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In mathematics, a primitive notion is a concept not defined in terms of previously defined concepts, but only motivated informally, usually by an appeal to intuition and everyday experience. For example in naive set theory, the notion of an 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.