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 ${\displaystyle \exists }$ (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 ${\displaystyle \exists x\in \mathbb {N} ,\,x=3+5}$.

In general, a statement of the form ${\displaystyle \exists x\,P(x)}$ is true if there is an x in the universe of discourse satisfying the predicate ${\displaystyle P}$, 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]

1. ↑ "Comprehensive List of Logic Symbols". Math Vault. 2020-04-06. Retrieved 2020-09-04.
2. ↑ "1.2 Quantifiers". www.whitman.edu. Retrieved 2020-09-04.
3. ↑ "Predicates and Quantifiers". www.csm.ornl.gov. Retrieved 2020-09-04.