[split] 0.999... equals 1

[Tiberius]

0.999... can be reduced to the following infinitely long series:

0.9 + 0.09 + 0.009 + 0.0009 ...

This can be further reduced to:

0.9 + (0.9 * 0.1) + (0.9 * 0.1 * 0.1) + (0.9 * 0.1 * 0.1 * 0.1) ...

This series follows the general pattern of infinite series, and so we can use the infinite sum formula to work out the total:

Total = a / (1 - r)

a being 0.9
r being 0.1

So, the sum of the infinite series obtained from breaking down 0.999... is:

0.999... = 0.9 / 1 - 0.1
0.999... = 0.9 / 0.9
0.999... = 1

Q. E. fuckin' D. bitches. (again)