Infinity is an abstract mathematical concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics. It really shouldn’t be thought of as number but more of a pattern or behaviour of a set or series numbers.

The English word infinity derives from Latin infinitas, meaning "being without finish", and which can be translated as "unboundedness", itself originating 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).

**Countable vs uncountable infinities**

For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.

**source**: http://en.wikipedia.org/w/index.php?title=Infinity&oldid=611362160

see also **infinities**