Hi I'm just starting to learn some analysis and I am wondering if when proving convergences of sequences, where a represents terms of the sequence, and L is the limit, is it sufficient to say:
∀ε> 0 ∃N ∈ Natural Numbers, such that ∀n ⩾ N, |a − L| < 2ε (rather than |a − L| < ε)?
Not sure if this is a stupid question, thanks.