# Thread: Nondenumberable

1. ## Nondenumberable

I have to prove that $\mathbb{N}^\mathbb{N}$is denumberable; hence, if I understood it right, The set of all mappings from $\mathbb{N}$ to $\mathbb{N}$..

We worked with these 0,1 tables, which I can work with if I get a mapping, but not if it should work for all mappings.

Could you help me?

2. Originally Posted by Frings
I have to prove that $\mathbb{N}^\mathbb{N}$is denumberable; hence, if I understood it right, The set of all mappings from $\mathbb{N}$ to $\mathbb{N}$..
We worked with these 0,1 tables, which I can work with if I get a mapping, but not if it should work for all mappings.
I am not sure that I understand.
But is this it? You have shown that $2^{\mathbb{N}}$, the set of all mappings $f:\mathbb{N}\mapsto\{0,1\}$, is uncountable?

But this question follows from $2^{\mathbb{N}}\subset \mathbb{N}^{\mathbb{N}}$.