In mathematics, cardinality is an intrinsic property of sets, roughly meaning the number of individual objects they contain, which may be infinite. The concept is understood through one-to-one correspondences between sets. That is, if their objects can be paired such that each object has a pair, and no object is paired more than once.
The basic concepts of cardinality go back as early as the 6th century BCE, and there are several close encounters with it throughout history, however, the results were generally dismissed as paradoxical. It is considered to have been first introduced formally to mathematics by Georg Cantor at the turn of the 20th century. Cantor's theory of cardinality was then formalized, popularized, and explored by many influential mathematicians of the time, and has since become a fundamental concept of mathematics.
