# Uncountable Sets

Learn about uncountable sets and Cantor’s diagonalization method.

## What is an uncountable set?

A set that is not countable is called an **uncountable** set. To establish that a set

As our first example, we will show that a set of real numbers is uncountable. For that, **Cantor’s diagonalization method** is a powerful argument—developed by Georg Cantor—to show the nonexistence of a bijection between a set of positive integers and a set of real numbers. This technique has applications in many areas of science and philosophy.

### A set of real numbers

In this section, we will prove that a set of real numbers

Get hands-on with 1200+ tech skills courses.