Actual and Potential Infinity

In the philosophy of mathematics, actual infinity, also called completed infinity, treats infinite entities as given, actual and completed objects, in contrast to potential infinity, where an endless process such as repeatedly adding one to a number produces a sequence with no last element and every individual result is still finite and reached in finitely many steps. Potential infinity is the kind of infinity built into standard formalizations of mathematical induction, infinite series, infinite products and limits. Actual infinity entered mathematics near the end of the nineteenth century through Georg Cantor's theory of infinite sets, later formalized into Zermelo-Fraenkel set theory, which contains the axiom of infinity asserting that the natural numbers form a set, and Cantor's further discovery that infinite sets themselves come in different sizes, with the cardinality of the real numbers strictly larger than that of the natural numbers. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/