# Definition:Transfinite Ordinal

## Definition

Let $\alpha$ be an ordinal.

Then $\alpha$ is said to be transfinite if and only if it is an infinite set.

### Countable Ordinal

Let $\alpha$ be an ordinal.

Then $\alpha$ is said to be countable if and only if it is an countable set.

### Uncountable Ordinal

Let $\alpha$ be an ordinal.

Then $\alpha$ is said to be uncountable if and only if it is an uncountable set.

## Also known as

A transfinite ordinal is also known as an infinite ordinal.