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cardinal number
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finite or infinite number that measures cardinality (size) of sets
A cardinal number tells you how many items are in a group or set—for example, the number 5 is a cardinal number because it describes the size of any collection with five things in it. Cardinal numbers matter because they're a fundamental way we count and compare the sizes of different groups, whether those groups are small (like five apples) or infinitely large (like all the whole numbers).
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A bijective function, f: X → Y, from set X to set Y demonstrates that the sets have the same cardinality, in this case equal to the cardinal number 4.
Aleph-null, the smallest infinite cardinal