existential quantifier
Quick Summary
In logic, an existential quantifier asserts that there exists at least one value for a variable. It is symbolized as (\u2203-) and can be read as "for some" or "there exists". For example, the statement "for some x, 2x + 5 = 8" uses an existential quantifier to indicate that there is at least one value of x that makes the equation true.12
This is contrasted with the universal quantifier, which asserts that a statement holds true for all possible values of a variable. Variables that are quantified are called bound variables.2
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foundations of mathematicsSet theoretic beginnings…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 of logic symbols…
Read More…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 of logic symbols…
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formal logicThe predicate calculus…read, “For all ”; and existential quantifiers, written as “(∃ ),” which may be read, “For some ” or “There is a such that.” (“Some” is to be understood as meaning “at least one.”) Thus, (∀x)ϕx is to mean “For all x, x is ϕ” or, more simply, “Everything is…
Read More…read, “For all ”; and existential quantifiers, written as “(∃ ),” which may be read, “For some ” or “There is a such that.” (“Some” is to be understood as meaning “at least one.”) Thus, (∀x)ϕx is to mean “For all x, x is ϕ” or, more simply, “Everything is…
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