3 spatial coordinates), the laws of physics and behaviour of physical systems would remain unchanged. However, experimental discovery of CP-violations prove this is not the case. If CP symmetry held, maybe you'd have an argument that negative numbers have no relevance to physical reality because you could just flip-flop signs and everything would remain the same. CP-violation, however, proves that the sign of charges and parity is relevant to physical reality.

Hello my friend, I'm sorry I haven't wrote you yet. I actually don't know a whole lot about CP symmetry, and it seems as though Physicists don't really understand it either. Is there anything about the CP violations that Complex Numbers can explain better than Positive Numbers? I'm sorry I just can't find a whole lot of information. Thank you my friend.
tarkovsky
Posts: 212
Add as Friend
Challenge to a Debate
Send a Message
6/20/2015 9:00:56 AM
Posted: 1 year ago
So negative numbers really are necessary as they form the basis for basically every meaningful mathematical structure. Groups, rings, fields, vector spaces, modules. You need additive inverses for these things to be additive groups or rings or fields etc. etc. In other words in order to do, say, physics, you need things like vector spaces which you won't have. So yes it is relevant to the physical insofar as math is relevant. Do numbers exist in the real world yada yada. Different question different conversation. Negatives help form meaningful mathematical structures and are certainly more than philosophical curiosities.
DizzyKnight
Posts: 19
Add as Friend
Challenge to a Debate
Send a Message
6/20/2015 12:55:18 PM
Posted: 1 year ago
I wish to contribute to this discussion in the best way I could, and it wouldn't be in the form of a short answer. I hope my friends here will spend the time to read through what I wrote below.

Mathematical objects are not "materialistic", like axioms, they are abstract objects we define with specific properties. For example, x is an even if number if it is divisible by two. Any object that satisfies the properties of an even number is an even number. What other properties it carries does not matter at all.

We can define mathematical objects and axioms in whatever way we want. However there are two concerns, 1) do they give rise to any contradictions, 2) why should we define them?

Like natural numbers, negative numbers and imaginary numbers are also defined by us. So within in the scope of mathematics, they are no less "real" than natural numbers, they are just less intuitive.

So far, negative numbers are not known to produce any contradictory results. The example anonymouswho has given about complex number is a famous mathematical fallacy documented in mathematical literature. The real problem lies in the assumption that sqrt(a) x sqrt(b) = sqrt(ab) holds for all real numbers a, b. This property only holds when at least one of a and b is positive (or 0). Just because negative numbers do not share some of the properties that positive numbers do, does not mean they are contradictory.

All you can validly deduce is, since negative numbers do not share this property, they are not positive numbers (nor 0 to be more accurate).

Actually, you could generalize the fallacious proof and add the following statements: "this is a contradiction, hence sqrt(a) x sqrt(b) != sqrt(ab) for negative numbers a and b." And voila, there's a completely rigorous mathematic proof using the technique "proof by contradiction". ALL you have shown is that negative numbers do not have this property that positive numbers do, and because of that, you reject the existence of negative numbers?

In a similar fashion: for every real number a and and non-zero real number b, a/b is a real number. Just because 0 does not share this property doesn"t mean it is contradictory (as dividing by zero is undefined). Not all numbers need to have the same properties.

So clearly negative numbers satisfies condition 1, it is not contradictory (so far, at least). But does it satisfy condition 2, in what way is this mathematical object useful to us?

In many real life situations, the scale of a quantity extends in opposite ways. Directions (left and right, up and down, north and south, east and west), charges/potentials (positive and negative), etc.

Certainly you could "avoid" the use of negative numbers in cartesian coordinates by assigning the qualifiers N and S, W and E, but in the end, this is no different than using negative numbers. As explained by above, a mathematical object is defined by its properties. The properties of N and S coordinates exactly mimics those of positive and negative coordinates. In other words, you are still using negative numbers, S is still on the other side of the scale compared to N. Instead of 4 and -3, you call them 4N and 3S, you now two qualifiers instead of a single negative sign. All you have done is changed and complicated the notations.

For electrical charges, are you going use a separate set of notations and call +4 coulombs 4P coulombs (P for proton) and -3 coulombs 3E coulombs (E for electrons)? Why not just use the universal notation of negative numbers?

Ultimately, you cannot avoid using the concept of negative numbers, quantities that progress on opposite directions, all you can do is call it a different name, and more complicated notations.

Thank you.

P.S. The fallacy that one equals negative one is documented in the book "Fallacies in Mathematics" by E. A. Maxwell, published by Cambridge University Press
https://books.google.com.hk...
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/21/2015 6:22:54 AM
Posted: 1 year ago
At 6/20/2015 12:55:18 PM, DizzyKnight wrote:
I wish to contribute to this discussion in the best way I could, and it wouldn't be in the form of a short answer. I hope my friends here will spend the time to read through what I wrote below.

Thank you very much for joining the discussion my friend. I look forward to discussing this with you.

Mathematical objects are not "materialistic", like axioms, they are abstract objects we define with specific properties. For example, x is an even if number if it is divisible by two. Any object that satisfies the properties of an even number is an even number. What other properties it carries does not matter at all.

We can define mathematical objects and axioms in whatever way we want. However there are two concerns, 1) do they give rise to any contradictions, 2) why should we define them?

Like natural numbers, negative numbers and imaginary numbers are also defined by us. So within in the scope of mathematics, they are no less "real" than natural numbers, they are just less intuitive.

So far, negative numbers are not known to produce any contradictory results. The example anonymouswho has given about complex number is a famous mathematical fallacy documented in mathematical literature. The real problem lies in the assumption that sqrt(a) x sqrt(b) = sqrt(ab) holds for all real numbers a, b. This property only holds when at least one of a and b is positive (or 0). Just because negative numbers do not share some of the properties that positive numbers do, does not mean they are contradictory.

All you can validly deduce is, since negative numbers do not share this property, they are not positive numbers (nor 0 to be more accurate).

Actually, you could generalize the fallacious proof and add the following statements: "this is a contradiction, hence sqrt(a) x sqrt(b) != sqrt(ab) for negative numbers a and b." And voila, there's a completely rigorous mathematic proof using the technique "proof by contradiction". ALL you have shown is that negative numbers do not have this property that positive numbers do, and because of that, you reject the existence of negative numbers?

In a similar fashion: for every real number a and and non-zero real number b, a/b is a real number. Just because 0 does not share this property doesn"t mean it is contradictory (as dividing by zero is undefined). Not all numbers need to have the same properties.

So clearly negative numbers satisfies condition 1, it is not contradictory (so far, at least). But does it satisfy condition 2, in what way is this mathematical object useful to us?

In many real life situations, the scale of a quantity extends in opposite ways. Directions (left and right, up and down, north and south, east and west), charges/potentials (positive and negative), etc.

This right here is exactly what I'm talking about. I don't care if we wish to use the (-) sign to "represent" direction, but we must understand that a negative does not dwell into the realm of "below zero". Therefore, if (-x) and (-y) are understood as S and W (or whatever we may be measuring), then they are still positive numbers. Then, if we wish to take the square root of 4SW, we will have 2SW. So, does it not make more sense to redefine how we multiply negative numbers (in such a way that they are positive) rather than make up something called i that doesn't exist and give it a definition?

Certainly you could "avoid" the use of negative numbers in cartesian coordinates by assigning the qualifiers N and S, W and E, but in the end, this is no different than using negative numbers. As explained by above, a mathematical object is defined by its properties. The properties of N and S coordinates exactly mimics those of positive and negative coordinates. In other words, you are still using negative numbers, S is still on the other side of the scale compared to N. Instead of 4 and -3, you call them 4N and 3S, you now two qualifiers instead of a single negative sign. All you have done is changed and complicated the notations.

For electrical charges, are you going use a separate set of notations and call +4 coulombs 4P coulombs (P for proton) and -3 coulombs 3E coulombs (E for electrons)? Why not just use the universal notation of negative numbers?

Ultimately, you cannot avoid using the concept of negative numbers, quantities that progress on opposite directions, all you can do is call it a different name, and more complicated notations.

Thank you.

P.S. The fallacy that one equals negative one is documented in the book "Fallacies in Mathematics" by E. A. Maxwell, published by Cambridge University Press
https://books.google.com.hk...

Yes I've looked through this as well. It all has to do with definitions. That is why I propose that we use negative numbers with the understanding that they are not really below zero. If they are simply positive numbers is the opposite direction, then there is no need for imaginaries or complex numbers. We simply redefine negative. What are your thoughts on Imaginary Time?

Thank you my friend and God bless you.
anonymouswho
Posts: 431
Add as Friend
Challenge to a Debate
Send a Message
6/23/2015 8:40:19 AM
Posted: 1 year ago
At 6/18/2015 9:46:07 PM, dee-em wrote:
At 6/18/2015 10:52:41 AM, anonymouswho wrote:
At 6/17/2015 8:36:52 PM, dee-em wrote:

Goal-post moving and irrelevant. We've been down this path before. There was no addition in any example I gave you.

Yes there was.

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1

You see, you added the two square roots of -1 and got 1. You can't do that because you have to work the (-1) first because it's the inner most parenthesis.

That addition is completely unrelated to the example you gave. It's one of the standard laws for indices. See rule #3:

http://mathematics.laerd.com...

This is all high-school level mathematics.

Actually, -1 shouldn't be in parenthesis by its self anyways. It should be:

-(1^((1/2)^2))

Why? You're just making up your own rules as you go along. i = (-1)^1/2. i<> -(1^1/2). By definition.

That would give you -1, but it's hardly the square root of -1 after you add all the parentheses. Anyways, when it comes to actually finding the square root of -1, we'd have to write

(-1^(1/2))

So if we square that, we get

(-1^(1/2))^2=

(-1^(1/2))"(-1^(1/2))=

There is no square root of -1, so this equation becomes

i x i

And then we must assume that because we've given i the definition of the square root of -1, then i x i is equal to -1. The problem is, we are taking two nonexistent numbers and "assuming" they equal -1.

You are lost in confusion. I don't know where to begin correcting you. You set out aiming to prove i^2 = 1. I showed you your error, in that squaring can only be done with an awareness of the loss of information about the sign. I also showed you the correct way to do it, giving the result of -1 as you would expect. You haven't identified any problem with my maths. I can't help you further.

i^2 is what you started out with. Well done. Lol.

Yes because that's the only thing that can be done.

If you set out to prove i^2 = i^2, then you succeeded.

See here:

http://www.friesian.com... (I will come back to this article often. It doesn't agree with what I'm presenting, but it does show the philosophical implications of imaginary numbers)

"That is what I find the most exasperating about a particular attitude. If the expression sqrt. -1 has a solution that is not a real number, what is that? Well, it is i. OK. But what then is i? It is sqrt. -1. So we are back where we started. This is a circular and question-begging procedure. We should listen to the logicians quietly snorting in the background. The expression "i" consists of a variable for an unknown. The unknown in this case will be a constant, and it will be the number that solves the expression "sqrt. -1." Since the expression is a square root, for which there are algorithms, and the root to be taken is of sqrt. -1, we might think that some algorithm will get us the answer. It doesn't"

More gish gallop.

I have absolutely no idea what you are getting at. Look up the rules for indices in any secondary school maths textbook.

I did, but only because you fooled me with your clever trick.

There was no trick.

I'm sorry for accusing you of tricking me.

Contrition. Good. There is hope for you yet.

No. You are arbitrarily choosing -1 x -1 = 1 in line 3. But 1 x 1 = 1. So you are obfuscating again. What's more you are now agreeing that i^2 = -1 in line 5 which directly contradicts your earlier 'proof'. In other words, you are accepting what you are trying to disprove!

No, I'm not accepting what I'm trying to disprove. I'm showing why this whole equation is nonsense, because the whole premises of negative numbers is nonsense.

Denying what you did in the face of the black and white evidence just makes you look foolish.

I don't agree that i^2 equals -1. Obviously I wrote this to show how ridiculous it is to say that i^2 equals -1, because that means 1=-1

And I clearly identified your error. Not once have you acknowledged the problem with squaring.

Thank you for that link. I really liked what one person in particular said:

"Start with a false proposition

e.g.: W22;2=+2

square both sides

(W22;2)^2=(+2)^2

and it becomes true (!?)

+4=+4

So the operation turns (some) false statements into true statements."

Because squaring both sides of an equation is fraught with danger as information is lost. I keep telling you that. If you had paid attention in maths class at school, you might even remember your teacher carefully explaining this to you. When you have an equation you must do exactly the same operation to both sides. Squaring violates this rule. In your example you multiplied the LHS by -2 and the RHS by +2. That is a different operation on each side. Enough said.

It looks like when I copied and pasted, some of the characters messed up.

In that equation, the number -2 is squared by +2, and the number +2 is squared by +2. Thus, the same operation was done for both sides. They both equal 4.

What does squaring by +2 mean? Squaring is the operation of multiplying a number by itself. The notation of a^2 is just shorthand for a x a. The LHS is -2 so it is multiplied by -2. The RHS is +2 so it is multiplied by +2. Different operations on each side. I'm not sure that this could be any clearer.

This is fun. The rest of it was a bunch of nonsense about Negative Numbers, which I deny.

Yes, denial is best when argument fails. Lol.

Denial is best when we're talking about something impossible to exist.

We're talking about mathematical constructs. Positive numbers don't have any more existence than negative numbers. Why are you a bigot against negative numbers?

Hey dee-em, I'm sorry. I've been writing on the Religious forum.

First, I want you to know that I understand how you're getting the -1 out of (-1(^1/2))^2, but it's only because of the rules that we've developed for negative numbers. However, if I ask you what (-1)^2 is, then we can clearly see a contradiction. That is why I think (-1)^2 should be redefined as a positive number with a directional indicator.

The whole point of this post was to discuss whether there is such a thing as "below zero". Do you believe that such a thing is possible, or should negative numbers only be understood as an opposite direction of positive numbers? Wouldn't it make more sense to redefine negative numbers as positive, rather than define the letter i as imaginary? I wasn't trying to prove that negative numbers are not useful. I just wanted to have a realistic conversation about how we should understand negatives. Thank you my friend.
dee-em
Posts: 6,481
Add as Friend
Challenge to a Debate
Send a Message
6/23/2015 8:56:51 AM
Posted: 1 year ago
At 6/23/2015 8:40:19 AM, anonymouswho wrote:
At 6/18/2015 9:46:07 PM, dee-em wrote:
At 6/18/2015 10:52:41 AM, anonymouswho wrote:
At 6/17/2015 8:36:52 PM, dee-em wrote:

Goal-post moving and irrelevant. We've been down this path before. There was no addition in any example I gave you.

Yes there was.

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1

You see, you added the two square roots of -1 and got 1. You can't do that because you have to work the (-1) first because it's the inner most parenthesis.

That addition is completely unrelated to the example you gave. It's one of the standard laws for indices. See rule #3:

http://mathematics.laerd.com...

This is all high-school level mathematics.

Actually, -1 shouldn't be in parenthesis by its self anyways. It should be:

-(1^((1/2)^2))

Why? You're just making up your own rules as you go along. i = (-1)^1/2. i<> -(1^1/2). By definition.

That would give you -1, but it's hardly the square root of -1 after you add all the parentheses. Anyways, when it comes to actually finding the square root of -1, we'd have to write

(-1^(1/2))

So if we square that, we get

(-1^(1/2))^2=

(-1^(1/2))"(-1^(1/2))=

There is no square root of -1, so this equation becomes

i x i

And then we must assume that because we've given i the definition of the square root of -1, then i x i is equal to -1. The problem is, we are taking two nonexistent numbers and "assuming" they equal -1.

You are lost in confusion. I don't know where to begin correcting you. You set out aiming to prove i^2 = 1. I showed you your error, in that squaring can only be done with an awareness of the loss of information about the sign. I also showed you the correct way to do it, giving the result of -1 as you would expect. You haven't identified any problem with my maths. I can't help you further.

i^2 is what you started out with. Well done. Lol.

Yes because that's the only thing that can be done.

If you set out to prove i^2 = i^2, then you succeeded.

See here:

http://www.friesian.com... (I will come back to this article often. It doesn't agree with what I'm presenting, but it does show the philosophical implications of imaginary numbers)

"That is what I find the most exasperating about a particular attitude. If the expression sqrt. -1 has a solution that is not a real number, what is that? Well, it is i. OK. But what then is i? It is sqrt. -1. So we are back where we started. This is a circular and question-begging procedure. We should listen to the logicians quietly snorting in the background. The expression "i" consists of a variable for an unknown. The unknown in this case will be a constant, and it will be the number that solves the expression "sqrt. -1." Since the expression is a square root, for which there are algorithms, and the root to be taken is of sqrt. -1, we might think that some algorithm will get us the answer. It doesn't"

More gish gallop.

I have absolutely no idea what you are getting at. Look up the rules for indices in any secondary school maths textbook.

I did, but only because you fooled me with your clever trick.

There was no trick.

I'm sorry for accusing you of tricking me.

Contrition. Good. There is hope for you yet.

No. You are arbitrarily choosing -1 x -1 = 1 in line 3. But 1 x 1 = 1. So you are obfuscating again. What's more you are now agreeing that i^2 = -1 in line 5 which directly contradicts your earlier 'proof'. In other words, you are accepting what you are trying to disprove!

No, I'm not accepting what I'm trying to disprove. I'm showing why this whole equation is nonsense, because the whole premises of negative numbers is nonsense.

Denying what you did in the face of the black and white evidence just makes you look foolish.

I don't agree that i^2 equals -1. Obviously I wrote this to show how ridiculous it is to say that i^2 equals -1, because that means 1=-1

And I clearly identified your error. Not once have you acknowledged the problem with squaring.

Thank you for that link. I really liked what one person in particular said:

"Start with a false proposition

e.g.: W22;2=+2

square both sides

(W22;2)^2=(+2)^2

and it becomes true (!?)

+4=+4

So the operation turns (some) false statements into true statements."

Because squaring both sides of an equation is fraught with danger as information is lost. I keep telling you that. If you had paid attention in maths class at school, you might even remember your teacher carefully explaining this to you. When you have an equation you must do exactly the same operation to both sides. Squaring violates this rule. In your example you multiplied the LHS by -2 and the RHS by +2. That is a different operation on each side. Enough said.

It looks like when I copied and pasted, some of the characters messed up.

In that equation, the number -2 is squared by +2, and the number +2 is squared by +2. Thus, the same operation was done for both sides. They both equal 4.

What does squaring by +2 mean? Squaring is the operation of multiplying a number by itself. The notation of a^2 is just shorthand for a x a. The LHS is -2 so it is multiplied by -2. The RHS is +2 so it is multiplied by +2. Different operations on each side. I'm not sure that this could be any clearer.

This is fun. The rest of it was a bunch of nonsense about Negative Numbers, which I deny.

Yes, denial is best when argument fails. Lol.

Denial is best when we're talking about something impossible to exist.

We're talking about mathematical constructs. Positive numbers don't have any more existence than negative numbers. Why are you a bigot against negative numbers?

Hey dee-em, I'm sorry. I've been writing on the Religious forum.

First, I want you to know that I understand how you're getting the -1 out of (-1(^1/2))^2, but it's only because of the rules that we've developed for negative numbers.

No, the rules apply to all numbers.

However, if I ask you what (-1)^2 is, then we can clearly see a contradiction.

What contradiction? Have you bothered to read anything I have written about the problem of squaring?

That is why I think (-1)^2 should be redefined as a positive number with a directional indicator.

What? What does (-1)^2 = +1 have to do with anything?

The whole point of this post was to discuss whether there is such a thing as "below zero". Do you believe that such a thing is possible, or should negative numbers only be understood as an opposite direction of positive numbers? Wouldn't it make more sense to redefine negative numbers as positive, rather than define the letter i as imaginary? I wasn't trying to prove that negative numbers are not useful. I just wanted to have a realistic conversation about how we should understand negatives. Thank you my friend.

I don't care about that. Redefine away. My only interest was to correct the flaws in your math. My job is done.
UndeniableReality
Posts: 1,897
Add as Friend
Challenge to a Debate
Send a Message
6/23/2015 9:24:07 AM
Posted: 1 year ago
At 6/23/2015 8:40:19 AM, anonymouswho wrote:
At 6/18/2015 9:46:07 PM, dee-em wrote:
At 6/18/2015 10:52:41 AM, anonymouswho wrote:
At 6/17/2015 8:36:52 PM, dee-em wrote:

Goal-post moving and irrelevant. We've been down this path before. There was no addition in any example I gave you.

Yes there was.

i^2=
((-1)^1/2)x((-1)^1/2)=
((-1)^(1/2 + 1/2)=
((-1)^1)=
-1

You see, you added the two square roots of -1 and got 1. You can't do that because you have to work the (-1) first because it's the inner most parenthesis.

That addition is completely unrelated to the example you gave. It's one of the standard laws for indices. See rule #3:

http://mathematics.laerd.com...

This is all high-school level mathematics.

Actually, -1 shouldn't be in parenthesis by its self anyways. It should be:

-(1^((1/2)^2))

Why? You're just making up your own rules as you go along. i = (-1)^1/2. i<> -(1^1/2). By definition.

That would give you -1, but it's hardly the square root of -1 after you add all the parentheses. Anyways, when it comes to actually finding the square root of -1, we'd have to write

(-1^(1/2))

So if we square that, we get

(-1^(1/2))^2=

(-1^(1/2))"(-1^(1/2))=

There is no square root of -1, so this equation becomes

i x i

And then we must assume that because we've given i the definition of the square root of -1, then i x i is equal to -1. The problem is, we are taking two nonexistent numbers and "assuming" they equal -1.

You are lost in confusion. I don't know where to begin correcting you. You set out aiming to prove i^2 = 1. I showed you your error, in that squaring can only be done with an awareness of the loss of information about the sign. I also showed you the correct way to do it, giving the result of -1 as you would expect. You haven't identified any problem with my maths. I can't help you further.

i^2 is what you started out with. Well done. Lol.

Yes because that's the only thing that can be done.

If you set out to prove i^2 = i^2, then you succeeded.

See here:

http://www.friesian.com... (I will come back to this article often. It doesn't agree with what I'm presenting, but it does show the philosophical implications of imaginary numbers)

"That is what I find the most exasperating about a particular attitude. If the expression sqrt. -1 has a solution that is not a real number, what is that? Well, it is i. OK. But what then is i? It is sqrt. -1. So we are back where we started. This is a circular and question-begging procedure. We should listen to the logicians quietly snorting in the background. The expression "i" consists of a variable for an unknown. The unknown in this case will be a constant, and it will be the number that solves the expression "sqrt. -1." Since the expression is a square root, for which there are algorithms, and the root to be taken is of sqrt. -1, we might think that some algorithm will get us the answer. It doesn't"

More gish gallop.

I have absolutely no idea what you are getting at. Look up the rules for indices in any secondary school maths textbook.

I did, but only because you fooled me with your clever trick.

There was no trick.

I'm sorry for accusing you of tricking me.

Contrition. Good. There is hope for you yet.

No. You are arbitrarily choosing -1 x -1 = 1 in line 3. But 1 x 1 = 1. So you are obfuscating again. What's more you are now agreeing that i^2 = -1 in line 5 which directly contradicts your earlier 'proof'. In other words, you are accepting what you are trying to disprove!

No, I'm not accepting what I'm trying to disprove. I'm showing why this whole equation is nonsense, because the whole premises of negative numbers is nonsense.

Denying what you did in the face of the black and white evidence just makes you look foolish.

I don't agree that i^2 equals -1. Obviously I wrote this to show how ridiculous it is to say that i^2 equals -1, because that means 1=-1

And I clearly identified your error. Not once have you acknowledged the problem with squaring.

Thank you for that link. I really liked what one person in particular said:

"Start with a false proposition

e.g.: W22;2=+2

square both sides

(W22;2)^2=(+2)^2

and it becomes true (!?)

+4=+4

So the operation turns (some) false statements into true statements."

Because squaring both sides of an equation is fraught with danger as information is lost. I keep telling you that. If you had paid attention in maths class at school, you might even remember your teacher carefully explaining this to you. When you have an equation you must do exactly the same operation to both sides. Squaring violates this rule. In your example you multiplied the LHS by -2 and the RHS by +2. That is a different operation on each side. Enough said.

It looks like when I copied and pasted, some of the characters messed up.

In that equation, the number -2 is squared by +2, and the number +2 is squared by +2. Thus, the same operation was done for both sides. They both equal 4.

What does squaring by +2 mean? Squaring is the operation of multiplying a number by itself. The notation of a^2 is just shorthand for a x a. The LHS is -2 so it is multiplied by -2. The RHS is +2 so it is multiplied by +2. Different operations on each side. I'm not sure that this could be any clearer.

This is fun. The rest of it was a bunch of nonsense about Negative Numbers, which I deny.

Yes, denial is best when argument fails. Lol.

Denial is best when we're talking about something impossible to exist.

We're talking about mathematical constructs. Positive numbers don't have any more existence than negative numbers. Why are you a bigot against negative numbers?

Hey dee-em, I'm sorry. I've been writing on the Religious forum.

First, I want you to know that I understand how you're getting the -1 out of (-1(^1/2))^2, but it's only because of the rules that we've developed for negative numbers. However, if I ask you what (-1)^2 is, then we can clearly see a contradiction. That is why I think (-1)^2 should be redefined as a positive number with a directional indicator.

The whole point of this post was to discuss whether there is such a thing as "below zero". Do you believe that such a thing is possible, or should negative numbers only be understood as an opposite direction of positive numbers? Wouldn't it make more sense to redefine negative numbers as positive, rather than define the letter i as imaginary? I wasn't trying to prove that negative numbers are not useful. I just wanted to have a realistic conversation about how we should understand negatives. Thank you my friend.

Redefine negative numbers as a positive numbers with a directional indicator? I have an idea: use + for one direction and - for the other.