Total Posts:87|Showing Posts:1-30|Last Page
Jump to topic:

(1 paradox)Why 0.999... is not equal to 1?

onlinephilosophy
Posts: 1
Add as Friend
Challenge to a Debate
Send a Message
2/28/2013 6:02:00 AM
Posted: 3 years ago
(1 paradox)Why 0.999... is not equal to 1?

Written in 2012

The current mathematic theory tells us, 1>0.9, 1>0.99, 1>0.999, ..., but at last it says 1=0.999..., a negation of itself. So it is totally a paradox, name it as 【1 paradox】. You see this is a mathematic problem at first, actually it is a philosophic problem. Then we can resolve it. Because math is a incomplete theory, only philosophy could be a complete one. The answer is that 0.999... is not equal to 1. Because of these reasons:

1. The infinite world and finite world.

We live in one world but made up of two parts: the infinite part and the finite part. But we develop our mathematic system based on the finite part, because we never entered into the infinite part. Your attention, God is in it.

0.999... is a number in the infinite world, but 1 is a number in the finite world. For example, 1 represents an apple. But then 0.999...? We don't know. That is to say, we can't use a number in the infinite world to plus a number in the finite world. For example, an apple plus an apple, we say it is 1+1=2, we get two apples, but if it is an apple plus a banana, we only can say we get two fruits. The key problem is we don't know what is 0.999..., we can get nothing. So we can't say 9+0.999...=9.999... or 10, etc.

We can use "infinite world" and "finite world" to resolve some of zeno's paradox, too.

2. lim0.999...=1, not 0.999...=1.

3.The indeterminate principle.

Because of the indeterminate principle, 1/9 is not equal to 0.111....

For example, cut an apple into nine equal parts, then every part of it is 1/9. But if you use different measure tools to measure the volume of every part, it is indeterminate. That is to say, you may find the volume could not exactly be 0.111..., but it would be 0.123, 0.1142, or 0.11425, etc.

Now we end a biggest mathematical crisis. But most important is this standpoint tells us, our world is only a sample from a sample space. When you realized this, and that the current probability theory is wrong, when you find the Meta-sample-space, you would be able to create a real AI-system. It will indicate that there must be one God-system in the system, which is the controller. Look our world, there must be one God, as for us, only some robots. Maybe we are in a God's game, WHO KNOWS?

More info, three other download points(written in Chinese):
crocko.com/AB4FAF96C6DF4DE59624CA4C0482A5D3/AiforSC.rar
localhostr.com/download/3LtuSLb/the%20end%20of%20the%20world.rar
bayfiles.com/file/F5tD/B8M4Xh/AiforSC.rar
Floid
Posts: 751
Add as Friend
Challenge to a Debate
Send a Message
2/28/2013 12:30:21 PM
Posted: 3 years ago
(1 paradox)Why 0.999... is not equal to 1?

1/9 = 0.111...

9 x 1/9 = 9 x 0.111...

1 = 0.999...

QED

I don't see the problem...
drafterman
Posts: 18,870
Add as Friend
Challenge to a Debate
Send a Message
2/28/2013 12:37:05 PM
Posted: 3 years ago
I love this:

1. If you cut an apple into 9ths and measure it, each piece won't exactly be 1/9th.
2. Ergo 0.999... =/= 1
3. Ergo AI
4. Ergo God
bossyburrito
Posts: 14,075
Add as Friend
Challenge to a Debate
Send a Message
2/28/2013 12:44:34 PM
Posted: 3 years ago
"The current mathematic theory tells us, 1>0.9, 1>0.99, 1>0.999, ..., but at last it says 1=0.999..."

Check your premises.
1 =/= 0.999... because 0.999... has a value that is not equal to 1.
Q.E.D.
It doesn't matter if it's infinitely long. You don't need to know the exact value of things to compare them. An ocean is larger than a swimming pool. Is that invalid because you can't measure the volume of the ocean? Of course not. Even if you could, you would not need to to determine the conclusion.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
natoast
Posts: 204
Add as Friend
Challenge to a Debate
Send a Message
2/28/2013 4:30:31 PM
Posted: 3 years ago
At 2/28/2013 12:30:21 PM, Floid wrote:
(1 paradox)Why 0.999... is not equal to 1?

1/9 = 0.111...

9 x 1/9 = 9 x 0.111...

1 = 0.999...

QED

I don't see the problem...

You just blew my mind.
Floid
Posts: 751
Add as Friend
Challenge to a Debate
Send a Message
3/1/2013 7:12:53 AM
Posted: 3 years ago
At 2/28/2013 12:37:05 PM, drafterman wrote:
I love this:

1. If you cut an apple into 9ths and measure it, each piece won't exactly be 1/9th.

Then you didn't really cut the apple into 9ths.
TheElderScroll
Posts: 643
Add as Friend
Challenge to a Debate
Send a Message
3/1/2013 8:24:10 AM
Posted: 3 years ago
For the apple part, it is about the degree of accuracy (just like the measurement of Pi). The modern technology can only go that far, therefore the measurement would not be absolutely perfect.
R0b1Billion
Posts: 3,733
Add as Friend
Challenge to a Debate
Send a Message
3/1/2013 1:01:42 PM
Posted: 3 years ago
If you took an object made of nine quarks, and removed one, there would be no theoretical inaccuracy in the size of the chunk you removed. However, until there is a technological solution as to achieving this, exactly, one can always say that such things are outside of our scope of influence.
Beliefs in a nutshell:
- The Ends never justify the Means.
- Objectivity is secondary to subjectivity.
- The War on Drugs is the worst policy in the U.S.
- Most people worship technology as a religion.
- Computers will never become sentient.
bossyburrito
Posts: 14,075
Add as Friend
Challenge to a Debate
Send a Message
3/1/2013 1:07:54 PM
Posted: 3 years ago
At 2/28/2013 12:30:21 PM, Floid wrote:
(1 paradox)Why 0.999... is not equal to 1?

1/9 = 0.111...

9 x 1/9 = 9 x 0.111...

1 = 0.999...

QED

I don't see the problem...

That doesn't make any theoretical sense.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
Floid
Posts: 751
Add as Friend
Challenge to a Debate
Send a Message
3/1/2013 9:31:59 PM
Posted: 3 years ago
That doesn't make any theoretical sense.

Please elaborate:

Do you dispute that:
1/9 = 0.111..
9 x 1/9 = 1
9 x 0.111... = 0.999...
or that for any real numbers a, b, and c, if a = b, then ac = bc
The_Fool_on_the_hill
Posts: 6,071
Add as Friend
Challenge to a Debate
Send a Message
3/2/2013 4:52:00 PM
Posted: 3 years ago
At 2/28/2013 12:37:05 PM, drafterman wrote:
I love this:

1. If you cut an apple into 9ths and measure it, each piece won't exactly be 1/9th.
2. Ergo 0.999... =/= 1
3. Ergo AI
4. Ergo God

The Fool: Wow you actually Proved God, Wow. I didn't think it could be done.

I NOW SEE THE LIGHT!. @t the red light district.
"The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another." G. W. F. HEGEL
bossyburrito
Posts: 14,075
Add as Friend
Challenge to a Debate
Send a Message
3/2/2013 4:54:13 PM
Posted: 3 years ago
At 3/1/2013 9:31:59 PM, Floid wrote:
That doesn't make any theoretical sense.

Please elaborate:

Do you dispute that:
1/9 = 0.111..
9 x 1/9 = 1
9 x 0.111... = 0.999...
or that for any real numbers a, b, and c, if a = b, then ac = bc

By definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
Cinco
Posts: 63
Add as Friend
Challenge to a Debate
Send a Message
3/2/2013 8:15:11 PM
Posted: 3 years ago
Crikeys - it's like fighting over that extra penny when you split the check! Sort of makes your head want to explode, doesn't it?
If your time, to you,
Is worth savin',
Then you better start swimmin'
Or you'll sink like a stone.
For the times they are a-changin'. - Bob Dylan
Floid
Posts: 751
Add as Friend
Challenge to a Debate
Send a Message
3/2/2013 8:46:42 PM
Posted: 3 years ago
By definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.

Except I gave you a simple proof that demonstrates that they are equal and apparently you can't present an argument against any portion of that proof. Instead you just say "that can't be".

Of course the formal reason that 0.999... = 1 would be stated:

The limit as x -> infinity of (x-1)/x = 1

But that really loses the fun of the simple algebraic example given above.
bossyburrito
Posts: 14,075
Add as Friend
Challenge to a Debate
Send a Message
3/2/2013 8:49:58 PM
Posted: 3 years ago
At 3/2/2013 8:46:42 PM, Floid wrote:
By definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.

Except I gave you a simple proof that demonstrates that they are equal and apparently you can't present an argument against any portion of that proof. Instead you just say "that can't be".
That's because contradictions cannot exist. One of your premises have to be wrong.


Of course the formal reason that 0.999... = 1 would be stated:

The limit as x -> infinity of (x-1)/x = 1

But that really loses the fun of the simple algebraic example given above.

So are you saying that .999 repeating is not .999 repeating?
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
Floid
Posts: 751
Add as Friend
Challenge to a Debate
Send a Message
3/2/2013 9:28:18 PM
Posted: 3 years ago
That's because contradictions cannot exist. One of your premises have to be wrong.

So point it out, which one is wrong?

So are you saying that .999 repeating is not .999 repeating?

I would say their is no point in stating a tautology. If I were to say A = B you wouldn't turn around and ask me "Are you saying A is not equal to A?" now would you?

But if it must be spelled out for you:

0.999... is equal to 0.999...
0.999... is equal to 1

Both of the above statements are mathematically true and demonstrated through the simple algebraic proof I included above and embodied in the idea of limits, a key concept used in many areas of mathematics.
bossyburrito
Posts: 14,075
Add as Friend
Challenge to a Debate
Send a Message
3/2/2013 9:36:29 PM
Posted: 3 years ago
At 3/2/2013 9:28:18 PM, Floid wrote:
That's because contradictions cannot exist. One of your premises have to be wrong.

So point it out, which one is wrong?
.999 repeating equaling 1.


So are you saying that .999 repeating is not .999 repeating?

I would say their is no point in stating a tautology. If I were to say A = B you wouldn't turn around and ask me "Are you saying A is not equal to A?" now would you?
I would if A is by definition not B.

But if it must be spelled out for you:

0.999... is equal to 0.999...
0.999... is equal to 1

Both of the above statements are mathematically true and demonstrated through the simple algebraic proof I included above and embodied in the idea of limits, a key concept used in many areas of mathematics.

If 0.999... is 0.999..., then it is not 1. That would be like saying that 1 = 2. 1 does not equal 2 because 1 by definition has a different value than 2.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
Enji
Posts: 1,022
Add as Friend
Challenge to a Debate
Send a Message
3/2/2013 10:24:29 PM
Posted: 3 years ago
At 3/2/2013 9:36:29 PM, bossyburrito wrote:
At 3/2/2013 9:28:18 PM, Floid wrote:
That's because contradictions cannot exist. One of your premises have to be wrong.

So point it out, which one is wrong?
.999 repeating equaling 1.


So are you saying that .999 repeating is not .999 repeating?

I would say their is no point in stating a tautology. If I were to say A = B you wouldn't turn around and ask me "Are you saying A is not equal to A?" now would you?
I would if A is by definition not B.

But if it must be spelled out for you:

0.999... is equal to 0.999...
0.999... is equal to 1

Both of the above statements are mathematically true and demonstrated through the simple algebraic proof I included above and embodied in the idea of limits, a key concept used in many areas of mathematics.

If 0.999... is 0.999..., then it is not 1. That would be like saying that 1 = 2. 1 does not equal 2 because 1 by definition has a different value than 2.

Clearly if 3/3 is 3/3, then it is not 1.
bossyburrito
Posts: 14,075
Add as Friend
Challenge to a Debate
Send a Message
3/2/2013 11:16:08 PM
Posted: 3 years ago
At 3/2/2013 10:24:29 PM, Enji wrote:
At 3/2/2013 9:36:29 PM, bossyburrito wrote:
At 3/2/2013 9:28:18 PM, Floid wrote:
That's because contradictions cannot exist. One of your premises have to be wrong.

So point it out, which one is wrong?
.999 repeating equaling 1.


So are you saying that .999 repeating is not .999 repeating?

I would say their is no point in stating a tautology. If I were to say A = B you wouldn't turn around and ask me "Are you saying A is not equal to A?" now would you?
I would if A is by definition not B.

But if it must be spelled out for you:

0.999... is equal to 0.999...
0.999... is equal to 1

Both of the above statements are mathematically true and demonstrated through the simple algebraic proof I included above and embodied in the idea of limits, a key concept used in many areas of mathematics.

If 0.999... is 0.999..., then it is not 1. That would be like saying that 1 = 2. 1 does not equal 2 because 1 by definition has a different value than 2.

Clearly if 3/3 is 3/3, then it is not 1.

By definition it is one. 0.999... is not equal to 1 because it is 0.999... and not one.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
Ore_Ele
Posts: 25,980
Add as Friend
Challenge to a Debate
Send a Message
3/3/2013 2:25:40 AM
Posted: 3 years ago
At 3/2/2013 4:54:13 PM, bossyburrito wrote:
At 3/1/2013 9:31:59 PM, Floid wrote:
That doesn't make any theoretical sense.

Please elaborate:

Do you dispute that:
1/9 = 0.111..
9 x 1/9 = 1
9 x 0.111... = 0.999...
or that for any real numbers a, b, and c, if a = b, then ac = bc

By definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.

No, it does, that is the thing. You are saying "by definition" but that is not true.
"Wanting Red Rhino Pill to have gender"
Ore_Ele
Posts: 25,980
Add as Friend
Challenge to a Debate
Send a Message
3/3/2013 2:28:30 AM
Posted: 3 years ago
The OP would also be suggesting that all limits are thus false, though we can test and prove them to be true through application. Most notably the Taylor series for SIN and COS.
"Wanting Red Rhino Pill to have gender"
Kinesis
Posts: 3,667
Add as Friend
Challenge to a Debate
Send a Message
3/3/2013 5:06:53 AM
Posted: 3 years ago
Here's the most ridiculous result in mathematics I've come across:

1=(2-1)
(1+2+4+8...) - - >infinite series where each number is double the last.
=1*(1+2+4+8...)
=(2-1)(1+2+4+8...)
Multiply out the brackets.
2+4+8+16...
-1-2-4-8...

Every number except -1 cancels out --> -1 = (1+2+4+8...)
bossyburrito
Posts: 14,075
Add as Friend
Challenge to a Debate
Send a Message
3/3/2013 5:23:33 AM
Posted: 3 years ago
At 3/3/2013 2:25:40 AM, Ore_Ele wrote:
At 3/2/2013 4:54:13 PM, bossyburrito wrote:
At 3/1/2013 9:31:59 PM, Floid wrote:
That doesn't make any theoretical sense.

Please elaborate:

Do you dispute that:
1/9 = 0.111..
9 x 1/9 = 1
9 x 0.111... = 0.999...
or that for any real numbers a, b, and c, if a = b, then ac = bc

By definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.

No, it does, that is the thing. You are saying "by definition" but that is not true.

If 0.999 repeating is equal to one, doesn't that mean that it is 0.999 repeating to infinity until a 1 at the end? You can't have an end to infinity.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
Cinco
Posts: 63
Add as Friend
Challenge to a Debate
Send a Message
3/3/2013 6:04:49 AM
Posted: 3 years ago
At 3/2/2013 8:15:11 PM, Cinco wrote:
Crikeys - it's like fighting over that extra penny when you split the check! Sort of makes your head want to explode, doesn't it?

Totally forgot - it's just a clash of perspectives. I have stepped across the threshold! Hallelujah! I LOVE a brain tilt!! Thanks!
If your time, to you,
Is worth savin',
Then you better start swimmin'
Or you'll sink like a stone.
For the times they are a-changin'. - Bob Dylan
Enji
Posts: 1,022
Add as Friend
Challenge to a Debate
Send a Message
3/3/2013 10:56:45 AM
Posted: 3 years ago
At 3/3/2013 5:23:33 AM, bossyburrito wrote:
At 3/3/2013 2:25:40 AM, Ore_Ele wrote:
At 3/2/2013 4:54:13 PM, bossyburrito wrote:
At 3/1/2013 9:31:59 PM, Floid wrote:
That doesn't make any theoretical sense.

Please elaborate:

Do you dispute that:
1/9 = 0.111..
9 x 1/9 = 1
9 x 0.111... = 0.999...
or that for any real numbers a, b, and c, if a = b, then ac = bc

By definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.

No, it does, that is the thing. You are saying "by definition" but that is not true.

If 0.999 repeating is equal to one, doesn't that mean that it is 0.999 repeating to infinity until a 1 at the end? You can't have an end to infinity.

It means that .9999 repeating infinitely has the same value as 1, as is shown with various mathematical proofs of differing rigor.
Skepsikyma
Posts: 8,285
Add as Friend
Challenge to a Debate
Send a Message
3/3/2013 12:55:26 PM
Posted: 3 years ago
I think that this is more of a limitation of a decimal numerical system than any sort of profound statement.
"The Collectivist experiment is thoroughly suited (in appearance at least) to the Capitalist society which it proposes to replace. It works with the existing machinery of Capitalism, talks and thinks in the existing terms of Capitalism, appeals to just those appetites which Capitalism has aroused, and ridicules as fantastic and unheard-of just those things in society the memory of which Capitalism has killed among men wherever the blight of it has spread."
- Hilaire Belloc -
Ore_Ele
Posts: 25,980
Add as Friend
Challenge to a Debate
Send a Message
3/3/2013 9:20:29 PM
Posted: 3 years ago
At 3/3/2013 5:06:53 AM, Kinesis wrote:
Here's the most ridiculous result in mathematics I've come across:

1=(2-1)
(1+2+4+8...) - - >infinite series where each number is double the last.
=1*(1+2+4+8...)
=(2-1)(1+2+4+8...)
Multiply out the brackets.
2+4+8+16...
-1-2-4-8...

Every number except -1 cancels out --> -1 = (1+2+4+8...)

The limit of (1+2+4+8+16...2^n...) as n -> infinite does not exist, so it cannot be used in a proof.
"Wanting Red Rhino Pill to have gender"
Wnope
Posts: 6,924
Add as Friend
Challenge to a Debate
Send a Message
3/4/2013 12:12:37 AM
Posted: 3 years ago
At 3/3/2013 12:55:26 PM, Skepsikyma wrote:
I think that this is more of a limitation of a decimal numerical system than any sort of profound statement.

Bingo.
Kinesis
Posts: 3,667
Add as Friend
Challenge to a Debate
Send a Message
3/4/2013 4:24:38 AM
Posted: 3 years ago
At 3/3/2013 9:20:29 PM, Ore_Ele wrote:
At 3/3/2013 5:06:53 AM, Kinesis wrote:
Here's the most ridiculous result in mathematics I've come across:

1=(2-1)
(1+2+4+8...) - - >infinite series where each number is double the last.
=1*(1+2+4+8...)
=(2-1)(1+2+4+8...)
Multiply out the brackets.
2+4+8+16...
-1-2-4-8...

Every number except -1 cancels out --> -1 = (1+2+4+8...)

The limit of (1+2+4+8+16...2^n...) as n -> infinite does not exist, so it cannot be used in a proof.

I wasn't aware that was a rule. Point to something explaining why that is? (or explain it).
THEVIRUS
Posts: 1,321
Add as Friend
Challenge to a Debate
Send a Message
3/4/2013 4:42:28 AM
Posted: 3 years ago
At 2/28/2013 12:30:21 PM, Floid wrote:
(1 paradox)Why 0.999... is not equal to 1?

1/9 = 0.111...

9 x 1/9 = 9 x 0.111...

1 = 0.999...

QED

I don't see the problem...

1>0.999... by a total of 0.000... for math to actually work. Otherwise every number in existence is rounded once the number exceeds 0.999... I think
"So you want me to go to the judge with 'unit, corps, God, country'?" - A Few Good Men

"And the hits just keep on comin'." -A Few Good Men