Poll: 0.999... = 1

[Georgie_Leech]

Guys, stop trying to use the intuition of infinity-1=/=infinity. That makes the invalid assumption that infinity has a value.

The entire point of logic and, by extension, the sub-category of mathematics, is to find true information where intuition fails us. Intuition requires us to gain original information using our senses. Our senses cannot comprehend infinity, neither infinitely small nor infinitely large. A disproof requires that the evidence is valid, and it is invalid to use our intuitive conception of infinity as "really large," as we have no evidence that intition is true, but in fact have mathematical evidence showing the opposite, that it has no intrinsic value.

 

[quhouv vhqwiufv qwiu]

It is one. You would round up to the nearest whole number, which is one.

You completely misunderstand what this thread is about.

 

[spinFX]

There is a pretty standard proof for it. I can't remember what it was because I wasn't a math major in college and I had it explained to me once. I found Graham's number more mind blowing that .9999... being equal to one.

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

Every math major I have talked to and showed that to has described that as "shady".

Whenever someone puts that up to me, I point to this shirt:

That one fails because you are dividing by 0. You can break any equation by diving both sides by zero.

 

[Shadowkire]

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

you sir fail at math.

you failed on line 2, when you add or subtract anything from one side of the = you need to do the EXACT same thing to the other side, so it should read from line 2:
Therefore, 10x - x = 9.999... - x
Which implies 9x = 9.999... - x
Now you can't do anything but fill in what you already assumed for x:
9(0.999) = 9.999... - 0.999...
Thus, 9(0.999) = 9

 

[Lyx]

It doesn't matter what kind of zero I'm talking about. If you subtract a number from another number that is not equal to the first, you do not get zero. Infinity does not necessarily equal infinity, so subtracting the two does not get you zero.

Actually, it does matter precisely for that

Infinitely much - infinitely much = 0

That only works for quantities (so, scenarios where the value cannot go below zero).

The reason why this works and results in a clean number, is because we aren't even doing subtraction here.... or rather, we aren't really subtracting numbers.

A practically more "realistic" setup is a program loop like this:

1: n = 0
2: n = n + 1
3: n = n - 1
4: goto 2

There you have it: two infinity-routines battling each other, and no matter at which iteration you stop it, the return is zero.

 

[Rabid Toilet]

Yeah, I think I was tired and thought he had started with something like 1 = .99...

That would be illegal.

Well, actually...

If you start with a statement you assume to be false, you can prove it to be false via Proof by Contradiction. You can't prove anything to be true by starting with a false statement, but you can disprove the original statement by running the proof until you hit a contradiction.

It's called reductio ad absurdum and is definitely legal and quite useful.

You're right, you can start with something like 1 = 2, add 1 to both sides (which should result in a true statement if the original statement was true), and get 2 = 3, which is false. Thus, the first statement must also be false.

I meant that you can't use that in a proof that tries to prove that something is true to begin with.

Edit:
Actually no, I take that back. You could multiply both sides by zero and get a true statement. I dunno, I don't know all of the complicated rules about proofs.

Double Edit:
No wait, you can prove that something is false, but can't prove something is true. I think that's it?

Gah, I never should have posted anything about proof logic in the first place.

 

[Troublesome Lagomorph]

It is one. You would round up to the nearest whole number, which is one.

You completely misunderstand what this thread is about.

I most likely have.

 

[Rabid Toilet]

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

you sir fail at math.

you failed on line 2, when you add or subtract anything from one side of the = you need to do the EXACT same thing to the other side, so it should read from line 2:
Therefore, 10x - x = 9.999... - x
Which implies 9x = 9.999... - x
Now you can't do anything but fill in what you already assumed for x:
9(0.999) = 9.999... - 0.999...
Thus, 9(0.999) = 9

I'm afraid his math is quite sound. He is doing the exact same thing to each side. From the left side, he subtracts x, and from the right side, he subtracts .99...

Since x = .99..., he is doing the exact same thing to both sides.

 

[Lyx]

It is one. You would round up to the nearest whole number, which is one.

You completely misunderstand what this thread is about.

I most likely have.

The original argument was, that both are equal *without* rounding.

 

[havass]

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

you sir fail at math.

you failed on line 2, when you add or subtract anything from one side of the = you need to do the EXACT same thing to the other side, so it should read from line 2:
Therefore, 10x - x = 9.999... - x
Which implies 9x = 9.999... - x
Now you can't do anything but fill in what you already assumed for x:
9(0.999) = 9.999... - 0.999...
Thus, 9(0.999) = 9

So continuing from your line,
9(0.999) = 9
divide both sides by 9, and you get:
0.999 = 1.

Yes?

 

[emeraldrafael]

Snip

actually 9(.999) = 8.991 rounded, thats 9, but as Lyx says here:

It is one. You would round up to the nearest whole number, which is one.

You completely misunderstand what this thread is about.

I most likely have.

The original argument was, that both are equal *without* rounding.

This is a thread about not rounding.

 

[emeraldrafael]

Snip

I think what they are getting at is yes, it does wind down to equaling .999=1 but .999=/=1 as they are two separate numbers.

 

[tthor]

Whenever someone puts that up to me, I point to this shirt:

Spoiler

It's funny because that shirt divided by 0.

Actually, it didn't :-/ That proof works.

The shirt divides both sides by (a - b). Because a = b, (a - b) = 0. Thus, the proof is invalid.

are you refering to canceling out (a - b) by dividing both sides by it? so, (a - b) / (a - b), and (a - b) = 0, so it would be 0 / 0, or simplified, 0, which is a mathematically correct term

What? 0/0 is not 0. It's not anything, because it divides by zero, and allowing division by zero produces contradictions like the one shown on the shirt.

upon rethinking that, ya, i think you're right

 

[SleeperAwake]

The human mind can only understand something so much larger then it self, as such only an infinite mind could ever hope to understand infinity. So we have to think that 0.9999999999...=1 but in "true math" it isn't.

 

[Rabid Toilet]

Snip

actually 9(.999) = 8.991 rounded, thats 9

I assumed that he meant to write .999..., rather than just .999.

 

[Naheal]

There is a pretty standard proof for it. I can't remember what it was because I wasn't a math major in college and I had it explained to me once. I found Graham's number more mind blowing that .9999... being equal to one.

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

Every math major I have talked to and showed that to has described that as "shady".

Whenever someone puts that up to me, I point to this shirt:

That one fails because you are dividing by 0. You can break any equation by diving both sides by zero.

Thus the caption "Don't drink and derive".

 

[Shadowkire]

THE PROOF

you sir fail at math.

you failed on line 2, when you add or subtract anything from one side of the = you need to do the EXACT same thing to the other side, so it should read from line 2:
Therefore, 10x - x = 9.999... - x
Which implies 9x = 9.999... - x
Now you can't do anything but fill in what you already assumed for x:
9(0.999) = 9.999... - 0.999...
Thus, 9(0.999) = 9

So continuing from your line,
9(0.999) = 9
divide both sides by 9, and you get:
0.999 = 1.

Yes?

LOL, I totally didn't realize that, you are correct in that it DOES NOT MATTER:
x = 0.999... is an assumption, one that requires proof, the fact that the proof ends as 0.999... = 1 means that the assumption is wrong

 

[havass]

Snip

I think what they are getting at is yes, it does wind down to equaling .999=1 but .999=/=1 as they are two separate numbers.

Ah, but I haven't stated whether I think they equal or not. I only proved it. I don't put my faith in the proof, but every step seems logical enough on the basic level.

 

[tthor]

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

I prefer:

b0.b1b2b3b4... = b0 + b1(1/10) + b2(1/10)^2 + b3(1/10)^3 + b4(1/10)^4 ...

if |r| < 1 then kr + kr^2 + kr^3 + ... = kr/(1-r)

So for 0.9...:

0.(9) = 9(1/10) + 9(1/10)^2 + 9(1/10)^3 + ... = (9(1/10))/(1-(1/10)) = 1

... you know what, I'm just gonna chalk this down to <link=http://en.wikipedia.org/wiki/Proof_by_intimidation>Proof by intimidation (cause this just confuses me)

tho that looks kinda like some of the proofs in <link=http://en.wikipedia.org/wiki/Invalid_proof>Mathematical fallacy, but i'm to lazy to dissect that whole equation just to tell you that 1 doesn't equal .999999

 

[havass]

THE PROOF

you sir fail at math.

you failed on line 2, when you add or subtract anything from one side of the = you need to do the EXACT same thing to the other side, so it should read from line 2:
Therefore, 10x - x = 9.999... - x
Which implies 9x = 9.999... - x
Now you can't do anything but fill in what you already assumed for x:
9(0.999) = 9.999... - 0.999...
Thus, 9(0.999) = 9

So continuing from your line,
9(0.999) = 9
divide both sides by 9, and you get:
0.999 = 1.

Yes?

LOL, I totally didn't realize that, you are correct in that it DOES NOT MATTER:
x = 0.999... is an assumption, one that requires proof, the fact that the proof ends as 0.999... = 1 means that the assumption is wrong

Actually, I have no faith in that proof. I was just getting you back for saying I failed at math. I couldn't care less if 0.99999.... = 1, the difference is so inconsequential that the only problem you'll have is when dealing with log functions. And even then it's still a very small difference.