0.999999... = 1?

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

>>180
Of course the real line doesn't include infinitesimals, so 0.999~ = 1 when you're using that, but introducing infinity, infinitesimals, or other weird numbers tends to mess things up, as is the case here. With infinitesimals, 0.999~ < 1.