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

[Your Computer]

We are talking about infinitely small numbers, which have to have their "last" digit as 1. My point is that the infinite number of zeroes never reach that point. Therefore, infinitely small.

Then any value with "..." is self-invalidated. If you can never reach 01 in 0.00...01 or 9 in 0.99...9, then you can never subtract from it, never add to it, etc. To say that i can is an assumption without evidence--or, more precisely, an assumption contrary to contrary evidence.

We are not talking about measurably small numbers, so "..." does not equal a finite number of places in this case. If "..." were a finite number of places then I would agree. But it isn't.

Would you say 1 is measurable? If so, then you are claiming that a measurable number equals a non-measurable number.

I'm not really sure what I did that put a stick up your ass, but whatever it is probably isn't relevant to the discussion.

Words on paper have no emotion, neither do words on a screen.

So while it seems counter intuitive. It is mathematically solid.

It's not just counter-intuitive, it's illogical.

Look at the following example:

Line 1: n = .99~
Line 2: 10n = 9.99~
Line 3: 10n-n = 9n
Line 4: 9n = 9
Line 5: n = 1

In order for line 3 to lead to line 4 i would have to assume that n is equal to 1. However, line 1 shows that it is equal to 0.99~. Likewise, evidence that n is equal to 1 has not yet been shown. In other words, i have to commit multiple logical fallacies to reach line 5. Of course, if we were to have divided 10 from 10n, therefore making n = .99~, we'd be back at line 1. Likewise, therefore, i would have proven that n cannot be anything but 0.99~, therefore 0.99~ can never equal 1.