Does a constant function describe convergent sequence?

Does a constant function $f : \mathbb{N} \mapsto \{c\}$ describe a sequence? Also, can that sequence be called convergent?

-

I do not know what you mean by a "function of type $\mathbb N \mapsto {0}$", but I presume you mean the sequence $(a_n)$ given by $a_n=0$ for all $n \in \mathbb N$. Indeed, this is a sequence. Also this sequence converges to the limit $0$. The proof is quite mechanical and easy, but this statement does need a proof. Perhaps you can do it as a exercise.