Poll: Does 0.999.. equal 1 ?

[Puzzlenaut]

The gap is infinitely small, but there is a gap.

Plus anyone who says they are the same is clearly a pretentious retard desperately trying to look clever to cover the fact that he has below average IQ and has a small penis.

So yeah >.>

Find the flaw in this logic

1/9 = 0.111111111111111...
0.111111111111111... * 9 = 0.99999999999999999...
Therefore 9/9 = 1 and 0.9999999999999...

Numbers cannot be synonyms. That is the flaw in this logic.

 

[Skratt]

The gap is infinitely small, but there is a gap.

Plus anyone who says they are the same is clearly a pretentious retard desperately trying to look clever to cover the fact that he has below average IQ and has a small penis.

So yeah >.>

Find the flaw in this logic

1/9 = 0.111111111111111...
0.111111111111111... * 9 = 0.99999999999999999...
Therefore 9/9 = 1 and 0.9999999999999...

hmm, I'll have to think about that.

 

[Rough Sausage]

The gap is infinitely small, but there is a gap.

Plus anyone who says they are the same is clearly a pretentious retard desperately trying to look clever to cover the fact that he has below average IQ and has a small penis.

So yeah >.>

Find the flaw in this logic

1/9 = 0.111111111111111...
0.111111111111111... * 9 = 0.99999999999999999...
Therefore 9/9 = 1 and 0.9999999999999...

Numbers cannot be synonyms. That is the flaw in this logic.

Statement: Numbers cannot be synonyms.
Counter example: 2/2 = 1/1 = 1. A synonym is the use of a different word to convey the same meaning; here I have used 2 different expressions for the number 1.

 

[Lord Kloo]

Simple calculation to prove they do not equal - in simple maths, I understand there are some areas where this may not be the case but I'm only a lay person..

If they equal then you can take one away from the other and get 0 as shown..

1 - 0.999 = 0.001 = therefore these two numbers are not equal although as they are so close most calculations would just round up to 1..

 

[Darth Crater]

Sigh.. Far too much of this thread is made up of people trying to apply intuition to math, when they could instead be looking up perfectly functional definitions. When infinite series, sets, or anything else get involved, math starts not working the way you think it does.

EDIT: also, far too many people are failing to understand what the "..." means (namely, that it's not 0.999, but shorthand for the sum of the series described below).

Short answer: 0.9... is equivalent to lim(x goes to infinity) of (sum(from 0 to x) 9 * (10^-x))), which is equivalent to 1.

Very short, possibly unprofessional proof: Suppose .9... and 1 were different real numbers. Then, by the density property, there exists another real number less than 1 but greater than 0.9... (in fact an infinite amount of such numbers). No such number exists. Thus, 0.9... = 1.

 

[Darth Crater]

0.999recurring doesnt equal 1 but it might aswell do because its 0.000recurring1 (if you dont know what i mean I mean 0.00000000......1).

this is why we use the fraction system rather than the decimal because when you express a third of some numbers you get a recurring number while with fractions you can just write 1/3

Doesn't work this way. The "..." means that it NEVER ends. There's no end to tack a 1 onto without there being more nines afterward to render the resulting sum greater than 1. Infinity is HARD.

 

[CM156_v1legacy]

I asked this question once to my professor, and he stated
"The diffrence between 1 and .9 is .1. the diffrence between 1 and .99 is .01. the diffrence between 1 and .999 is .001. Contine this logic, and the diffrence between 1 and .99999(ad infinitum) is .00000000000(ad infinitum)1. Because the zeros go on forever, there can be no one, so there is no diffrence."

 

[Puzzlenaut]

The gap is infinitely small, but there is a gap.

Plus anyone who says they are the same is clearly a pretentious retard desperately trying to look clever to cover the fact that he has below average IQ and has a small penis.

So yeah >.>

Find the flaw in this logic

1/9 = 0.111111111111111...
0.111111111111111... * 9 = 0.99999999999999999...
Therefore 9/9 = 1 and 0.9999999999999...

Numbers cannot be synonyms. That is the flaw in this logic.

Statement: Numbers cannot be synonyms.
Counter example: 2/2 = 1/1 = 1. A synonym is the use of a different word to convey the same meaning; here I have used 2 different expressions for the number 1.

But those aren't single numbers are they? That's like if I said there was no synonym for silver (I don't care if there is) and you countered with "Silver!"

 

[Rough Sausage]

The gap is infinitely small, but there is a gap.

Plus anyone who says they are the same is clearly a pretentious retard desperately trying to look clever to cover the fact that he has below average IQ and has a small penis.

So yeah >.>

Find the flaw in this logic

1/9 = 0.111111111111111...
0.111111111111111... * 9 = 0.99999999999999999...
Therefore 9/9 = 1 and 0.9999999999999...

Numbers cannot be synonyms. That is the flaw in this logic.

Statement: Numbers cannot be synonyms.
Counter example: 2/2 = 1/1 = 1. A synonym is the use of a different word to convey the same meaning; here I have used 2 different expressions for the number 1.

But those aren't single numbers are they? That's like if I said there was no synonym for silver (I don't care if there is) and you countered with "Silver!"

Either way, my argument shows there are at least 2 ways to write any one number, do you dispute this?

 

[Fidelias]

Okay, from what I understood in mathematics, when using 0.999... in a problem, you are to approximate using 1 instead of 0.999 recurring. However, the answer would be an approximation, not a chiseled-in-stone correct answer. The only reason why you substitute 0.999... for 1 is because it is impossible to use an infinite number in a math problem. In reality, 0.999... does NOT equal 1.

An example:

5= (x) + 0.999...
5~ (x) + 1
4~ (X)

X does not equal 4. X is approximately 4.

So 0.999...=/=1

0.999... ~ 1

 

[maninahat]

The straight dope article gives a practicle example of this problem, known as Zeno's paradox: If a man is racing against a tortoise, and the tortoise has a ten meter head start, you would expect the man to reach the tortoise very quickly. But by the time the man has run the ten metres, the tortoise has moved foward 1 meter. By the time the man has run another meter, the tortoise will have gone on another .10 meter, and so on and so forth. If this goes on for infinity, how can the man ever overtake the tortoise?

Zeno's paradox confuses by talking about distance, but measuring with time. Given the Paradox as it stands, the Man can never pass the tortoise because the time at which he does is never reached.

Yes, but that is where it deviates from real life. Although the logic of the paradox is correct, it does not prevent the man from over taking the tortoise in real life, much like how the recurring 0.9s fails to prevent three thirds making 1.0 instead of 0.999....

This is why the equivalency was brought in, but also why 0.9 recurring cannot equal 1. Because .9 recurring cannot finitely exist; it is, in itself, an irrational number - therefore it has a rational equivalency of 1. It can't equal 1, because 1 is rational.

repeating decimals like 0.999... or 1.252525... are rational numbers. Numbers like Pi are irrational. The best way of knowing whether a number can be rational is whether it can be converted to a simple fraction. 1 = 1/1, 1.25 = 5/4, 1.1111 = 1/9 etc. 0.9999 = 1/3*3, (0.333*3). In otherwords, it is 3/3s. Or just 1/1. Irrational numbers like Pi can't be expressed as a fraction.

 

[Tetranitrophenol]

yes, if you are an Engineer.
no, if you are a Mathematician

It's more the other way around actually. The engineer is the on likely doing calculations by saying "whatever, it's there but just infinitely small" while the mathematicians would mess around with limits and such.

But I guess this is a troll thread. Not only is a large amount voting no, but a majority is. WoW!

There's no rounding going on, there's no approximation, it's no "flaw" in our mathematics involved, a !quirk" in the decimal system, but no flaw.

But whatever, if multiple proofs are not enough (it should be, ONE correct proof should be enough actually) and you think that somehow all the mathematicians in the world got it wrong and YOU are the only one to see the truth, you come up with a proof for your side.

Here, I'll help with the start because there's one really simple way to prove that they are in fact not equal. Here it is:

Find a number x such that:

0.999... < x < 1

If there is a number that fits between them, xlearly they are not equal. And I'll say it right now that no, "zero point zero with an infinite amount of zeroes and then a one" does not work, because if there's an infinit amount of something there's no "and then".

hmm, not sure where you are getting with this post. Ok, 0.9999.... is not 1 in reality. But for the sake of calculations it IS 1 whether you like it or not...sorry... >__>

 

[PxDn Ninja]

As a software engineer I can tell you this,

0.999... != 1.0;

However, depending on the system you are using, it's possible that indeed the two will be equal. It also depends on the current state of the system. I have seen our code say it was true on one run, and false on the other.

As for mathematics in general, no they are not equal.

 

[Puzzlenaut]

The gap is infinitely small, but there is a gap.

Plus anyone who says they are the same is clearly a pretentious retard desperately trying to look clever to cover the fact that he has below average IQ and has a small penis.

So yeah >.>

Find the flaw in this logic

1/9 = 0.111111111111111...
0.111111111111111... * 9 = 0.99999999999999999...
Therefore 9/9 = 1 and 0.9999999999999...

Numbers cannot be synonyms. That is the flaw in this logic.

Statement: Numbers cannot be synonyms.
Counter example: 2/2 = 1/1 = 1. A synonym is the use of a different word to convey the same meaning; here I have used 2 different expressions for the number 1.

But those aren't single numbers are they? That's like if I said there was no synonym for silver (I don't care if there is) and you countered with "Silver!"

Either way, my argument shows there are at least 2 ways to write any one number, do you dispute this?

2/2 is a sum; it literally means 2 divided by 2. It is more than one number.

What I am saying is that there is no way of writing the same (single) number in two different ways.

 

[Hgame]

Yes, there is a very short mathematical proof already mentioned on this thread, but I will repeat it:

x is used to represent 0.9999999.....

Therefore x=0.9999999.....

10x= 0.9999999.....*10 = 9.9999999.....

9x = 10x - 1 = 9.9999999..... - 0.9999999..... = 9

9x = 9 Therefore x = 1

0.9999999..... = 1

 

[Amphoteric]

The gap is infinitely small, but there is a gap.

Plus anyone who says they are the same is clearly a pretentious retard desperately trying to look clever to cover the fact that he has below average IQ and has a small penis.

So yeah >.>

Find the flaw in this logic

1/9 = 0.111111111111111...
0.111111111111111... * 9 = 0.99999999999999999...
Therefore 9/9 = 1 and 0.9999999999999...

Numbers cannot be synonyms. That is the flaw in this logic.

Prove that they can't be.

 

[mps4li3n]

The gap is infinitely small, but there is a gap.

Plus anyone who says they are the same is clearly a pretentious retard desperately trying to look clever to cover the fact that he has below average IQ and has a small penis.

So yeah >.>

Find the flaw in this logic

1/9 = 0.111111111111111...
0.111111111111111... * 9 = 0.99999999999999999...
Therefore 9/9 = 1 and 0.9999999999999...

A Wizard did it... or was it a Mass Effect field?! Can never remember.

It's infinity, it's like dividing by zero, it always screws things up...

 

[Spencer Petersen]

This is getting tiresome, this isn't a matter of opinion any more than putting that 1 + 1 = 2 up to a vote is.

 

[Darth Crater]

As a software engineer I can tell you this,

0.999... != 1.0;

However, depending on the system you are using, it's possible that indeed the two will be equal. It also depends on the current state of the system. I have seen our code say it was true on one run, and false on the other.

As for mathematics in general, no they are not equal.

As a computer scientist, I can tell you that what you're seeing is a floating point rounding error. In general mathematics, they are equal, but (being infinitely long) the series is impossible to represent in digital form.

This is getting tiresome, this isn't a matter of opinion any more than putting that 1 + 1 = 2 up to a vote is.

Please, preach your soothing wisdom further.