Corollary: Difference between revisions
Copyedit |
No edit summary |
||
| Line 1: | Line 1: | ||
{{wiktionary}} |
{{wiktionary}} |
||
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. Sometimes a corollary has a proof that explains the derivation; sometimes the derivation is considered to be self-evident. |
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 of B if its mathematical consequences are as significant as B's. Sometimes a corollary has a proof that explains the derivation; sometimes the derivation is considered to be self-evident. |
||
[[Category:Mathematical terminology]] |
[[Category:Mathematical terminology]] |
||
Revision as of 04:04, 13 October 2007
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 of B if its mathematical consequences are as significant as B's. Sometimes a corollary has a proof that explains the derivation; sometimes the derivation is considered to be self-evident.
 | This mathematics-related article is a stub. You can help Wikipedia by expanding it. |