Primitive notion: Difference between revisions

Revision as of 22:53, 25 April 2013

Revision as of 00:40, 26 April 2013

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'''Examples'''. In:

* [[Naive set theory]], the [[empty set]] is a primitive notion. (To assert that it exists would be an implicit [[axiom]].)

* [[Peano arithmetic]], the [[successor function]] and the number [[zero]] (or number one) are primitive notions.

* [[Axiomatic system]]s, the primitive notions will depend upon the set of axioms chosen for the system. This was discussed by [[Alessandro Padoa]] at the [[International Congress of Mathematicians]] in Paris in 1900.

* [[Euclidean geometry]], under [[David Hilbert|Hilbert]]'s axiom system the primitive notions are ''point, line, plane, congruence, betweeness'' and ''incidence''.