# Uncountable set

set with cardinal number larger than that of the set of all natural numbers

An uncountable set is an infinite set that is impossible to count. If we try to count the elements, we will always skip some. It does not matter what size step we take. The set of real numbers, often written as ${\displaystyle \mathbb {R} }$,[1] is an uncountable set.[2] There are many other uncountable sets, such as the interval ${\displaystyle [0,1]}$.[3] An uncountable set is bigger than an infinite countable set. We know that because Georg Cantor proved it. He showed that any list of numbers is not complete. This is true even if the list is infinite.

## References

1. "Comprehensive List of Set Theory Symbols". Math Vault. 2020-04-11. Retrieved 2020-09-05.
2. Taylor, Courtney (September 8, 2018). "The Most Commonly Encountered Uncountable Sets". ThoughtCo. Retrieved 2020-09-05.`{{cite web}}`: CS1 maint: url-status (link)
3. Nykamp, Duane. "Uncountable definition". Math Insight. Retrieved September 5, 2020.`{{cite web}}`: CS1 maint: url-status (link)