No it doesnt depend on representation. 2/3=.6666... the equals sign means that whatever is true with oneis true with the other since they are equal. Just because one representation makes more sense doesn't mean the other one is invalid

You cannot apply this so easily. The 'proof' you showed made the error, that the case differentiation in step 5 for divisions wasn't made. You always have to cover for the case, that you divide by zero. So step 6 and 7 are only allowed for the case A != B. But the initial statement was A=B.

That cannot be applied to the first though. The only division that is made is, that something is divided by 3. We know 3 is not equal to zero.

I keep claiming that multiplying 0.111... with 9 is 1 and not 0.999..., as the a carry from infinity brings the sum up. But it doesn't matter. If we say it calculates to 0.999... it is in any case equal to 1. It is just another representation, as 1.0, 1.00, 1.000, 1/1, 10/10 and so on. A misleading representation, that's why I prefer to say it is an error.

This thread is funny.

Mentioned in this thread before:
"1) A = B First statement
2) A^2 = AB Multiply both sides by A
3) A^2-B^2=AB-B^2 Subtract B^2 from both sides
4) (A+B)(A-B)=B(A-B) Factor both sides
5) A+B=B Divide both sides by (A-B)
6) 2B=B Since A=B we can replace A with B
7) 2=1 Divide both sides by B"

Why are we dividing by B at the end? I would have taken B off. so B=0, A=B so A = 0.

No, I'm making a different point here. That, a proof that looks like it 'makes sense' may actually be wrong if you don't know or realise all of the rules. I don't know enough maths to construct the reals from first principles and prove this, but I believe the words of those who can. Nothing in this thread so far is adequate proof.

That's also invalid; everything after step 5 is nonsense.

I got that just by reading it/your explanation earlier. I just find it funny. Like why are they minusing B^2? It's like a string of letters thrown together just to prove something is valid when it isn't.

There's nothing wrong with subtracting B^2 from both sides.  In mathematics, the route to proving something is often far from obvious.  You make it sound like they should only be following one set path, which is just as silly.

There are many reasons why I can say that .999... does not equal 1 and why every proof I've seen does not work.
If 0.999... is equal to 1, you acknowledge that you do not understand infinity because it is a concept, not a number. 0.999 and any number that "approaches" a value but never reaches it is infinite and is not an actual number.
You can always add another 9 to the list, yes. However, it never stops. It keeps going, but it never reaches 1 either.

I can disprove the geometric series argument, the 1/3 and the 9/9's argument. The geometric series argument is disproved by the fact that if you try representing the series visually, you can actually see that there will always be a space that is not taken up with each new set. In just pure math, that space will continue to get smaller and smaller, but will always exist as well.
Now for the 1/3 and 9/9's argument, you would have to redefine the way we count our decimals.
If we only counted to 2 before going to the next place, you can represent 1/3 as 0.1
If we only counted to 8 before going to the next place, you can represent 1/9 as 0.1
then 3/3 = 1 and 9/9 = 1.
With .999... as it is gathered from infinite series, for the first example it would be written as 0.222...
and for the second it would be written as 0.888...
Due to that fact, you can see why those arguments do not work. 0.999... will still be represented as an infinitely continuing decimal, no matter how you put it. Because it represents a concept of something that continually gets closer to 1 and never does.

I don't know how clearly I am presenting this, but I know that 0.999... does not equal 1.
It is also impossible to visualize 0.999... just as it is impossible for you to visualize infinity. It is as good as 1 in that regard, but in the end they are still different things.

This thread is really getting on my nerves. People who don't understand mathematics are trying to argue about mathematics.

It's simple, really. The decimal system is flawed in the sense that one number can have to different decimal expressions. A number isn't how it's expressed in the decimal system, a number is something else. The decimal expression is just one way to express a number. As for those arguments that are trying to be logical or trust intuition: Forget it, you're doing it wrong. Intuition goes right out of the window when you're dealing with limits and infinities. 0.999... and 1 are different only in their printed form but mathematically, they are exactly the same number.