this is very elemetary, but i'm not following the logic at all. i'm trying to explain to myself after reading the book defn, but still, no luck.(adsbygoogle = window.adsbygoogle || []).push({});

Ok, so the defintion of limit is If Given e > 0, there exists a d > 0 such that if x belongs to A and 0 < |x- c| < d, then |f(x) - L| < e.

here, e = epsilon, and d = delta.

ok, so i'm explaining this to myself as, " if I let e > 0. I can find a delta > 0, that if x is in a, and x - c(with x not = c) is less then delta, then f(x) - L < e.

So when I do a problem, such as "the limit (from x to c) x = c, i'm having trouble how the book solves it.

the book does: let g(x) = x for all x in R. If e > 0, let delta = e. then if 0 < | x-c| <d, then |g(x) - c| = |x - c| < e. since e > 0, it proves it.

===================================

so I try to explain this to myself:

first, the book assigns g(x) = x.

then it goes through the definition. It lets e = d. so now, if 0 < |x - c| < d, then it means |x - c| < e.

so why does that prove it?

I dotn know why I can't get it...I think i'm missing something simple here.

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# Cannot decipher and solve limits help

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