# 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?

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## 1 Answer

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.

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Yes, that what I meant by "type" of function (I edited the question to be clearer). The convergence can be proven using the neighboring interval method, I was just curios if this special case had anything more to it. :) – Paul Manta Oct 17 '11 at 11:15