I had to learn the epsilon-delta definition before I really understood limits. As far as insanely small goes, as you must know, the definition is equivalent to

I had to learn the epsilon-delta definition before I really understood limits. As far as insanely small goes, as you must know, the definition is equivalent to "for every epsilon < M, there exists a delta >0, ..." where M is some positive constant (it could be 1 or 1/10^100...). Sometimes it helps to play with the quantifiers...