In predicate logic, universal quantification formalizes the notion that something (a logical predicate) is true for everything, or every relevant thing. It is usually denoted by the turned A (∀) logical operator symbol which is interpreted as "given any" or "for all", and which, when used together with a predicate variable, is called a universal quantifier. Universal quantification is distinct from existential quantification ("there exists"), which asserts that the property or relation holds for at least one member of the domain.
Quantification in general is covered in the article on quantification. Symbols are encoded U+2200 ∀ for all (HTML: ∀ ∀ as a mathematical symbol).
Read more about Universal Quantification: Basics, Universal Closure
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“We have had many harbingers and forerunners; but of a purely spiritual life, history has afforded no example. I mean we have yet no man who has leaned entirely on his character, and eaten angels’ food; who, trusting to his sentiments, found life made of miracles; who, working for universal aims, found himself fed, he knew not how; clothed, sheltered, and weaponed, he knew not how, and yet it was done by his own hands.”
—Ralph Waldo Emerson (1803–1882)