## ::Infinity

### ::concepts

Infinite::**infinity** Number::first Title::numbers Infty::**infinity** Books::space Theory::which

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**Infinity** (symbol: ∞) is an abstract concept describing something *without any limit* and is relevant in a number of fields, predominantly mathematics and physics.
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 natural or 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; see 1/∞.

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).<ref>{{#invoke:citation/CS1|citation |CitationClass=book }}, Extract of page 616 </ref> For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.<ref>{{#invoke:Footnotes|harvard_citation_no_bracket}}</ref>

**Infinity sections**

Intro History Mathematics Physics Logic Computing Arts and cognitive sciences See also Notes References Further reading External links

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