Countable set

We can call a set $A$ countable if it is either finite or there is a [[Bijection (function)|bijection]] between $A$ and $\mathbb N$.

For example:

• ${\text{id}}_N:\mathbb{N}\to \mathbb{N}$ is a bijection hence $N$ is countable.
• Given Odd is the set of odd natural numbers, we find that even if $\text{Odd}\subset \mathbb{N}$, it still has the same size as $\mathbb{N}$. The function $f:\mathbb{N}\to \text{Odd}$ defined by $\boxed{f(x)=2x+1}$ is a bijection.