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Difference between revisions of "Universal quantifier"

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A logical operator which serves to form propositions using the expression  "for all x" . In formal languages the universal quantifier is most often denoted by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095720/u0957201.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095720/u0957202.png" />, or <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095720/u0957203.png" />. Also used are the notations <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095720/u0957204.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095720/u0957205.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095720/u0957206.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095720/u0957207.png" />.
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A logical operator which serves to form propositions using the expression  "for all x" . In formal languages the universal quantifier is most often denoted by $\forall x$, $(\forall x)$, or $(x)$. Also used are the notations $(\mathbf{A} x)$, $\cap_x$, $\wedge_x$, $\Pi_x$.
  
  
  
 
====Comments====
 
====Comments====
See also [[Quantifier|Quantifier]].
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See also [[Quantifier]].

Latest revision as of 12:39, 24 December 2014

A logical operator which serves to form propositions using the expression "for all x" . In formal languages the universal quantifier is most often denoted by $\forall x$, $(\forall x)$, or $(x)$. Also used are the notations $(\mathbf{A} x)$, $\cap_x$, $\wedge_x$, $\Pi_x$.


Comments

See also Quantifier.

How to Cite This Entry:
Universal quantifier. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Universal_quantifier&oldid=35864
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article