Prove $\mid\mathbb{N}\mid \leq \, \mid \mathbb{N}^{\mathbb{N}} \mid$

Question

I need to prove that $$\mid\mathbb{N}\mid \leq \, \mid \mathbb{N}^{\mathbb{N}} \mid$$

I assume that I need to show that there is function $ f: \mathbb{N} \rightarrow \mathbb{N}^{\mathbb{N}}$ which is one-to-one , But I couln't find one.. :\

Can you find such function ? or maybe a different way to prove this ? Thanks.

Answer 1

There are many choices, but one simple one is: $$ f(n)=(n,n,n,\dots)$$ That is, map each natural number $n$ to the sequence in which every term is $n$.