The number of elements in a set, representing the size or count of the collection. For finite sets, cardinality is simply the count of objects; for infinite sets, it describes different 'sizes' of infinity.
From Latin 'cardō' meaning hinge or that on which something turns, suggesting cardinal numbers as the fundamental 'hinge' numbers for counting. The term was formalized by Georg Cantor in the late 19th century during his groundbreaking work on set theory.
Cardinality reveals one of mathematics' most mind-bending discoveries - that some infinities are larger than others! Cantor showed that while the counting numbers and fractions have the same cardinality (both countably infinite), the real numbers have a strictly larger cardinality, revolutionizing our understanding of the infinite.
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