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

[BAndrew]

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.

No it doesn't. You have 10x - x which is equal to 9x. You are probably refering to 9n = 9 which is indeed a mistake as we don't know n = 1(that's it if you don't accept that 9,99... - 0,9999 = 9).

See the proof with the limits which is mathematically accepted.