Difference between revisions of "Infinity"
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| − | '''[[Infinity]]''' (symbol: <big><big>∞</big></big>) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics. The English word infinity derives from Latin '''infinitas''', which can be translated as "unboundedness", itself calqued from the Greek word apeiros, meaning "'''endless'''". | + | '''[[Infinity]]''' ([[symbol]]: <big><big>∞</big></big>) is an abstract {{Wiki|concept}} describing something without any limit and is relevant in a number of fields, predominantly [[mathematics]] and [[physics]]. The English [[word]] [[infinity]] derives from {{Wiki|Latin}} '''infinitas''', which can be translated as "unboundedness", itself calqued from the {{Wiki|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). For example, the set of integers is countably [[infinite]], while the [[infinite]] set of real numbers is uncountable. | + | 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. {{Wiki|Georg Cantor}} formalized many [[ideas]] related to [[infinity]] and [[infinite]] sets during the late 19th and early 20th centuries. In the {{Wiki|theory}} he developed, there are [[infinite]] sets of different "sizes" (called cardinalities). For example, the set of integers is countably [[infinite]], while the [[infinite]] set of real numbers is uncountable. |
{{W}} | {{W}} | ||
[[Category:Buddhist Terms]] | [[Category:Buddhist Terms]] | ||
Latest revision as of 17:58, 9 December 2015
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics. The English word infinity derives from Latin infinitas, which can be translated as "unboundedness", itself calqued 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). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.
