12 - Countability of Sets

Sets being Finite / Infinite

Let $A$ be a set

1. $A$ is finite if $A=\varnothing$ or there exists $n\in N$ with bijection $f:A\to \{1,\cdots ,n\}$
2. $A$ is infinite if it is not finite

Types of Countability of Sets

Let $A$ be a set then $A$ is

1. Countably infinite if there is a bijection $f:A\to \mathbb{N}$
2. Countable if there is an injection $f:A\to \mathbb{N}$
3. Uncountable if $A$ is not countable