*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

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## Infinity

Few concepts in mathematics are more fascinating or confounding than infinity. While mathematicians have a longstanding disagreement over its very definition, one can start with the notion that infinity (denoted by the symbol ∞) is an unbounded number greater than all real numbers.

Writing about infinity dates back to at least the Greek philosopher Aristotle (384 B.C.E.–322 B.C.E.). He stated that infinities come in two varieties; actual infinities (of which he could find no examples) and potential infinities, which he taught were legitimate only as thought. Indeed, the German Karl Gauss (1777–1855) once scolded a fellow mathematician for using the concept, stating that use of infinity "is never permitted in mathematics."

The French mathematician and philosopher René Descartes (1595–1650) proposed that because "finite humans" are incapable of producing the concept of infinity, it must come to us by way of an...

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