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Difference between revisions of "Proof (mathematics)"

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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.

Latest revision as of 21:09, 12 August 2020

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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.