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In [[axiomatic set theory]] the fundamental concept is an example of a primitive notion. As [[Mary Tiles]] wrote:
:[The] 'definition' of 'set' is less a definition than an attempt at explication of something which is being given the status of a primitive, undefined, term.
As evidence, she quotes [[Felix Hausdorff]]: "A set is formed by the grouping together of single objects into a whole. A set is a plurality thought of as a unit."
When an [[axiomatic system]] begins with its [[axiom]]s, the primitive notions may be forgotten. Susan Haak (1978) wrote, "A set of axioms is sometimes said to give an implicit definition of its primitive terms."
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