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axiom of ZFC
The '''Axiom of Empty Set''' asserts that a [[set]] exists which is [[Empty_set|empty]]. It does not assert the uniqueness of this set; using the other [[Axiom|axioms]] of [[Zermelo-Fraenkel]] set theory, this set can be shown to be unique.
This axiom is sometimes called the zeroth axiom of set theory (see [[Zeroth Law of Thermodynamics]]) because it states something so obvious that it's easy to forget to formally state it as a rule.
The Axiom of Empty Set and the [[Axiom of Choice]] are the only two axioms of set theory that [[Constructive_proof|non-constructively]] assert the existence of a set.
[[Category:Set Theory]][[Category:Mathematics]]
This axiom is sometimes called the zeroth axiom of set theory (see [[Zeroth Law of Thermodynamics]]) because it states something so obvious that it's easy to forget to formally state it as a rule.
The Axiom of Empty Set and the [[Axiom of Choice]] are the only two axioms of set theory that [[Constructive_proof|non-constructively]] assert the existence of a set.
[[Category:Set Theory]][[Category:Mathematics]]