That's what comes of trying to translate maths into English. When I say 'for any number, epsilon', read 'for every number, epsilon'.

But since I've been obliged to repost, I'll take the chance to explain a little more. '1', '0.999 recurring', etc, are not, strictly speaking, numbers, but representations of numbers. Every (rational) number has lots of different representations: In fractional notation we could have 1/2, 2/4, 3/6 and so on, all representing the same number. We are used to that, so we are taught in schools to always use the simplest form, but all the others are equally valid. And it is the same in decimal notation: every rational number has two representations, and we always pick the simplest. So we normally write 0.5 rather than 0.499999recurring, but both represent exactly the same number in the way 1/2, 2/4 do.