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Encyclopedia: Universal quantification

In predicate logic, universal quantification is an attempt to formalize the notion that something (a logical predicate) is true for everything, or every relevant thing. The resulting statement is a universally quantified statement, and we have universally quantified over the predicate. In symbolic logic, the universal quantifier (typically ) is the symbol used to denote universal quantification, and is often informally read as "given any" or "for all".

Translations

How to say "Universal quantification" in other languages:

	(Chinese)	全称量化
	(Japanese)	全称記号
	(German)	Quantor
	(Spanish)	Cuantificador universal
	(Italian)	Quantificatore universale (simbolo)

Search results

Open sentence

used to describe the solutions to the open sentence in symbolic logic using universal quantification... have (usually implicitly) a universe of discourse describing which numbers are under consideration... example 2 above, 5/2 is a solution if the universe of discourse is all real numbers, but not if the...

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List of topics in logic

U Unification -- Universal quantification -- Uniqueness quantification V Vacuous truth -- Validity... -- Exclusive disjunction -- Existential fallacy -- Existential quantification F Fallacy of distribution... logics -- Paradox -- Pierce's law -- [Plural quantification]] --Polish notation -- Polylogic...

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Logical conjunction

conjunction for a (possibly infinite) family of statements is universal quantification, which is part...

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Quantification

operation. The two fundamental kinds of quantification in predicate logic are universal quantification and... universal quantification : For any natural number n , n ·2 = n + n . A similar analysis applies to the... quantifiers So far we have only considered universal, existential and uniqueness quantification as used in...

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Counterexample

exception to a proposed general rule, i.e., a specific instance of the falsity of a universal quantification (a "for all" statement). For example, consider the proposition "all students are lazy... FORALL x P (x ) is true. By universal substantiation, deduce P (c ) from this. Next, form the...

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Equaliser

entire domain X , since the universal quantification in the definition is vacuously true. Difference... universal property, which allows the notion to be generalised from the category of sets to arbitrary... . In any universal algebraic category, including the categories where difference kernels are used, as...

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Table of mathematical symbols

¬( A�∧ B )�⇔ (¬ A)�∨ (¬ B); x �∉ S ��⇔� ¬( x�∈ S ) ∀ universal quantification...��� n�∈ N : n 2�≥ n ∃ existential quantification there exists predicate logic ∃� x: P (x...

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List of mathematical topics (S-U)

Universal gas equation -- Universal property Universal property -- Universal quantification Universal quantification -- Universe (mathematics) Universe (mathematics) -- Unknot Unknot -- Unsigned Lah... -- Topology glossary Topology glossary -- Topology of the universe Topology of the universe -- Topos Topos...

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Logical fallacy

better than eternal happiness. In fact it is semantically equivalent to a universal quantification...

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