Infinity
Infinity is an abstract concept describing something
without any limit and is relevant in a number of fields, predominantly mathematics and physics. The English word
infinity derives from Latin
infinitas, meaning
"being without finish", and which can be translated as "unboundedness", itself calqued from the Greek word
apeiros, meaning "endless". In mathematics, "infinity" is often treated as if it were a number but it is not the same sort of number as the real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number. Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes. For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.