∑

Quantifier Symbols (∀, ∃)

★★☆☆☆Middle School

📖Definition

∀ (universal quantifier) means 'for all', ∃ (existential quantifier) means 'there exists'. Used for precise mathematical statements.

∀ x ∈ A, P(x)

P(x) is true for all x in A

∃ x ∈ A, P(x)

There exists x in A such that P(x)

∃! x, P(x)

There exists unique x satisfying P(x)

¬(∀ x, P(x)) ≡ ∃ x, ¬ P(x)

Negation of quantifiers

예제 1

What does ∀x ∈ ℝ, x² ≥ 0 mean?

예제 2

What does ∃x ∈ ℤ, x² = 2 mean?

Discovered by: Gerhard Gentzen (1935)

Modern form established based on symbolic logic of Frege and Peano.

Propositional and predicate logic

Theorem statements, proofs

Program verification

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