Difference between revisions of "Axiom of empty set"
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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. | 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. | + | This axiom is sometimes called the zeroth axiom of set theory (see [[Thermodynamics|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. | 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]] | [[Category:Set Theory]][[Category:Mathematics]] | ||
Revision as of 11:22, February 19, 2008
The Axiom of Empty Set asserts that a set exists which is empty. It does not assert the uniqueness of this set; using the other 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 non-constructively assert the existence of a set.
