Existence quantifier
In mathematics and logic, the existence quantifier is a quantifier used to state that a proposition is true for at least one element in the universe of discourse. The existence quantifier is commonly written as [math]\displaystyle{ \exists }[/math] (a mirrored E), and is read as "there exists".[1] An example involving an existence quantifier is the statement "some natural number is equal to 3+5", which can be written as [math]\displaystyle{ \exists x \in \mathbb{N},\, x = 3+5 }[/math].
In general, a statement of the form [math]\displaystyle{ \exists x \, P(x) }[/math] is true if there is an x in the universe of discourse satisfying the predicate [math]\displaystyle{ P }[/math], and is false otherwise.[2] An existence quantifier is different from a universal quantifier, which is used to state that a proposition is true for all elements in the universe of discourse.[3]
Related pages
References
- ↑ "Comprehensive List of Logic Symbols". Math Vault. 2020-04-06. Retrieved 2020-09-04.
- ↑ "1.2 Quantifiers". www.whitman.edu. Retrieved 2020-09-04.
- ↑ "Predicates and Quantifiers". www.csm.ornl.gov. Retrieved 2020-09-04.
