Question

Explanation of an answer: could someone please clarify a few points that an answerer on stack.exchange made? Thanks.

Answer 1

http://math.stackexchange.com/questions/450967/interpretation-of-epsilon-delta-limit-definition#450976

Answer 2

Basically, I can follow the answerer until he says "to ϵ in the definition of continuity at x for a function f...", at which point it just makes less and less sense to me and falls apart. I'm haveing an especially hard time understanding what he means by δ(−).

Answer 3

I'm not sure what the definition of continuity can be applied here, and I don't know what δ(−) is - I looked up modulus of continuity on wikipedia, but it really hurt more than it helped

Answer 4

I'm sure there are better explanations around for understanding epsilon delta limit definition. Try to understand only what is relevant and necessary.

Answer 5

The main issue is that I can't see how this is linked to the non-rigorous intuitive defintion that people give in the basic calculus courses

Answer 6

namely, if delta can increase as epsilon decreases, then how is f(x) converging to some value L?

Answer 7

I found a good explanation for this somewhere, but I can't remember where. Maybe mathwords.com