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Existential quantifier

from class:

Calculus I

Definition

An existential quantifier is a symbol used in mathematical logic to express that there exists at least one element in a domain which satisfies a given property. It is denoted by the symbol $\exists$.

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5 Must Know Facts For Your Next Test

  1. The existential quantifier $\exists$ is typically used in conjunction with variables and predicates to form logical statements.
  2. In the precise definition of a limit, the existence of certain values fulfilling specific conditions is often expressed using $\exists$.
  3. A statement involving an existential quantifier has the general form $\exists x \, P(x)$, which reads as 'there exists an x such that P(x)'.
  4. Existential quantifiers are foundational in defining limits rigorously by indicating the presence of values within specified bounds.
  5. When proving limits, showing that some $\delta$ or $\epsilon$ exists to satisfy conditions often involves using existential quantifiers.

Review Questions

  • What does the symbol $\exists$ represent in mathematical logic?
  • How is an existential quantifier used in the precise definition of a limit?
  • Can you provide an example of a statement involving an existential quantifier?
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