Corollary: Difference between revisions
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A '''corollary''' is a statement which follows readily from a previously proven statement. In [[mathematics]] a corollary typically follows a [[theorem]]. The use of the term ''corollary'', rather than ''proposition'' or ''theorem'', is intrinsically subjective. Proposition ''B'' is a corollary of proposition ''A'' if ''B'' can readily be deduced from ''A'', but the meaning of ''readily'' varies depending upon the author and context. The importance of the corollary is often considered secondary to that of the initial theorem; ''B'' is unlikely to be termed a corollary if its mathematical consequences are as significant as those of ''A''. Sometimes a corollary has a proof that explains the derivation; sometimes the derivation is considered to be self-evident. |
A '''corollary''' is a statement which follows readily from a previously proven statement. In [[mathematics]] a corollary typically follows a [[theorem]]. The use of the term ''corollary'', rather than ''proposition'' or ''theorem'', is intrinsically subjective. Proposition ''B'' is a corollary of proposition ''A'' if ''B'' can readily be deduced from ''A'', but the meaning of ''readily'' varies depending upon the author and context. The importance of the corollary is often considered secondary to that of the initial theorem; ''B'' is unlikely to be termed a corollary if its mathematical consequences are as significant as those of ''A''. Sometimes a corollary has a proof that explains the derivation; sometimes the derivation is considered to be self-evident. |
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Corollaries have also been proposed or constructed to add to laws. Examples include the Fourth Law that Clarke has added to his previous three. |
Corollaries have also been proposed or constructed to add to laws. Examples include the Fourth Law that Clarke has added to his previous three.{{clarifyme}} |
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==See also== |
==See also== |
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*[[Lemma (mathematics)|Lemma]] |
* [[Lemma (mathematics)|Lemma]] |
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[[Category:Mathematical terminology]] |
[[Category:Mathematical terminology]] |
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Revision as of 00:25, 11 September 2008
A corollary is a statement which follows readily from a previously proven statement. In mathematics a corollary typically follows a theorem. The use of the term corollary, rather than proposition or theorem, is intrinsically subjective. Proposition B is a corollary of proposition A if B can readily be deduced from A, but the meaning of readily varies depending upon the author and context. The importance of the corollary is often considered secondary to that of the initial theorem; B is unlikely to be termed a corollary if its mathematical consequences are as significant as those of A. Sometimes a corollary has a proof that explains the derivation; sometimes the derivation is considered to be self-evident.
Corollaries have also been proposed or constructed to add to laws. Examples include the Fourth Law that Clarke has added to his previous three.[clarification needed]
See also
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