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In [[mathematics]], <!-- NOTE: '''corollary''' has meanings outside mathematics --> a '''corollary''' is a statement which follows readily from a previously proven statement, typically a mathematical [[theorem]]. The use of the term ''corollary'', rather than ''proposition'' or ''theorem'', is essentially subjective. Proposition ''A'' is a corollary of proposition ''B'' if ''A'' can readily be deduced from ''B'', but the meaning of ''readily'' varies depending upon the author and context. Often the importance of the corollary is considered secondary to that of the initial theorem; ''A'' is unlikely to be termed a corollary |
In [[mathematics]], <!-- NOTE: '''corollary''' has meanings outside mathematics --> a '''corollary''' is a statement which follows readily from a previously proven statement, typically a mathematical [[theorem]]. The use of the term ''corollary'', rather than ''proposition'' or ''theorem'', is essentially subjective. Proposition ''A'' is a corollary of proposition ''B'' if ''A'' can readily be deduced from ''B'', but the meaning of ''readily'' varies depending upon the author and context. Often the importance of the corollary is considered secondary to that of the initial theorem; ''A'' is unlikely to be termed a corollary if its mathematical consequences are as significant as those of ''B''. Sometimes a corollary has a proof that explains the derivation; sometimes the derivation is considered to be self-evident. |
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[[Category:Mathematical terminology]] |
[[Category:Mathematical terminology]] |
Revision as of 04:05, 13 October 2007
Look up corollary in Wiktionary, the free dictionary.
In mathematics, a corollary is a statement which follows readily from a previously proven statement, typically a mathematical theorem. The use of the term corollary, rather than proposition or theorem, is essentially subjective. Proposition A is a corollary of proposition B if A can readily be deduced from B, but the meaning of readily varies depending upon the author and context. Often the importance of the corollary is considered secondary to that of the initial theorem; A is unlikely to be termed a corollary if its mathematical consequences are as significant as those of B. Sometimes a corollary has a proof that explains the derivation; sometimes the derivation is considered to be self-evident.