Primitive notion: Difference between revisions

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In [[mathematics]], a '''primitive notion''' is somethinga that isconcept not defined in terms of previously defined terms. That isconcepts, itbut isonly somethingmotivated thatinformally, isusually taken to be true asby an [[axiom]]appeal ratherto thanintuition somethingand thateveryday can be proved from a set of further axiomsexperience. For example in [[naive set theory]], the notion of the existence of thean [[empty set]] is primitive. (That it exists is an implicit axiom.) For a more formal discussion of the foundations of mathematics see the [[axiomatic set theory]] article. In an axiomatic theory or formal system, the role of a primitive notion is analogous to that of axiom. In axiomatic theories, the primitive notions are sometimes said to be "defined" by the axioms, but this can be misleading.

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