Logical quantifier

In logic, a quantifier is a way to state that a certain number of elements fulfill some criteria. For example, every natural number has another natural number larger than it. In this example, the word "every" is a quantifier. Therefore, the sentence "every natural number has another natural number larger than it" is a quantified expression.

Quantifiers and quantified expressions are a useful part of formal languages. They are useful because they let rigorous statements claim how widespread a criteria is. Two basic kinds of quantifiers used in predicate logic are universal and existential quantifiers. A universal quantifier states that all the elements considered fulfill the criteria. The universal quantifier is symbolized with "∀", an upside down "A", to stand for "all". An existence quantifier (symbolized with "∃") states that at least one element considered fits the criteria. The existential quantifier is symbolized with "∃", a backwards "E", to stand for "exists".^[1][2][3]

Quantifiers are also used in natural languages. Examples of quantifiers in English include for all, for some, many, few, a lot, and no.

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