# .99999 does not equal 1

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#### Oscar Wilde

• 3781
##### Re: .99999 does not equal 1
« Reply #90 on: August 11, 2008, 05:25:56 PM »
Dear God! Make it stop!

#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #91 on: August 11, 2008, 05:27:11 PM »
If the naysayers are ever actually able to back their position up let me know.  Otherwise, it's clearly been sufficiently proven that .999... = 1.
Where did you educate the biology, in toulet?

#### Wendy

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##### Re: .99999 does not equal 1
« Reply #92 on: August 11, 2008, 05:27:58 PM »
Wasn't that like, 20 years ago?
Here's an explanation for ya. Lurk moar. Every single point you brought up has been posted, reposted, debated and debunked. There is a search function on this forum, and it is very easy to use.

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#### cbarnett97

• 2746
##### Re: .99999 does not equal 1
« Reply #93 on: August 11, 2008, 05:34:17 PM »
The thing is that it doesn't work that way if you have an infinite amount of nines. Infinity plus one is just infinity again. You can't put something at the end of infinity. Your sig does ring true., cbarnett.
Same Idea different numbers:  F(x)=1/x when does x=0

Or f(x)=1/(1-x) when does x=1
« Last Edit: August 11, 2008, 05:35:48 PM by cbarnett97 »
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #94 on: August 11, 2008, 05:38:32 PM »
If the naysayers are ever actually able to back their position up let me know.  Otherwise, it's clearly been sufficiently proven that .999... = 1.
Where did you educate the biology, in toulet?

#### Raist

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##### Re: .99999 does not equal 1
« Reply #95 on: August 11, 2008, 05:40:17 PM »
The thing is that it doesn't work that way if you have an infinite amount of nines. Infinity plus one is just infinity again. You can't put something at the end of infinity. Your sig does ring true., cbarnett.
Same Idea different numbers:  F(x)=1/x when does x=0

Or f(x)=1/(1-x) when does x=1
x equals one at an undefined point in the equation. That has nothing to do with .99 repeating.

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#### cbarnett97

• 2746
##### Re: .99999 does not equal 1
« Reply #96 on: August 11, 2008, 05:41:18 PM »
The thing is that it doesn't work that way if you have an infinite amount of nines. Infinity plus one is just infinity again. You can't put something at the end of infinity. Your sig does ring true., cbarnett.
Same Idea different numbers:  F(x)=1/x when does x=0

Or f(x)=1/(1-x) when does x=1
x equals one at an undefined point in the equation. That has nothing to do with .99 repeating.
what set of numbers makes this equation valid?
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

#### Raist

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##### Re: .99999 does not equal 1
« Reply #97 on: August 11, 2008, 05:44:36 PM »
The thing is that it doesn't work that way if you have an infinite amount of nines. Infinity plus one is just infinity again. You can't put something at the end of infinity. Your sig does ring true., cbarnett.
Same Idea different numbers:  F(x)=1/x when does x=0

Or f(x)=1/(1-x) when does x=1
x equals one at an undefined point in the equation. That has nothing to do with .99 repeating.
what set of numbers makes this equation valid?
You gave a domain of 1 number. Therefore no numbers in this set give f(x) a defined value. Welcome to make a point or stfu.

#### cmdshft

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• swiggity swooty
##### Re: .99999 does not equal 1
« Reply #98 on: August 11, 2008, 05:46:31 PM »
Welcome to make a point or stfu.

Sig'd.

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#### cbarnett97

• 2746
##### Re: .99999 does not equal 1
« Reply #99 on: August 11, 2008, 05:47:00 PM »
The thing is that it doesn't work that way if you have an infinite amount of nines. Infinity plus one is just infinity again. You can't put something at the end of infinity. Your sig does ring true., cbarnett.
Same Idea different numbers:  F(x)=1/x when does x=0

Or f(x)=1/(1-x) when does x=1
x equals one at an undefined point in the equation. That has nothing to do with .99 repeating.
what set of numbers makes this equation valid?
You gave a domain of 1 number. Therefore no numbers in this set give f(x) a defined value. Welcome to make a point or stfu.
Let me slow down for you.........

Could x be .99999repeating forever and still give a defined result?
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

#### cmdshft

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• 13146
• swiggity swooty
##### Re: .99999 does not equal 1
« Reply #100 on: August 11, 2008, 05:48:54 PM »
The thing is that it doesn't work that way if you have an infinite amount of nines. Infinity plus one is just infinity again. You can't put something at the end of infinity. Your sig does ring true., cbarnett.
Same Idea different numbers:  F(x)=1/x when does x=0

Or f(x)=1/(1-x) when does x=1
x equals one at an undefined point in the equation. That has nothing to do with .99 repeating.
what set of numbers makes this equation valid?
You gave a domain of 1 number. Therefore no numbers in this set give f(x) a defined value. Welcome to make a point or stfu.
Let me slow down for you.........

Could x be .99999repeating forever and still give a defined result?

Yes, when you use the proof I supplied.

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#### cbarnett97

• 2746
##### Re: .99999 does not equal 1
« Reply #101 on: August 11, 2008, 05:51:08 PM »
The thing is that it doesn't work that way if you have an infinite amount of nines. Infinity plus one is just infinity again. You can't put something at the end of infinity. Your sig does ring true., cbarnett.
Same Idea different numbers:  F(x)=1/x when does x=0

Or f(x)=1/(1-x) when does x=1
x equals one at an undefined point in the equation. That has nothing to do with .99 repeating.
what set of numbers makes this equation valid?
You gave a domain of 1 number. Therefore no numbers in this set give f(x) a defined value. Welcome to make a point or stfu.
Let me slow down for you.........

Could x be .99999repeating forever and still give a defined result?

Yes, when you use the proof I supplied.
So when F(x)1/(1-x) x can be .9999 repeating forever and be valid but it can never=1 so how can .99999....=1
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

#### cmdshft

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• swiggity swooty
##### Re: .99999 does not equal 1
« Reply #102 on: August 11, 2008, 05:52:37 PM »
so how can .99999....=1

3/3 = 1

1/3= .33333...

Therefore, (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) = 1

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#### cbarnett97

• 2746
##### Re: .99999 does not equal 1
« Reply #103 on: August 11, 2008, 05:53:18 PM »
so how can .99999....=1

3/3 = 1

1/3= .33333...

Therefore, (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) roughly equal 1
Fixed
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #104 on: August 11, 2008, 05:54:46 PM »
If the naysayers are ever actually able to back their position up let me know.
Where did you educate the biology, in toulet?

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#### Oscar Wilde

• 3781
##### Re: .99999 does not equal 1
« Reply #105 on: August 11, 2008, 05:57:03 PM »

#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #106 on: August 11, 2008, 05:57:50 PM »
Still trying to convince me that my calculator is wrong.

In fact, my calculator just proved that my proof is correct.

Divide 1 by 3, so you get (.3333333...). Don't clear the screen. Multiply that result by 3, and tell me what you get.

Then, remember that basic maths tell us that multiplying (.333333...) by three is the same as performing (.33333333....) + (.33333333....) + (.33333333....). So if the result of multiplying (.333333...) by 3 = 1, so does (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) = 1.

Go ahead, call all calculators liars.

#### Raist

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##### Re: .99999 does not equal 1
« Reply #107 on: August 11, 2008, 06:00:15 PM »
Still trying to convince me that my calculator is wrong.

In fact, my calculator just proved that my proof is correct.

Divide 1 by 3, so you get (.3333333...). Don't clear the screen. Multiply that result by 3, and tell me what you get.

Then, remember that basic maths tell us that multiplying (.333333...) by three is the same as performing (.33333333....) + (.33333333....) + (.33333333....). So if the result of multiplying (.333333...) by 3 = 1, so does (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) = 1.

Go ahead, call all calculators liars.
This isn't technically proof since the calculator rounds the number off after a certain number of digits....

#### Taters343

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##### Re: .99999 does not equal 1
« Reply #108 on: August 11, 2008, 06:01:44 PM »
I think this arguement should just end now, since they are obviously quite equal to eachother.

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#### cbarnett97

• 2746
##### Re: .99999 does not equal 1
« Reply #109 on: August 11, 2008, 06:02:32 PM »
Still trying to convince me that my calculator is wrong.

In fact, my calculator just proved that my proof is correct.

Divide 1 by 3, so you get (.3333333...). Don't clear the screen. Multiply that result by 3, and tell me what you get.

Then, remember that basic maths tell us that multiplying (.333333...) by three is the same as performing (.33333333....) + (.33333333....) + (.33333333....). So if the result of multiplying (.333333...) by 3 = 1, so does (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) = 1.

Go ahead, call all calculators liars.
Go ahead tell your calculator to give you the square root of 2 and then give that answer to a college professor when he wants the exact answer
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #110 on: August 11, 2008, 06:06:07 PM »
Quote
In mathematics, the recurring decimal 0.999, which is also written as 0.\bar{9} , 0.\dot{9} or \ 0.(9), denotes a real number equal to 1. In other words, the notations "0.999" and "1" represent the same real number. The equality has long been accepted by professional mathematicians and taught in textbooks. Various proofs of this identity have been formulated with varying rigour, preferred development of the real numbers, background assumptions, historical context, and target audience.

from http://en.wikipedia.org/wiki/0.999...

Quote
.9 is not 1; neither is .999, nor .9999999999. In fact if you stop the
expansion of 9s at any finite point, the fraction you have (like .9999
= 9999/10000) is never equal to 1. But each time you add a 9, the
error is less. In fact, with each 9, the error is ten times smaller.

You can show (using calculus or other methods) that with a large
enough number of 9s in the expansion, you can get arbitrarily close to
1, and here's the key:

THERE IS NO OTHER NUMBER THAT THE SEQUENCE GETS ARBITRARILY CLOSE TO.

Thus, if you are going to assign a value to .9999... (going on
forever), the only sensible value is 1.

There is nothing special about .999...  The idea that 1/3 = .3333...
is the same. None of .3, .33, .333333, etc. is exactly equal to 1/3,
but with each 3 added, the fraction is closer than the previous
approximation. In addition, 1/3 is the ONLY number that the series
gets arbitrarily close to.

from http://mathforum.org/library/drmath/view/55748.html

Quote
As before, 0.999... = 0.9 + 0.09 + 0.009 + ... = 9/10 + 9/100 + 9/1000 + ... The expression 0.999... implies an infinite sum, i.e., a sum of an infinite number of terms. In mathematics, such infinite sums are called series. Series are introduced and studied rigorously in Calculus, where a distinction is made: some series are convergent, some are divergent. Every convergent series has a unique number associated with it, its sum. Divergent series are not so lucky. All infinite decimal fractions, like 0.999..., are shown to correspond to convergent series (which converge to their respective sums.) 0.999... converges to 1 which is expressed simply as 0.999... = 1. Similarly, 0.333... is a convergent series whose sum is 1/3: 0.333... = 1/3.

from http://www.cut-the-knot.org/arithmetic/999999.shtml

Three sources, all of which state that .999... = 1.  The ball is in your corner to dispute these points, backed up with sources of your own, cbarnett.
Where did you educate the biology, in toulet?

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#### cbarnett97

• 2746
##### Re: .99999 does not equal 1
« Reply #111 on: August 11, 2008, 06:10:51 PM »
"Thus, if you are going to assign a value to .9999... (going on
forever), the only sensible value is 1."

Now where does it say that they are equal?

It says basically that while it does not equal 1 it is just a whole lot easier to write one instead of an infinte number of 9's
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #112 on: August 11, 2008, 06:13:23 PM »
Still trying to convince me that my calculator is wrong.

In fact, my calculator just proved that my proof is correct.

Divide 1 by 3, so you get (.3333333...). Don't clear the screen. Multiply that result by 3, and tell me what you get.

Then, remember that basic maths tell us that multiplying (.333333...) by three is the same as performing (.33333333....) + (.33333333....) + (.33333333....). So if the result of multiplying (.333333...) by 3 = 1, so does (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) = 1.

Go ahead, call all calculators liars.
This isn't technically proof since the calculator rounds the number off after a certain number of digits....

Only in the display. But in memory, the number is fully crunched. Else, when I did the multiplication, it would not have told me simply "1". It would have been less than 1. But the fact that even though it only showed me a limited number of 3's and showed me the result as "1" is proof enough that my proof is 100% correct.

I have a video displaying my proof. Once it's done processing, I will link to it. Then you can try and disprove it and the three sources Roundy posted.

#### Raist

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##### Re: .99999 does not equal 1
« Reply #113 on: August 11, 2008, 06:17:52 PM »
Still trying to convince me that my calculator is wrong.

In fact, my calculator just proved that my proof is correct.

Divide 1 by 3, so you get (.3333333...). Don't clear the screen. Multiply that result by 3, and tell me what you get.

Then, remember that basic maths tell us that multiplying (.333333...) by three is the same as performing (.33333333....) + (.33333333....) + (.33333333....). So if the result of multiplying (.333333...) by 3 = 1, so does (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) = 1.

Go ahead, call all calculators liars.
This isn't technically proof since the calculator rounds the number off after a certain number of digits....

Only in the display. But in memory, the number is fully crunched. Else, when I did the multiplication, it would not have told me simply "1". It would have been less than 1. But the fact that even though it only showed me a limited number of 3's and showed me the result as "1" is proof enough that my proof is 100% correct.

I have a video displaying my proof. Once it's done processing, I will link to it. Then you can try and disprove it and the three sources Roundy posted.
In the computers memory it probably holds maybe a couple hundred digits. In order for it to hold all the numbers it would have to have infinite RAM. So it rounds it off after so many decimals. Since 3 rounds down, you get straight nines.

#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #114 on: August 11, 2008, 06:19:23 PM »
You're not seeing the point. If the calculator did, in fact, round it off, why did I get 1 and not some rounded version of .99999999999999?

My calculator displayed 0.33333333333333333333333333333333. So add that to itself 3 times, and you would get 0.999999999999999999999999999999.

EDIT: Just to make things clear, the calculator doesn't display (...) to represent the infinite decimal places. But the number displayed is infinitely long, because------------
|
VŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ
But I got 1 when multiplying it in the calculator. You can see the steps I took in the video when I link to it.

EDIT: " class="bbc_link" target="_blank">Video. Watch fullscreen.
« Last Edit: August 28, 2008, 02:18:40 PM by Hara Taiki »

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#### cbarnett97

• 2746
##### Re: .99999 does not equal 1
« Reply #115 on: August 11, 2008, 06:28:09 PM »
You're not seeing the point. If the calculator did, in fact, round it off, why did I get 1 and not some rounded version of .99999999999999?

My calculator displayed 0.33333333333333333333333333333333. So add that to itself 3 times, and you would get 0.999999999999999999999999999999.

But I got 1 when multiplying it in the calculator. You can see the steps I took in the video when I link to it.

EDIT: " class="bbc_link" target="_blank">Video. Watch fullscreen.
when I get home I will run it through mathematica and see what I get
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

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#### Oscar Wilde

• 3781
##### Re: .99999 does not equal 1
« Reply #116 on: August 11, 2008, 06:29:00 PM »
Do I seriously need to post my diagrams of Oscar Wilde action figures representing an infinite number of nines?

#### Raist

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##### Re: .99999 does not equal 1
« Reply #117 on: August 11, 2008, 06:30:05 PM »
You're not seeing the point. If the calculator did, in fact, round it off, why did I get 1 and not some rounded version of .99999999999999?

My calculator displayed 0.33333333333333333333333333333333. So add that to itself 3 times, and you would get 0.999999999999999999999999999999.

But I got 1 when multiplying it in the calculator. You can see the steps I took in the video when I link to it.

EDIT: " class="bbc_link" target="_blank">Video. Watch fullscreen.
oh. I misread. Sorry. So it's a scientific calculator that either recomputes every step each time, or did all the equations at once at the end. Good job hara. Sorry for being a retard.

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#### [][][]

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• Man of science.
##### Re: .99999 does not equal 1
« Reply #118 on: August 11, 2008, 06:35:12 PM »
I think the problem with this thread is that one person does not seem to understand that the infinite series representation of .9999... sums exactly to one, not approximatly. Not signaling anyone out but... *cough* just look at the proof again. If you feel there is a disproof, express it as a formal mathmatical (dis)proof.
« Last Edit: August 11, 2008, 06:39:02 PM by [][][] »
The folly of mistaking a paradox for a discovery, a metaphor for a proof, a torrent of verbiage for a spring of capital truths, and oneself for an oracle, is inborn in us. -Some Frenchy

#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #119 on: August 11, 2008, 06:53:24 PM »
"Thus, if you are going to assign a value to .9999... (going on
forever), the only sensible value is 1."

Now where does it say that they are equal?

It says basically that while it does not equal 1 it is just a whole lot easier to write one instead of an infinte number of 9's

It says it all over the quotes I provided.  You picked one ambiguous-sounding passage to scrutinize.  Bully for your selective vision and lack of ability to recognize logical and mathematical fact.

So you have an opinion.  That's great.  Can you back it up with any actual facts?  Any sources to back up your opinion that .999... does not equal 1?  No?  Didn't think so.

Back up your position with more than your own ill-informed opinion, or else accept that you are a fucking moron.  You might want to lean toward the latter option in advance because you won't find anything reputable backing up your opinion, though.
Where did you educate the biology, in toulet?