**Unendlichkeit**

**Infinity** (symbol: **∞**) refers to something *without any limit*, and is a concept relevant in a number of fields, predominantly mathematics and physics. The English word *infinity* derives from Latin *infinitas*, 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 (i.e., it counts or measures things: "an infinite number of terms") 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 (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.

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