# .99999 does not equal 1

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#### lolz at trollz

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##### Re: .99999 does not equal 1
« Reply #120 on: August 11, 2008, 06:53:44 PM »
Do I seriously need to post my diagrams of Oscar Wilde action figures representing an infinite number of nines?

Umm?  can you really comprehend people not wanting to see that?

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#### Trekky0623

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##### Re: .99999 does not equal 1
« Reply #121 on: August 11, 2008, 06:56:45 PM »
Quote from: xkcd forums
WE ALREADY KNOW ABOUT THE .999 --> 1 THING (and 0/0 etc)

There are threads about it already, if not here then definitely in Logic Puzzles. Any more threads about it are just going to be deleted. It's been done to death, guys.

(If you disagree that 0.999... = 1, or are in an argument with someone who disagrees, go to the Wikipedia article on it. There are plenty of proofs and explanations there. If you or the person you're arguing with still doubts it after that, it's a good sign of some sort of brain damage or, at best, a complete lack of good mathematical understanding, and there is nothing any of us here will be able to do. So seriously, NO MORE POSTS ABOUT IT!)

Edit by Spitvalve:

What is 0/0 equal to?
The aeroplane on a treadmill puzzle. There's a good writeup here for the answer.
Any variant on the Monty Hall / 3 Door problem. Again Wikipedia knows all.

#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #122 on: August 11, 2008, 06:58:49 PM »
(If you disagree that 0.999... = 1, or are in an argument with someone who disagrees, go to the Wikipedia article on it. There are plenty of proofs and explanations there. If you or the person you're arguing with still doubts it after that, it's a good sign of some sort of brain damage or, at best, a complete lack of good mathematical understanding, and there is nothing any of us here will be able to do.

Good point, it's obvious that cbarnett lacks the mental capacity to understand this concept.  It's so sad and still kind of funny all at the same time.
Where did you educate the biology, in toulet?

#### Raist

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##### Re: .99999 does not equal 1
« Reply #123 on: August 11, 2008, 07:13:10 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.
We understand it. Read all the posts. We're just talking now.

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#### DigCamara

• 13
##### Re: .99999 does not equal 1
« Reply #124 on: August 11, 2008, 07:31:49 PM »
Well, strictly speaking .99999 does not equal 1. It equals 99999/100000.

On that note, look at the Repeating decimal entry in Wikipedia. Specifically, look at this quote:

Quote from: Wikipedia
In fact, a real number has an ultimately periodic decimal representation if and only if it is a rational number, that is, a number that can be expressed in the form a⁄b where a and b are integers and b is non-zero, that is, a vulgar fraction. On the one hand, the decimal representation of a rational number is ultimately periodic because it can be determined by a long division process, which must ultimately become periodic as there are only finitely many different remainders and so eventually it will find a remainder that has occurred before. On the other hand, each repeating decimal number satisfies a linear equation with integral coefficients, and its unique solution is a rational number. To illustrate the latter point, the number α = 5.8144144144... above satisfies the equation 10000α − 10α = 58144.144144... − 58.144144... = 58086, whose solution is α = 58086⁄9990 = 3227⁄555.

How, then, can you represent 0.999... (a repeating decimal, by definition) via an equation in the form a/b, where a and b are integers and b is non-zero? You could, for instance take 0.333... (again, a repeating decimal, by definition), where a=1 and b=3 and multiply it by 3... thus obtaining an equation where a=9 and b=9... or, perhaps, you could take 0.111... (with a=1 and b=9) and multiply it by 9. And so on.

In other words: you're fighting a definition, used by mathematicians to simplify things. You may not like the definition but it will still be used the way it should be.

(BTW: limits? Are an entirely different thing. They don't have anything to do with the OP).

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#### Oscar Wilde

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##### Re: .99999 does not equal 1
« Reply #125 on: August 11, 2008, 07:53:08 PM »

#### Guessed

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##### Re: .99999 does not equal 1
« Reply #126 on: August 11, 2008, 07:54:48 PM »
You should demonstrate ALL of your arguments using diagrams.
Is Dino open source?

Quote from: grogberries

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#### Oscar Wilde

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##### Re: .99999 does not equal 1
« Reply #127 on: August 11, 2008, 07:56:15 PM »
So far, all of my diagrams are yet to be proven wrong.

#### Guessed

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##### Re: .99999 does not equal 1
« Reply #128 on: August 11, 2008, 07:56:59 PM »
Exactly my point, Mr.Wilde. You should replace the FAQ answers with diagrams.
Is Dino open source?

Quote from: grogberries

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#### Oscar Wilde

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##### Re: .99999 does not equal 1
« Reply #129 on: August 11, 2008, 07:57:53 PM »
I'll get to work on a Wilde Edition of the FAQ as soon as possible!

#### Guessed

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##### Re: .99999 does not equal 1
« Reply #130 on: August 11, 2008, 08:01:49 PM »
The RE proponents would have to believe then, I mean, you'd be offering photographic proof.
Is Dino open source?

Quote from: grogberries

#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #131 on: August 11, 2008, 09:04:00 PM »
Not signaling anyone out but... *cough* just look at the proof again.

Are you referring to my proof (simple) or the limit proof (complex)?

#### Jack

• 5179
##### Re: .99999 does not equal 1
« Reply #132 on: August 11, 2008, 09:21:07 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

Your stupidity has leveled up again.  It says the error becomes ten times smaller for each "9" inserted. Thus, since 0.999... has infinite 9s, the error becomes so small that it literally becomes negligible. Thus, they are equal.

#### Trekky0623

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##### Re: .99999 does not equal 1
« Reply #133 on: August 11, 2008, 10:40:02 PM »
Jeez.  If you're going to debate math, debate something at least a little controversial in the world of professional mathematics.

In math, there is no argument over this.  0.999... = 1.  It just does.  Look at the proofs.  Math is not something that is easily bent.  A proof is a proof, not an argument.

Now, here's something a little more interesting to debate:

00 = 1

because we need it that way

DISCUSS THIS CONTRADICTION IN THE WORLD OF MATH!
« Last Edit: August 11, 2008, 10:44:36 PM by Trekky0623 »

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#### Oscar Wilde

• 3781
##### Re: .99999 does not equal 1
« Reply #134 on: August 11, 2008, 10:42:49 PM »
So long as we all agree that Poe point Wilde Wilde Wilde Wilde Wilde (indefinitely) equals one, I see no contradiction in mathematics whatsoever.

#### lindelof

• 422
##### Re: .99999 does not equal 1
« Reply #135 on: August 11, 2008, 10:45:49 PM »

00 = 1

DISCUSS THIS CONTRADICTION IN THE WORLD OF MATH!

Anything to the zero is one.  By definition.  The way that you define powers is recursively,

x^0 = 1

x^(n+1) = (x^n) * x.

0^0 = 1 is pretty weird, though.

Also, it does make sense, when x is veeeeery close to zero, x^x is close to 1.

.00001^.00001 = 0.999884877
« Last Edit: August 11, 2008, 10:48:12 PM by lindelof »

#### Trekky0623

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##### Re: .99999 does not equal 1
« Reply #136 on: August 11, 2008, 10:51:47 PM »
0x = 0

x0 = 1

00 = undefined...or 1...or...AHHG.

Quote from: Donald Benson
The choice whether to define 00 is based on convenience, not on correctness.

Quote from: Concrete Mathematics
Some textbooks leave the quantity 00 undefined, because the functions 0x and x0 have different limiting values when x decreases to 0. But this is a mistake. We must define x0 = 1 for all x , if the binomial theorem is to be valid when x = 0 , y = 0, and/or x = −y . The theorem is too important to be arbitrarily restricted! By contrast, the function 0x is quite unimportant.
« Last Edit: August 11, 2008, 10:54:08 PM by Trekky0623 »

#### narcberry

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##### Re: .99999 does not equal 1
« Reply #137 on: August 11, 2008, 11:25:22 PM »
Sometimes I really like you trekky.

#### Parsifal

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##### Re: .99999 does not equal 1
« Reply #138 on: August 12, 2008, 12:40:54 AM »
00 = 01 * 0-1 = 0/0 = undefined
I'm going to side with the white supremacists.

#### Wendy

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##### Re: .99999 does not equal 1
« Reply #139 on: August 12, 2008, 04:24:54 AM »
The above three posts are correct, but x0=1 is too.
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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#### platypus

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##### Re: .99999 does not equal 1
« Reply #140 on: August 12, 2008, 08:05:16 AM »
If .999... != 1, then what is 1 - 0.999... ?

#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #141 on: August 12, 2008, 09:00:46 AM »
If .999... != 1, then what is 1 - 0.999... ?

0

#### Jack

• 5179
##### Re: .99999 does not equal 1
« Reply #142 on: August 12, 2008, 09:21:18 AM »
If .999... != 1, then what is 1 - 0.999... ?
Infinite != finite, so it's 0.

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#### Bushido

##### Re: .99999 does not equal 1
« Reply #143 on: August 12, 2008, 10:06:32 AM »
I think people who disagree that 0.(9) = 1 on the grounds that infinity does not exist make the same logical fallacy as the ancient philosopher Zenon who described the so called Zenon's paradox:

"Achilles is much faster than a tortoise. He can travel a certain distance x in 9/10’s of a minute. The tortoise can cover the same distance in 9 minutes, meaning that the tortoise is 10 times slower than Achilles or Achilles is 10 times faster than the tortoise, whichever you prefer.

Now, suppose that the tortoise is that particular distance x in front of Achilles. If someone was to ask when Achilles would gain upon the tortoise, we would say:

-If the time it takes Achilles to overtake the tortoise is t, then he would travel a distance which is t/(9/10 min) compared to the distance x in the problem. The tortoise would cover a distance which is only t/(9 min) compared to the distance x given in the problem. But, if Achilles overtook the tortoise, this would mean that

t*x/(9/10 min) = x + t*x/(9 min)

10*t*x/(9 min) = x + t*x/(9 min)            / * (9 min) <- Least common multiple of all the denominators

10*t*x = (9 min)*x + t*x                      / : x <- common multple

10*t = 9 min + x

9*t = 9 min                                         / : 9

t = 1 min

Piece of cake! But, not quite. What if the guy who was solving the problem was ‘narcberry’? He would reason in the following manner:

- If Achilles is to gain on the tortoise he would first have to cross the distance that was initially between them. We know that he can cross this distance in 9/10 minute. However, during this time the tortoise would move a small distance, actually 1/10 (because it would cover 10 times smaller distance than Achilles did) of the initial distance, so Achilles still did not gain upon the tortoise. In order to gain upon the tortoise, Achilles needs 1/10*(9/10) = 9/102 minute to cross this distance. But, the tortoise would move an even smaller distance during this time, actually, (1/10)2 of the initial distance. This is enough for him to “prove” that, since in every step the tortoise moves away by an ever decreasing, but still nonzero distance, Achilles would never gain upon the tortoise. Never meaning it would take him an infinite amount of time! But, little does ‘narcberry’ know that:

9/10 min + 9/102 min + 9/103 min + … + 9/10n min + … =
= (9/10)/(1 – 1/10) min = 1 min

The sum of infinite terms on the left is called an infinite series. The Ancient Greeks, just as ‘narcberry’ had trouble acknowledging the fact that a sum of infinite terms can itself be finite. Notice that I intentionally chose the numbers so that the infinite series on the left exactly represents the number 0.(9) = 0.99….

#### lolz at trollz

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##### Re: .99999 does not equal 1
« Reply #144 on: August 12, 2008, 10:12:13 AM »
The tortoise wins cos it is similar to a turtle and the turtle has a flat earth on him back and flat earth always win, so tortoise win!
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#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #145 on: August 12, 2008, 10:14:14 AM »
For the record, it was Zeno, not Zenon.
Where did you educate the biology, in toulet?

#### divito the truthist

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##### Re: .99999 does not equal 1
« Reply #146 on: August 12, 2008, 10:16:34 AM »
Thus, since 0.999... has infinite 9s, the error becomes so small that it literally becomes negligible. Thus, they are equal.

Negligible does not erase that the error still exists, no matter how small it ends up being. Regardless if it is approximately one, if you were dealing with extreme accuracy, it does not equate to 1. "Just as good as," or "the only sensible option" are phrases that are used on purpose because they are not 100% equal.
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#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #147 on: August 12, 2008, 10:18:31 AM »
Thus, since 0.999... has infinite 9s, the error becomes so small that it literally becomes negligible. Thus, they are equal.

Negligible does not erase that the error still exists, no matter how small it ends up being. Regardless if it is approximately one, if you were dealing with extreme accuracy, it does not equate to 1. "Just as good as," or "the only sensible option" are phrases that are used on purpose because they are not 100% equal.

Well if you can back that statement up with an outside source, as I have done with several that say that .999... does equate 1 and this is a fact agreed upon by mathematicians, let us all know.
« Last Edit: August 12, 2008, 10:46:25 AM by Roundy the Truthinessist »
Where did you educate the biology, in toulet?

#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #148 on: August 12, 2008, 10:22:38 AM »
Shh, go away for now, us adults are talking.

#### Wendy

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##### Re: .99999 does not equal 1
« Reply #149 on: August 12, 2008, 10:22:45 AM »
Thus, since 0.999... has infinite 9s, the error becomes so small that it literally becomes negligible. Thus, they are equal.

Negligible does not erase that the error still exists, no matter how small it ends up being. Regardless if it is approximately one, if you were dealing with extreme accuracy, it does not equate to 1. "Just as good as," or "the only sensible option" are phrases that are used on purpose because they are not 100% equal.

It's not 'negligible' like 'insignificant', it's negligible because it doesn't exist.
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.