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− | [[Image:lighterstill.jpg]] | + | [[Image:lighterstill.jpg]][[Image:Infinity.jpg|right|frame]] |
− | [[Image:Infinitysymbol.jpg|right]] | + | |
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| 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]]. |
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| 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]]. |
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| + | <center>For lessons on the [[topic]] of '''''Infinity''''', follow [https://nordan.daynal.org/wiki/index.php?title=Category:Infinity '''''this link'''''].</center> |
| === Logic === | | === Logic === |
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| 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]]. |
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| === Infinity symbol === | | === Infinity symbol === |
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| [[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> |
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| 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. |