Let (an) be a convergent sequence of real numbers and let A be the set of all its

terms, i.e.A = {a1, a2, . . . , an, . . . }

Does A has a minimum or A has a maximum (or both) ?

Attempt:

Since the series converges A is bounded .Let s=sup A and i = inf A.

if s>a and e>0=>|an-s|<e=>|an|<s+e or |an|>s-e .....this implies that there exist and ak belonging to A such that ak>s-e.By def s= max{a1......an0}=>an=<s and s belongs to A.

The same goes for i=inf A.

Is this correct?