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0.9repeating equals one

PotBelliedGeek
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1/16/2014 8:19:08 PM
Posted: 2 years ago
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.
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GarretKadeDupre
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1/16/2014 8:26:08 PM
Posted: 2 years ago
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

Disclaimer: I'm an uneducated, brain-damaged retard who has never studied math, however...

I'd say that 0.9 repeating cannot be one, because it isn't a number.

1 is a number

0.9 repeating isn't

They are both concepts, but one is a number and the other isn't

just my thoughts
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PotBelliedGeek
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1/16/2014 8:28:35 PM
Posted: 2 years ago
At 1/16/2014 8:26:08 PM, GarretKadeDupre wrote:
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

Disclaimer: I'm an uneducated, brain-damaged retard who has never studied math, however...

Dude I'm really sorry if I came across as saying that. I really am.


I'd say that 0.9 repeating cannot be one, because it isn't a number.

1 is a number

0.9 repeating isn't

They are both concepts, but one is a number and the other isn't

It is technically a number, but not an integer. Otherwise, I agree with you.


just my thoughts
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GarretKadeDupre
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1/16/2014 8:30:13 PM
Posted: 2 years ago
At 1/16/2014 8:28:35 PM, PotBelliedGeek wrote:
At 1/16/2014 8:26:08 PM, GarretKadeDupre wrote:
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

Disclaimer: I'm an uneducated, brain-damaged retard who has never studied math, however...

Dude I'm really sorry if I came across as saying that. I really am.

sorry i didnt mean it like that, i was trying to be lighthearted about it lol



I'd say that 0.9 repeating cannot be one, because it isn't a number.

1 is a number

0.9 repeating isn't

They are both concepts, but one is a number and the other isn't

It is technically a number, but not an integer. Otherwise, I agree with you.

is it technically a number? i didnt know that. what about infinity? Is that technically a number?

What is the definition of number...?


just my thoughts
Proof that people witnessed living dinosaurs:
http://www.debate.org...
PotBelliedGeek
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1/16/2014 8:38:58 PM
Posted: 2 years ago
At 1/16/2014 8:30:13 PM, GarretKadeDupre wrote:
At 1/16/2014 8:28:35 PM, PotBelliedGeek wrote:
At 1/16/2014 8:26:08 PM, GarretKadeDupre wrote:
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

Disclaimer: I'm an uneducated, brain-damaged retard who has never studied math, however...

Dude I'm really sorry if I came across as saying that. I really am.

sorry i didnt mean it like that, i was trying to be lighthearted about it lol



I'd say that 0.9 repeating cannot be one, because it isn't a number.

1 is a number

0.9 repeating isn't

They are both concepts, but one is a number and the other isn't

It is technically a number, but not an integer. Otherwise, I agree with you.

is it technically a number? i didnt know that. what about infinity? Is that technically a number?

What is the definition of number...?


just my thoughts

Here is a simple definition:
An arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity.
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GarretKadeDupre
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1/16/2014 8:40:05 PM
Posted: 2 years ago
At 1/16/2014 8:38:58 PM, PotBelliedGeek wrote:
At 1/16/2014 8:30:13 PM, GarretKadeDupre wrote:
At 1/16/2014 8:28:35 PM, PotBelliedGeek wrote:
At 1/16/2014 8:26:08 PM, GarretKadeDupre wrote:
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

Disclaimer: I'm an uneducated, brain-damaged retard who has never studied math, however...

Dude I'm really sorry if I came across as saying that. I really am.

sorry i didnt mean it like that, i was trying to be lighthearted about it lol



I'd say that 0.9 repeating cannot be one, because it isn't a number.

1 is a number

0.9 repeating isn't

They are both concepts, but one is a number and the other isn't

It is technically a number, but not an integer. Otherwise, I agree with you.

is it technically a number? i didnt know that. what about infinity? Is that technically a number?

What is the definition of number...?


just my thoughts

Here is a simple definition:
An arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity.

I'd say that "0.9 repeating" (what's the symbol for that?) doesn't represent a quantity.
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Floid
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1/16/2014 8:51:25 PM
Posted: 2 years ago
A simple algebraic proof would be:

1 / 9 = 0.11111...

1/9 x 9 = 0.11111... x 9

1 = 0.99999....

Using the ideas of limits an alternative proof would be:

0.9999 = lim n->oo (1 - 1 / 10^n)

since 1/10^oo = 0 then:

0.999 = (1 - 1/10^oo) = (1 - 0) = 1
Floid
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1/16/2014 9:02:46 PM
Posted: 2 years ago
I'd say that "0.9 repeating" (what's the symbol for that?) doesn't represent a quantity.

Typically you the symbol would be 0.999... or 0.9 with a line over the 9 indicating it repeats indefinitely.

0.999... is a perfectly fine number. It is 1!

I think to clarify the idea might be to think of 1 as really being 1.000...

So 1.000 - 0.999 = 0.001 and 1.000000 - 0.999999 = 0.000001, but how can you take a difference between 1.000... and 0.999... because you never reach the "end" at which you can start the subtraction. The difference between 1.000... and 0.999... is infinitesimally small (1/infinity) and 1/infinity = 0.
GarretKadeDupre
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1/16/2014 9:03:22 PM
Posted: 2 years ago
At 1/16/2014 8:51:25 PM, Floid wrote:
A simple algebraic proof would be:

1 / 9 = 0.11111...

1/9 x 9 = 0.11111... x 9

1 = 0.99999....


Using the ideas of limits an alternative proof would be:

0.9999 = lim n->oo (1 - 1 / 10^n)

since 1/10^oo = 0 then:

0.999 = (1 - 1/10^oo) = (1 - 0) = 1

now i dont understand most of that but...

Can 1/9 really be expressed like 0.1111...?

Think about language. Maybe its a case of not being able to fully translate. So 0.111... is just the product of trying to translate 1/9 into an incompatible language.

But I digress, because im prolly missing something lol
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GarretKadeDupre
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1/16/2014 9:05:24 PM
Posted: 2 years ago
At 1/16/2014 9:02:46 PM, Floid wrote:
I'd say that "0.9 repeating" (what's the symbol for that?) doesn't represent a quantity.

Typically you the symbol would be 0.999... or 0.9 with a line over the 9 indicating it repeats indefinitely.

0.999... is a perfectly fine number. It is 1!

I think to clarify the idea might be to think of 1 as really being 1.000...

So 1.000 - 0.999 = 0.001 and 1.000000 - 0.999999 = 0.000001, but how can you take a difference between 1.000... and 0.999... because you never reach the "end" at which you can start the subtraction. The difference between 1.000... and 0.999... is infinitesimally small (1/infinity) and 1/infinity = 0.

So it's just semantics, basically? Since we can comprehend 1, but we can't comprehend 0.999 repeating for ever, we just equate the two?
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Floid
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1/17/2014 6:12:52 AM
Posted: 2 years ago
So it's just semantics, basically? Since we can comprehend 1, but we can't comprehend 0.999 repeating for ever, we just equate the two?

I would agree it is sort of semantics. What we can't comprehend is an infinitesimally small number which is why we equate 1 / infinity = 0. The result of that equality leads to all sorts of things such as 0.999... = 1, infinite series converging, etc.

Think of it this way. Say we had a really small object and you said it is smaller than 1 and I said it had to be 1. We got out a ruler and started to measure it.

We might find that it is either 0.999 inches or 1 inch but if we couldn't tell we keep zooming in to get more accuracy.

We might find it is either 0.999mm or 1mm but if we couldn't tell we keep zooming in to get more accuracy.

We might find it is either 0.999 the width of an atom or the 1 width of an atom but if we couldn't tell we keep zooming in to get more accuracy.

But if we keep infinitely zooming in and can never figure out if it is either some
definitive 0.999 of some unit then who wins? I would.

That act of infinite zooming is taking 0.999... out infinite places. The fact that even though we keep getting smaller and smaller but can never find an end point to say "Ah Ha! It truly is not 1" means that it must be 1.
slo1
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1/17/2014 9:00:07 AM
Posted: 2 years ago
At 1/17/2014 5:58:55 AM, Floid wrote:
Can 1/9 really be expressed like 0.1111...?

Yes, just calculate 1/9 using long division.

Technically if you started doing that you can never stop.

New rule for kids to add to the don't make faces or your face will freeze in that position rule.

Don't ever start dividing things that result in an infinite repeating decimal or you will never be able to stop.
Enji
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1/17/2014 4:36:15 PM
Posted: 2 years ago
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

.9r can only not be equal to 1 if there are non-zero infinitesimals. But since most colloquial mathematical discussion relates to the real numbers and the real number system does not have non-zero infinitesimals, .9r is 1. Going beyond the real number system (for example, the hyperreals), however, it is possible to prove that .9r < 1.
Ramshutu
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1/17/2014 5:10:41 PM
Posted: 2 years ago
At 1/17/2014 4:36:15 PM, Enji wrote:
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

.9r can only not be equal to 1 if there are non-zero infinitesimals. But since most colloquial mathematical discussion relates to the real numbers and the real number system does not have non-zero infinitesimals, .9r is 1. Going beyond the real number system (for example, the hyperreals), however, it is possible to prove that .9r < 1.

1/9 = 0.111 recurring.

0.111 recurring * 9 = 0.999

1/9 * 9 != 1.

Infinities always make my head hurt:

I'm an atheist who is going to hell for an infinity long time. But I'm sure a God will let me off with serving half the time for good behaviour.
Floid
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1/18/2014 5:21:00 AM
Posted: 2 years ago
At 1/17/2014 5:10:41 PM, Ramshutu wrote:
1/9 = 0.111 recurring.

0.111 recurring * 9 = 0.999

There is an error in this step. 0.111... x 9 = 0.999... and not 0.999.

1/9 * 9 != 1.
Gold
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1/18/2014 10:49:34 AM
Posted: 2 years ago
I'll try to break this down as simple as possible without that much knowledge of math needed, but limits are truly the best way to supply a "proof" for it.

A real number can either be equal or not equal to another real number. If a real number is not equal to another number, there exist at least one real number between the two.

So let's say .999... = x and 1 = z

What number is between x and z?
See here: x < y < z

The number .00...1 does not exist and therefore there are no numbers between .999... and 1, rendering them equal to one another.
GarretKadeDupre
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1/18/2014 11:23:29 PM
Posted: 2 years ago
At 1/18/2014 10:49:34 AM, Gold wrote:
I'll try to break this down as simple as possible without that much knowledge of math needed, but limits are truly the best way to supply a "proof" for it.

A real number can either be equal or not equal to another real number. If a real number is not equal to another number, there exist at least one real number between the two.

So let's say .999... = x and 1 = z

What number is between x and z?
See here: x < y < z

The number .00...1 does not exist and therefore there are no numbers between .999... and 1, rendering them equal to one another.

awesome answer
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tarkovsky
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1/24/2014 1:55:50 PM
Posted: 2 years ago
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

It's a geometric series. Can be solved with as little Cal II:

0.999...= 0.9+0.09+0.009+...
= Sum(9(1/10)^(i)), where the index i is going from 1 to infinity
= 9/10 (Sum(1/10)^(i)), where the index i is going from 0 to infinity
Since r = 1/10 and 0<abs(1/10)<1 we get that
= 9/10(Sum(1/10)^(i)) = 9/10 (1/(1-(1/10))) = 9/10 (1/(9/10)) = (9/10)(10/9)=1

So

0.999... = 1

That's all.

Here's a link. Forums won't let me put in latex or images so that's the best i can do. Here they have the actual notation rendered: http://www.purplemath.com...
tarkovsky
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1/24/2014 1:57:35 PM
Posted: 2 years ago
At 1/24/2014 1:55:50 PM, tarkovsky wrote:
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

It's a geometric series. Can be solved with as little Cal II:

0.999...= 0.9+0.09+0.009+...
= Sum(9(1/10)^(i)), where the index i is going from 1 to infinity
= 9/10 (Sum(1/10)^(i)), where the index i is going from 0 to infinity
Since r = 1/10 and 0<abs(1/10)<1 we get that
= 9/10(Sum(1/10)^(i)) = 9/10 (1/(1-(1/10))) = 9/10 (1/(9/10)) = (9/10)(10/9)=1

So

0.999... = 1

That's all.

Here's a link. Forums won't let me put in latex or images so that's the best i can do. Here they have the actual notation rendered: http://www.purplemath.com...

On second thought that link is kind of crappy. But maybe it's easier without the proper notation.
slo1
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1/24/2014 2:19:27 PM
Posted: 2 years ago
At 1/17/2014 5:10:41 PM, Ramshutu wrote:
At 1/17/2014 4:36:15 PM, Enji wrote:
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

.9r can only not be equal to 1 if there are non-zero infinitesimals. But since most colloquial mathematical discussion relates to the real numbers and the real number system does not have non-zero infinitesimals, .9r is 1. Going beyond the real number system (for example, the hyperreals), however, it is possible to prove that .9r < 1.

1/9 = 0.111 recurring.

0.111 recurring * 9 = 0.999

1/9 * 9 != 1.

Infinities always make my head hurt:

I'm an atheist who is going to hell for an infinity long time. But I'm sure a God will let me off with serving half the time for good behaviour.

I just read somewhere that this infinite sequence, 1-1+1-1+1-1+1...., is proven to = 1/2.
infinity is jacked up!
theta_pinch
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1/24/2014 7:19:42 PM
Posted: 2 years ago
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

Every two distinct numbers have an infinite number of infinitesmals between them(for example 0.9 and 0.91 have an infinite number of infinitesmals between them); there is no infinitesmal between 0.999999repeating and 1; therefore they are the same number.
Any sufficiently complex phenomenon is indistinguishable from magic--Me

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Sidewalker
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1/24/2014 8:19:13 PM
Posted: 2 years ago
Here are three proofs:

Proof 1

1/9 = 0.111...
Multiply both sides by 9 to get
9/9 = 0.999...
9/9 = 1
1 = 0.999...

Proof 2
1/3 = 0.333...
2/3 = 0.666...
1/3 +2/3 = 0.333... + 0.666...
3/3 = 0.999...
3/3 = 1 = 0.999...

Proof 3
x = 0.999...
10x = 9.999...
10x -1 = 9.999... - 0.999...
9x = 9
x = 1
0.999... = 1
"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
MysticEgg
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1/25/2014 3:04:17 AM
Posted: 2 years ago
This isn't nearly as short as the proofs, but I think this is a nice way of explaining it:

0.9rec + (Something) = 1

The "something" is 0.000[...]1. However, when do you put the one in? After you run out of 9s. However, since 9.9rec has an infinite number of 9s, you never reach the one.

Therefore, 0.9rec + 0 = 1.

Therefore, 0.9rec = 1.

My thoughts.
Sidewalker
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1/25/2014 9:53:55 AM
Posted: 2 years ago
At 1/16/2014 8:40:05 PM, GarretKadeDupre wrote:
At 1/16/2014 8:38:58 PM, PotBelliedGeek wrote:
At 1/16/2014 8:30:13 PM, GarretKadeDupre wrote:
At 1/16/2014 8:28:35 PM, PotBelliedGeek wrote:
At 1/16/2014 8:26:08 PM, GarretKadeDupre wrote:
At 1/16/2014 8:19:08 PM, PotBelliedGeek wrote:
We don't have a mathematics thread, so this goes in science instead. I don't believe this statement is true, and have yet to see a proof that I cannot falsify.

Disclaimer: I'm an uneducated, brain-damaged retard who has never studied math, however...

Dude I'm really sorry if I came across as saying that. I really am.

sorry i didnt mean it like that, i was trying to be lighthearted about it lol



I'd say that 0.9 repeating cannot be one, because it isn't a number.

1 is a number

0.9 repeating isn't

They are both concepts, but one is a number and the other isn't

It is technically a number, but not an integer. Otherwise, I agree with you.

is it technically a number? i didnt know that. what about infinity? Is that technically a number?

What is the definition of number...?


just my thoughts

Here is a simple definition:
An arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity.

I'd say that "0.9 repeating" (what's the symbol for that?) doesn't represent a quantity.

The most commonly used symbol is 0.999...

And it does represent a quantity, the quantity 1.

I find it very mysterious that so many people have a problem accepting 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
Dazz
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1/25/2014 10:27:16 AM
Posted: 2 years ago
At 1/18/2014 10:49:34 AM, Gold wrote:
I'll try to break this down as simple as possible without that much knowledge of math needed, but limits are truly the best way to supply a "proof" for it.

A real number can either be equal or not equal to another real number. If a real number is not equal to another number, there exist at least one real number between the two.

So let's say .999... = x and 1 = z

What number is between x and z?
See here: x < y < z

The number .00...1 does not exist and therefore there are no numbers between .999... and 1, rendering them equal to one another.

Q. So 1.999.........= 1+ 0.999.......=1+1=2
Then, what's 1.11........ and 1.555...... equal to?
Remove the "I want", remainder is the "peace". ~Al-Ghazali~
"This time will also pass", a dose to cure both; the excitement & the grievance. ~Ayaz~
Dazz
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1/25/2014 10:35:50 AM
Posted: 2 years ago
At 1/24/2014 8:19:13 PM, Sidewalker wrote:
Here are three proofs:

Proof 1

1/9 = 0.111...
Multiply both sides by 9 to get
9/9 = 0.999...
9/9 = 1
1 = 0.999...

Proof 2
1/3 = 0.333...
2/3 = 0.666...
1/3 +2/3 = 0.333... + 0.666...
3/3 = 0.999...
3/3 = 1 = 0.999...

Proof 3
x = 0.999...
Starting 1st assumption, then.........
10x = 9.999...
10x -1 = 9.999... - 0.999...
.....You used the conclusion 1=0.99..... as your 2nd assumption, here?

9x = 9
x = 1
0.999... = 1
Remove the "I want", remainder is the "peace". ~Al-Ghazali~
"This time will also pass", a dose to cure both; the excitement & the grievance. ~Ayaz~
Sidewalker
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1/25/2014 10:44:14 AM
Posted: 2 years ago
Nobody seems to have a problem accepting that 1/3 plus 2/3 equals One, so why does the decimal notation of it seem so mysterious?

A mathematically repeating series doesn't represent the existence of an actual infinity or anything like that, it is just a repeating series. It's just a simple mathematical fact that doesn't relate to metaphysical contemplations about an actual infinity.

I don't think anyone sees the concept of 1/3 as complex, but represent that ratio as a decimal notation and people think it's a God thing or some kind of mysterious metaphysical statement or something, I just don't get 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
Dazz
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1/25/2014 11:12:42 AM
Posted: 2 years ago
At 1/24/2014 8:19:13 PM, Sidewalker wrote:
Here are three proofs:

Proof 1

1/9 = 0.111...
Multiply both sides by 9 to get
9/9 = 0.999...
9/9 = 1
Error 1: Oh you've again used here the conclusion as assumption.
1 = 0.999...

Proof 2
1/3 = 0.333...
2/3 = 0.666...
1/3 +2/3 = 0.333... + 0.666...
Error 2: That must be 1/3+1/3= 2/3

3/3 = 0.999...
3/3 = 1 = 0.999...

Proof 3
x = 0.999...
10x = 9.999...
10x -1 = 9.999... - 0.999...
Error3: Conclusion as assumption.

9x = 9
x = 1
0.999... = 1
Remove the "I want", remainder is the "peace". ~Al-Ghazali~
"This time will also pass", a dose to cure both; the excitement & the grievance. ~Ayaz~
AlbinoBunny
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1/25/2014 2:06:04 PM
Posted: 2 years ago
The fact that 1/9 equals 0.111... just signifies a flaw in our mathematical system (in base 12, 1/9 = 0.14). 9/9 is obviously one. 0.999... is effectively one, there is an infinitesimal difference between the two numbers, and infinity and infinitesimal aren't numbers (I think... lol), they seem more like bounds to me. Then we go into cardinality... whoops.

I think that 0.999... tends towards one, in the same way that the infinite series of 1 + 1/2 + 1/4 + 1/8... tends towards 2.
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