1. The people that rate OP dumb have never taken higher level math classes.
Agree x 8 Artistic x 2 (list)

2. 0.999... = 1 is true in the same way that 0.000... = 0.

It just doesn't look that way because your brain goes:

.9 =/= 1
.99 =/= 1
.999 =/= 1
.9999 =/= 1

So it would intuitively follow that no matter how many nines you put, it will never equal 1. The problem is that when you put an infinite number of nines, it equals 1.
I would like to see an actual proof of this.

3. They're different numbers, it's just that one is only possible (to measure, at least) in theory.
No, they're the same number. They are both 1. 1 can be measured, and exists. Therefore both exist, and can be measured.
Agree x 2 Disagree x 2 (list)

4. 0.3 repeating isn't 1/3. It's a decimal APPROXIMATION of 1/3 which means it isn't the exact value (of 1/3). 0.3333 to the infinity * 3 is not the same as 1/3 * 3. One is a multiplication using absolute values while the other is an approximation. They're two different numbers.

Either that or I'm just too stupid enough to understand why 0.9 repeating is the same as 1.
it's the second choice i'm afraid :(

5. I would like to see an actual proof of this.
Jesus, fine. But if you can't understand the math behind the proof, you aren't allowed to rebut it.

Here's my white-board ghetto-proof.

Agree x 6 Winner x 3 Funny x 1 (list)

6. http://en.wikipedia.org/wiki/Numerical_analysis

Go read it and stop claiming 0.9999.. = 1 ; If u keep doing it, I will hold u accountable the next time a bridge collapses.
Dumb x 11 (list)

7. http://en.wikipedia.org/wiki/Numerical_analysis

Go read it and stop claiming 0.9999.. = 1 ; If u keep doing it, I will hold u accountable the next time a bridge collapses.
You make the mistake of assuming that 0.999... is an approximation. It is not. It is exact. It is exactly 1.
Agree x 3 (list)

8. I wish I was better at math.
Agree x 2 (list)

9. Jesus, fine. But if you can't understand the math behind the proof, you aren't allowed to rebut it.

Here's my white-board ghetto-proof.

You can also use this to show that limit 'n' tends to zero, for 0.00000000........1 = 0
Convergence on zero.

10. You make the mistake of assuming that 0.999... is an approximation. It is not. It is exact. It is exactly 1.
Touché - my point is wrong
People simply shouldnt claim that 1/3 * 3 = 0.9999.. - its not
Disagree x 2 Dumb x 2 (list)

11. corrected because I'm an idiot and put numbers where numbers should not have been

0.333... = 1/3

0.333... + 0.333... + 0.333... = 0.999...

0.999... = 3/3

0.999... = 1
Funny x 1 (list)

12. 3.333... = 1/3

3.333... x 3.333... = 9.999...

9.999... = 3/3

9.999... = 1

I'm not great at maths, but that's what someone told me on YouTube, so there we go.
Besides being late, 3.333... =/= 1/3

0.333... = 1/3
Agree x 2 (list)

13. 3.333... = 1/3 - WRONG

3.333... x 3.333... = 9.999... - WRONG

9.999... = 3/3 - WRONG

9.999... = 1 - WRONG

I'm not great at maths, but that's what someone told me on YouTube, so there we go.
Good job being wrong 4 times in a single post. U just failed math.
Dumb x 1 (list)

14. Jesus, fine. But if you can't understand the math behind the proof, you aren't allowed to rebut it.

Here's my white-board ghetto-proof.

If I were to solve this in a math test by saying that the limit of 10^n as n approaches -infinity, I would agree with you by saying that the answer infinitely approaches 0, hence the (1 - 0 = 1). However, the problem with the limit method is that it is an approximation of the answer for whatever value of n it is approaching. If I were to use a simple algebraic method, this wouldn't hold.
Dumb x 1 (list)

15. 3.333... = 1/3

3.333... x 3.333... = 9.999...

9.999... = 3/3

9.999... = 1

I'm not great at maths, but that's what someone told me on YouTube, so there we go.
3.333... * 3.333... is actually somewhere around 11.1099999~

16. The people that rate OP dumb have never taken higher level math classes.
I rated it dumb because it was dumb, and because this thread and threads like it have been made way too many times, not because I disagreed with the fact that 0.99... = 1.

17. If I were to use a simple algebraic method, this wouldn't hold.
So do it.

18. I'm confused why people are rating the OP dumb.
because every other thread regarding this topic that has been posted on fp did not end well

Edited:

as summed up in the first post:

Oh god, not this shit again.
Agree x 2 (list)

19. Isn't the only reason people still dont understand this because they dont understand infinity? If the number of nines is just insanely super mega high, 1 does not equal it, but with infinite nines, 1 does. It's just that people think that infinity is just a really long number, that does end, that can be treated just like other numbers...
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20. I bet that girls vagina is oozing smegma.
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21. 0.333..... is the decimal representation of the fraction (1/3).

It's the same thing.
no, the key word is there

"representation"

you'd need an infinite numbers of 3333s, and the more you'd have, the closer you'd get to 1

it's not the same thing, and that's why the whole 0.999 = 1 is BS
Dumb x 8 (list)

22. So do it.
Would you agree with me that using the limit method that you showed to find the real value is an approximation, good for maybe an explanation in theory but not for a concrete answer? Using simple mathematical operations, if you were to subtract 0.9 to the infinity from 1, you wouldn't get 0 unless you're using an approximation of the value.

23. shitstorm successful
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24. Its simple ...

1/3 is NOT 0.3333.. ; however, 0.3333... is an APPROXIMATION of 1/3 - it is CLOSE to it
So doing 0.3333.. * 3 = 0.9999.. - Which is CLOSE to 1 - but its NOT 1!

And doing 1/3 * 3 = 1 ; which is infact true!
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25. the problem with the limit method is that it is an approximation of the answer for whatever value of n it is approaching.
No it's not. lims give exact answers.

26. I remember there being another rule that applies to this which says that if there is no real number between two 'Numbers', they must be the same as there is literally nothing between them.

27. if you were to subtract 0.9 to the infinity from 1, you wouldn't get 0 unless you're using an approximation of the value.
Yes, you would. I think you don't really grasp the concept of infinity well.
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28. No it's not. lims give exact answers.
It depends, in Smashmaster's example, it is one.

29. It depends, in Smashmaster's example, it is one.
What I mean is, lims are never approximates. limits give you precise numbers, whether they are rational or irrational. You choose where to cut them into an approximate.

30. Would you agree with me that using the limit method that you showed to find the real value is an approximation, good for maybe an explanation in theory but not for a concrete answer? Using simple mathematical operations, if you were to subtract 0.9 to the infinity from 1, you wouldn't get 0 unless you're using an approximation of the value.
I wouldn't. Saying there is a number infinitely close to 1, but not equal to 1, is a contradiction. It's like saying there is an object that is colored entirely red, and colored a little blue. You have to be careful when working with infinity. You can't round infinity, and you can't approximate infinity. If you multiply something by infinity, you get infinity. If you divide by it, you get zero. You don't get 'almost infinity' or 'almost zero.' That's just how it works.

31. I wouldn't. Saying there is a number infinitely close to 1, but not equal to 1, is a contradiction. It's like saying there is an object that is colored entirely red, and colored a little blue.
The idea is that the limit value of 10^n as n approaches -infinity tends to 0. I get what you're saying with infinitely approaching 1, but if what you're saying is true, then if you start with 1 and you keep infinitely dividing by 2, you would eventually reach 0. I'm not so sure about that.

32. It's like saying there is an object that is colored entirely red, and colored a little blue.
That doesn't actually work, since that would mean saying there's a number that's exactly one, but isn't one.

You have to be careful when working with infinity. You can't round infinity, and you can't approximate infinity.
You seem to be doing a fine job of it.

33. shitstorm successful
Caused by fucking decimals, no less.

34. Good job being wrong 4 times in a single post. U just failed math.
Good job being wrong two times in a single post. You just failed English.

Besides, it was pretty obvious that I'd just made a couple of typos because I wasn't thinking straight. I'm not dumb enough to actually think that 9.999 recurring is equal to one, I meant 0.999 recurring, and accidentally put the number at the beginning instead of a zero. But whatever, this is obviously really important to you all, so I'll just leave you guys to it.
Dumb x 1 (list)

35. if what you're saying is true, then if you start with 1 and you keep infinitely dividing by 2, you would eventually reach 0. I'm not so sure about that.
I can prove that it does in 10 different ways. You can't prove that it doesn't in even 1 way.

realistically speaking Infinity + 2 is greater than infinity although I would understand why you wouldn't accept this answer.
∞ + 2 > ∞
Undefined operation

36. The idea is that the limit value of 10^n as n approaches -infinity tends to 0.
That's because you can't really get to infinity. Saying "I got to infinity" is contradicting yourself, because infinity is defined as a point that you cannot reach no matter how much you add and try. Now, in theory, if you could somehow jump to this magical point called infinity (by maybe advancing an infinite amount of steps at once), you would see that yes, it equals zero.

My logic goes as this. If I have a chocolate bar, and I want to divide it to an infinite number of people, the only reasonable quantity I can give to anyone is zero, because if I gave any tangible amount, then it will eventually run out before I can divide it equally to everyone. I can't give them an infinitely small piece because it's the same as zero. 0.00000...001 is not infinitely small. Why? Because the fact that I just ended that number with a 1 contradicts my previous statement that it never ends. And if it never ends, then there can't be a number like that.

My point is, in order for anyone to get some amount, you have to stick that one somewhere, but you can't, because you'll be contradicting yourself.
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37. I can prove that it does in 10 different ways. You can't prove that it doesn't in even 1 way.