I'm trying to do some revision for my analysis exam and when it comes to proofs whereε is usedI dont understand what these proofs mean.

Like for example

Given $\displaystyle \epsilon > 0, \forall n \in N: \left|{x_n - l}\right| < \epsilon$

which is something to do with the limit of the sequence xn being l

why not use

$\displaystyle \left|{x_n - l}\right| = 0$?

(Headbang) analysis just makes no sense D: