A real sequence is a function whose domain is the set of positive integers and range is a subset of the set of real numbers, i.e.,
Let , then is a sequence in .
Limit of Sequence:
We say that a sequence of real numbers converges to a real number if for every there is an such that i.e., a sequence converges at all it has to converge to a unique real number which we call its limit, we express this by
where the symbol stands for approaches or tends to.
If and then,