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", "there exists an x such that" ). In formalized languages, existential quantifiers are denoted by $\exists x$, $(\exists x)$, $\cup_x$, $\vee_x$, $\Sigma_x$. | 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 $\exists x$, $(\exists x)$, $\cup_x$, $\vee_x$, $\Sigma_x$. | ||
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<TR><TD valign="top">[a1]</TD> <TD valign="top"> A. Grzegorczyk, "An outline of mathematical logic" , Reidel (1974)</TD></TR> | <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> | + | <TR><TD valign="top">[b1]</TD> <TD valign="top"> S.C. Kleene, "Mathematical Logic" repr. Dover (2013) {{ISBN|0486317072}}</TD></TR> |
</table> | </table> | ||
Latest revision as of 05:42, 22 April 2023
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