Why do we have this: For $x = o(1)$, $1 - x = \exp(-x-O(x^2))$? I know the idea is from the Taylor's formula, but it sounds weird to me. I would like to know a clear explanation for it?
To be more clear, I know that these two things are asymptotically equal, as a calculus problem, but I like to look at it from the reverse; I mean I want to know how can I create an equality like this? It is not clear here how can we take inside the exponential function the term $O(x^2)$?