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* [[Peano arithmetic]], the [[successor function]] and the number [[zero]] are primitive notions.
* [[Axiomatic system|Axiomatic systems]], the primitive notions will depend upon the set of axioms choosen 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''.
* [[Euclidean geometry]], under [[Giuseppe Peano|Peano]]'s axiom system the primitive notions are ''point, segment'' and ''motion''.
* [[Philosophy of mathematics]], [[Bertrand Russell]] considered the "indefinables of mathematics" to build the case for [[logicism]] in his book [[The Principles of Mathematics]] (1903).
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