>You'll see people say things like "0.999... approaches 1"; This is somewhat correct. At least it is the correct way to think. A real number is an equivalence

>You'll see people say things like "0.999... approaches 1"; This is somewhat correct. At least it is the correct way to think. A real number is an equivalence class of cauchy series. 0.999... is one representative of 1, as it is shorthand for the Cauchy series (0.9,0.99,0.999,...).