Uncountable set

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In mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than aleph-null, the cardinality of the natural numbers.

Examples of uncountable sets include the set ⁠${\displaystyle \mathbb {R} }$⁠ of all real numbers and set of all subsets of the natural numbers.