Cardinality

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In mathematics, the cardinality of a set means the number of its elements. For example, the set A = {2, 4, 6} contains 3 elements, and therefore A has a cardinality of 3.

Infinite sets[change | change source]

Cardinality is also used for determining the "size" of infinite sets. Although one might first think that all infinite sets are equally large, this is not always true. Infinite sets can be broken down into two types, countable and uncountable.

An infinite set is considered countable if they can be listed without missing any. Examples include the rational numbers, integers, and natural numbers. Such sets have a cardinality that we call \aleph_0 (read as: aleph null, aleph naught or aleph zero). Sets such as the real numbers are not countable. If given any finite or infinite list of real numbers, you can create a number not on that list. The real numbers have a cardinality of c.

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