existential quantifier

Thân thiện

A student writes an existential quantifier in a logic proof.

Definition

1. Noun:
   • A logical quantifier that asserts the existence of at least one element in a domain for which a given predicate is true: In formal logic and mathematics, an existential quantifier is a symbol or operator used to state that there is at least one member of a set that satisfies a specified property or condition. It is typically denoted by the symbol ∃ (a backwards "E").

Usage Examples

• Noun:
  • The statement "∃x (x > 5)" uses an existential quantifier to assert that there exists at least one number x such that x is greater than 5.
  • In the predicate calculus, the existential quantifier is essential for formalizing statements about existence.

Advanced Usage

• "Existential quantification": The formal process or statement that involves an existential quantifier.
  • The proof relied on a careful application of existential quantification.
• "Existentially quantified formula": A logical formula that contains an existential quantifier.
  • The theorem applies to any existentially quantified formula in the system.

Variants and Related Words

• Existential quantifier symbol (∃): The specific typographical symbol representing the quantifier.
• Universal quantifier (∀): A related logical quantifier that asserts a predicate is true for elements in a domain, often contrasted with the existential quantifier.

Synonyms

• Existential operator: A synonymous term used in logic.
• "There exists" quantifier: A descriptive synonym based on its verbal interpretation.

Related Phrases

• "There exists an x such that...": The natural language phrase corresponding to the symbolic expression ∃x.
  • The formal logic statement translates to "There exists an x such that x is prime."

Học thuật

Noun

1. a logical quantifier of a proposition that asserts the existence of at least one thing for which the proposition is true

Từ đồng nghĩa

• existential operator