Cardinality
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Cardinality is a measure of the size of a set. For finite sets, its cardinality is simply the number of elements in it. In general, two sets have the same cardinality if there is a bijection between them. That is, the elements of one set can be put into one-to-one correspondence with those of the other.
For example, the set of even numbers, and the set of all multiples of 3 is the same, as they can be put into one-to-one correspondence as follows: 2:3,4:6,6:9,8:12,10:15,..2n:3n...
Both sets are countable, as they have the same cardinality as the set of natural numbers (0,1,2...).