Cardinality in mathematics
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Cardinality is a way of measuring how big a collection of objects is. We say that two sets A and B have the same cardinality if you can pair up elements in A with elements in B in such a way that each element in A is paired with exactly on element in B, and each element in B is paired with exactly one element in A (this is called a bijection). For example the set {cat, dog, mouse} and the set {1, 2, 3} have the same cardinality because I can pair up
cat <–> 1
dog <–>2
mouse <–> 3.
Less intuitively, the set of all whole numbers {1, 2, 3, …} and the set of all even whole numbers {2, 4, 6, 8, …} have the same cardinality because I can pair up
1 <–> 2
2 <–> 4
3 <–> 6
…
An important fact about cardinality is that the set of all (real) numbers has a larger cardinality than the set of all whole numbers.
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