universal quantifier

… (⊃), negation (¬), and the universal (∀) and existential (∃) quantifiers (formalized by the German mathematician Gottlob Frege [1848–1925]). (The modern notation owes more to the influence of the English logician Bertrand Russell [1872–1970] and the Italian mathematician Giuseppe Peano [1858–1932] than to that of Frege.) For an extensive discussion…

…are two kinds of quantifiers: universal quantifiers, written as “(∀   )” or often simply as “(   ),” where the blank is filled by a variable, which may be read, “For all   ”; and existential quantifiers, written as “(∃   ),” which may be read, “For some   ” or “There is a…

The universal quantifier, symbolized by (∀-) or (-), where the blank is filled by a variable, is used to express that the formula following holds for all values of the particular variable quantified. The existential quantifier, symbolized (∃-), expresses that the formula following holds for some…