# Uncountability

Sizes of infinity fall into two broad classes: *countable* infinities, and *uncountable* infinities.

A set \(S\) is *uncountable* if it is not countable.

Children:

- Uncountability: Intro (Math 1)
Not all infinities are created equal. The infinity of real numbers is infinitely larger than the infinity of counting numbers.

- Uncountability: Intuitive Intro
Are all sizes of infinity the same? What does “the same” even mean here?

- Uncountability (Math 3)
Formal definition of uncountability, and foundational considerations.

- Real numbers are uncountable
The real numbers are uncountable.

Parents:

- Mathematics
Mathematics is the study of numbers and other ideal objects that can be described by axioms.