Difference between revisions of "Existential quantifier"
From Encyclopedia of Mathematics
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| − | A logical operation used in forming statements with the expression "for a certain x" ( "an x exists for which" ). In formalized languages, existential quantifiers are denoted by | + | {{TEX|done}} |
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| + | A logical operation used in forming statements with the expression "for a certain x" ( "an x exists for which", "there exists an x such that" ). In formalized languages, existential quantifiers are denoted by $\exists x$, $(\exists x)$, $\cup_x$, $\vee_x$, $\Sigma_x$. | ||
====Comments==== | ====Comments==== | ||
| − | + | The ''unique existential quantifier'' forms the assertion that "there exists exactly one x such that" and is denoted $\exists!x$. | |
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> A. Grzegorczyk, "An outline of mathematical logic" , Reidel (1974)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> A. Grzegorczyk, "An outline of mathematical logic" , Reidel (1974)</TD></TR> | ||
| + | <TR><TD valign="top">[b1]</TD> <TD valign="top"> S.C. Kleene, "Mathematical Logic" repr. Dover (2013) ISBN 0486317072</TD></TR> | ||
| + | </table> | ||
Revision as of 19:32, 23 December 2014
A logical operation used in forming statements with the expression "for a certain x" ( "an x exists for which", "there exists an x such that" ). In formalized languages, existential quantifiers are denoted by $\exists x$, $(\exists x)$, $\cup_x$, $\vee_x$, $\Sigma_x$.
Comments
The unique existential quantifier forms the assertion that "there exists exactly one x such that" and is denoted $\exists!x$.
References
| [a1] | A. Grzegorczyk, "An outline of mathematical logic" , Reidel (1974) |
| [b1] | S.C. Kleene, "Mathematical Logic" repr. Dover (2013) ISBN 0486317072 |
How to Cite This Entry:
Existential quantifier. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Existential_quantifier&oldid=35849
Existential quantifier. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Existential_quantifier&oldid=35849
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article