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

[Bridge]

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.

1) Look dude, calculators are not magical devices that were just discovered. A calculator is just a small computer that performs only mathematical operations. It has a microprocessor just like a computer, some memory where it can store numbers, a simple means of drawing graphics and a keyboard through which you can input data. That's a fact (look it up!). There is absolutely no difference between computers and calculators other than the fact that dedicated calculators specialize only in mathematics.

2) Well of course! That's basically what I just said. The number infinity is uncountable and therefore cannot be used by a computer at all. Did you even read my post? Memory is finite, and numbers take up a determinable amount of space in memory. If you were truly using infinity, it would take up an infinite amount of bytes, which would mean your memory chips would be larger than the universe. You always need to approximate (you don't think programmers actually type in all of the 500.000 some decimal places Pi has when defining it, do you?).

3) Infinitely small, not non-existent. Computers cannot at the moment calculate infinitesimals but there is a distinct possibility that quantum computers will be able to (since they are millions of times more powerful than the most powerful supercomputer in existence). I don't have any proof, but some day it may be revealed that there does exist a number between 0.9~ and 1. You do realize that at some point people did not believe there were any numbers between 0 and 1. The laws of science and mathematics are volatile.

Now please read my post carefully before responding.