if the sequence is finite, then if it converges to some real number that will be in the set..
For this we have to add if limit exists!
We can take 1,1,1,1,.... sequence which has a finite set of 1. Thus its limit is 1 or say seq. converges to 1. This satisfies the a) condition but for the formal proof should I use the definition of countability of sets ? Can you help me out with this ?