1 = 0,99........

[BAndrew]

It's totally irrelevant though. No computer is capable of computing infinitesimals so 1 - 0.9~ on any calculator will always be 1 x 10^-∞. Personally it makes my brain hurt so I have a hard time accepting it.

A calculator is a computer. I realize it is legit on paper but it is simply not practical. Almost all big calculations are handled by computers. You probably already know this, but there is no such thing as infinite memory. The number infinity has no calculable value and the value of 0.9~ requires an infinitesimal to precisely calculate and by definition computers need measurable data to calculate. Therefore neither of these operations are possible to truly calculate on computers. You always need to approximate, and with approximation comes a loss of data.

EDIT: I'm not saying I don't believe it, I just question its usefulness and whether or not the two numbers should be equal. When quantum computers become a reality we will most likely be able to precisely calculate the distance between 0.9~ and 1, because there is one, no matter how small, and the numbers will cease to be equal.

A computer is not the same as a calculator.

A computer can't calculate infinite numbers, but it can calculate the result of infinite series with limits. It doesn't calculate every number as it goes into infinity, as you don't when you are solving something with limits. You don't count into infinity. You use some properties. That's what the computer can do.

This should change your mind:

http://www.wolframalpha.com/input/?i=lim...lk=4&num=1

How did it calculate it if a computer can't?

There is no distance between 0,9~ and 1. If there is it is infinitely small which doesn't make sense. The numbers are the same.