Question

from: http://math.stackexchange.com/questions/450967/interpretation-of-epsilon-delta-limit-definition
The epsilon-delta definition for limits states that (from Wikipedia) for all real ϵ>0 there exists a real δ>0 such that for all x with 0<|x−c|<δ, we have |f(x)−L|<ϵ - however, the definition of the limit requires only the existence of some δ>0 for any ϵ>0. The part I am having trouble understanding is why there are no details as to the "intuitive" decrease of the δ as ε grows smaller.

I realize that saying that as ε approaches zero δ also approaches zero would use the nonrigorous intuition

Answer 1

of a limit in a definition meant to make the limit a rigorous part of mathematics, but why is it unnecessary to show the relationship between epsilon and delta besides the proof of existence? Is there some other implication of a function that I am missing that is the reason only the proof of existence is in this definition?

calculus limits

Answer 2

oh

Answer 3

actually in some cases, it might not have to

Answer 4

lets say you have the function y = 2

Answer 5

yeah...

Answer 6

with that function delta is always infinity