0.999999... = 1?

What the fuck. Why is that true. They got different numbers in them.

lol at axiomatic proofs.

also, 0.000...1  can exist and not mess with .999~ = 1, it would be lim n->inf 1*10^-n
= 0

so 0.999~ - .000...1 = 0.999...8 = 1
since 0.999...8 = [sum i=1 to inf 9*10^-i] - [lim n->inf 1*10^-n] = 1 - 0 = 1

.999~ = .999...8 = .999...7
you never get any farther from 1 doing that though, since theres still an infinite number of 9's before that non-existent last digit.