Chapter 11.1, Problem 71E

To determine

With explanation,which of the below two statements is equivalent to the assertion $\underset{n\to \infty }{\lim }{a}_n=L$

(a) For every $\epsilon >0$, the interval $(L-\epsilon ,L+\epsilon )$ contains at least one element of the sequence $\left\{a_n\right\}$

(b) For every $\epsilon >0$, the interval $(L-\epsilon ,L+\epsilon )$ contains all but at most finitely many elements of the sequence $\left\{a_n\right\}$