## anonymous 5 years ago what is limit of sequence...?

1. anonymous

Let $\varepsilon > 0$ be arbitrary. Then $\exists N \in \mathbb{N} : |a_n - l| < \varepsilon \hspace{0.3cm} \forall n > N$ There is a dependence of $\varepsilon$ on $N$ and it's written as $\varepsilon = \varepsilon (N).$ In the above, $a_n$ are just terms of your sequence for $n>N.$

2. anonymous

$l$ being the limit of your sequence. If you are given that $l$ exists for your sequence, then the above is true by definition.

3. anonymous

actually more properly, $N=N(\varepsilon )$ is the dependence as epsilon is arbitrary.