It's simply a matter of formalism - the author chose to take and used in the definition of continuity.
Hi,
I was reading the proof for the first fundamental theorem in Apostol, and one part of it says the following.
Continuity of at tells us that, if is given, there is a positive such that
whenever
I do not see how must be less than . I do see why it has to be less than though..
Any hints?
Thanks.