What are examples of uncountable sets?

Uncountable sets are those that cannot be put into a one-to-one correspondence with the natural numbers. Examples include the set of real numbers, the set of points on a line segment, and the set of all subsets of natural numbers (the power set of natural numbers). These sets have a greater cardinality than countable sets, such as the set of integers or rational numbers. The existence of uncountable sets was famously demonstrated by Cantor's diagonal argument.