Proof (mathematics): Difference between revisions
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imported>Peter Schmitt (a modest start for a dificult topic) |
imported>Pat Palmer (adding links) |
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In [[mathematics]], a '''proof''' of a statement | In [[mathematics]], a '''proof''' of a statement | ||
(called theorem, proposition, lemma, etc. according to the context and its importance) | (called [[theorem]], [[proposition]], [[lemma]], etc. according to the context and its importance) | ||
is a series of arguments which show that the assumptions of the statement imply its conclusion. | is a series of arguments which show that the assumptions of the statement imply its conclusion. | ||
Besides the assumptions listed explicitely in the statement to be proven, | Besides the assumptions listed explicitely in the statement to be proven, | ||
the arguments — which have to be based on inference rules of mathematical logic — | the arguments — which have to be based on inference rules of mathematical logic — | ||
may use the axioms of the theory and previously proven statements. | may use the axioms of the theory and previously proven statements. | ||
Revision as of 15:09, 12 August 2020
In mathematics, a proof of a statement (called theorem, proposition, lemma, etc. according to the context and its importance) is a series of arguments which show that the assumptions of the statement imply its conclusion. Besides the assumptions listed explicitely in the statement to be proven, the arguments — which have to be based on inference rules of mathematical logic — may use the axioms of the theory and previously proven statements.