Which statement best defines a mathematical sequence?

A function whose domain is the set of positive integers $\{1,2,3,\cdots \}$ and whose output is the term $a_n$.

A function whose domain is the set of all real numbers $(-\infty ,\infty )$ and whose output is a term $a_n$.

A relation where the order of elements is not fixed and terms are not indexed by integers.

A mapping where each term $a_n$ must be an integer, regardless of the input $n$.