Exercise 558Logic, sets and proofs › Quantifiers and negationL1Added 3 Nov 2026

Bounded quantifiers

#bounded quantifiers#notation#domain

Statement

Rewrite $\forall x\in[0,1],\ f(x)\ge0$ using an unbounded quantifier.

Hint

$[0,1]$ is defined by a predicate on $\mathbb{R}$ .

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Bounded form. $\forall x\in[0,1],\ f(x)\ge0$ .

Unbounded form. $\forall x\in\mathbb{R},\ (0\le x\le1\Rightarrow f(x)\ge0)$ .

Conclusion. Bounded quantifiers are abbreviations for unbounded quantifiers with a membership predicate.