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[[Image:Infinity2_2_2.jpg |right|thumb|"geometric tiling"]]

 

The word '''infinity''' comes from the [[Latin]] ''infinitas'' or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end") which arise in [[philosophy]], [[mathematics]], and [[theology]].

The word '''infinity''' comes from the [[Latin]] ''infinitas'' or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end") which arise in [[philosophy]], [[mathematics]], and [[theology]].

In [[mathematics]], "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" than the [[real numbers]].  Infinity is related to [[limit (mathematics)|limit]]s, [[aleph number]]s, [[class (set theory)|class]]es in [[set theory]], [[Dedekind-infinite set]]s, [[large cardinal]]s,Large cardinals are quantitative infinities defining the number of things in a [[Set|collection]], which are so large that they cannot be proven to exist in the ordinary mathematics of [[ZFC|Zermelo-Fraenkel plus Choice]] (ZFC).[[Russell's paradox]], [[non-standard arithmetic]], [[hyperreal number]]s, [[projective geometry]], [[Affinely extended real number system|extended real number]]s and the [[absolute Infinite]].

In [[mathematics]], "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" than the [[real numbers]].  Infinity is related to [[limit (mathematics)|limit]]s, [[aleph number]]s, [[class (set theory)|class]]es in [[set theory]], [[Dedekind-infinite set]]s, [[large cardinal]]s,Large cardinals are quantitative infinities defining the number of things in a [[Set|collection]], which are so large that they cannot be proven to exist in the ordinary mathematics of [[ZFC|Zermelo-Fraenkel plus Choice]] (ZFC).[[Russell's paradox]], [[non-standard arithmetic]], [[hyperreal number]]s, [[projective geometry]], [[Affinely extended real number system|extended real number]]s and the [[absolute Infinite]].

=== Logic ===

=== Logic ===

In [[mathematics]], "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" than the [[real numbers]].  Infinity is related to [[limit (mathematics)|limit]]s, [[aleph number]]s, [[class (set theory)|class]]es in [[set theory]], [[Dedekind-infinite set]]s, [[large cardinal]]s,<ref>Large cardinals are quantitative infinities defining the number of things in a [[Set|collection]], which are so large that they cannot be proven to exist in the ordinary mathematics of [[ZFC|Zermelo-Fraenkel plus Choice]] (ZFC).</ref> [[Russell's paradox]], [[non-standard arithmetic]], [[hyperreal number]]s, [[projective geometry]], [[Affinely extended real number system|extended real number]]s and the [[absolute Infinite]].

In [[mathematics]], "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" than the [[real numbers]].  Infinity is related to [[limit (mathematics)|limit]]s, [[aleph number]]s, [[class (set theory)|class]]es in [[set theory]], [[Dedekind-infinite set]]s, [[large cardinal]]s,<ref>Large cardinals are quantitative infinities defining the number of things in a [[Set|collection]], which are so large that they cannot be proven to exist in the ordinary mathematics of [[ZFC|Zermelo-Fraenkel plus Choice]] (ZFC).</ref> [[Russell's paradox]], [[non-standard arithmetic]], [[hyperreal number]]s, [[projective geometry]], [[Affinely extended real number system|extended real number]]s and the [[absolute Infinite]].

=== Infinity symbol ===

=== Infinity symbol ===

[[John Wallis]] is usually credited with introducing ∞ as a symbol for infinity in [[1655]] in

[[John Wallis]] is usually credited with introducing ∞ as a symbol for infinity in [[1655]] in

his ''De sectionibus conicis''. One conjecture about why he chose this symbol is that he derived it from a [[Roman numeral]] for 1000 that was in turn derived from the [[Etruscan numerals|Etruscan numeral]] for 1000, which looked somewhat like <font face="Arial Unicode MS, Lucida Sans Unicode">CIƆ</font> and was sometimes used to mean "many." Another conjecture is that he derived it from the Greek letter ω ([[omega]]), the last letter in the [[Greek alphabet]].<ref>[http://www.roma.unisa.edu.au/07305/symbols.htm#Infinity The History of Mathematical Symbols], By Douglas Weaver, Mathematics Coordinator, Taperoo High School with the assistance of Anthony D. Smith, Computing Studies teacher, Taperoo High School.</ref>

his ''De sectionibus conicis''. One conjecture about why he chose this symbol is that he derived it from a [[Roman numeral]] for 1000 that was in turn derived from the [[Etruscan numerals|Etruscan numeral]] for 1000, which looked somewhat like <font face="Arial Unicode MS, Lucida Sans Unicode">CIƆ</font> and was sometimes used to mean "many." Another conjecture is that he derived it from the Greek letter ω ([[omega]]), the last letter in the [[Greek alphabet]].<ref>[https://www.roma.unisa.edu.au/07305/symbols.htm#Infinity The History of Mathematical Symbols], By Douglas Weaver, Mathematics Coordinator, Taperoo High School with the assistance of Anthony D. Smith, Computing Studies teacher, Taperoo High School.</ref>

Another possibility is that the symbol was chosen because it was easy to rotate an "8" character by 90° when [[typesetting]] was done by hand.  The symbol is sometimes called a "lazy eight", evoking the image of an "8" lying on its side.

Another possibility is that the symbol was chosen because it was easy to rotate an "8" character by 90° when [[typesetting]] was done by hand.  The symbol is sometimes called a "lazy eight", evoking the image of an "8" lying on its side.