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Is there formal notation for saying "there is no x for which P(x)" or is it simply something like $( \neg \exists x) P(x)$?

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    $\begingroup$ There's nothing informal about using words. Words are great. $\endgroup$ – Misha Lavrov Jan 8 '19 at 20:48
  • $\begingroup$ @MishaLavrov Sorry, I meant formal notation. I will revise my wording. $\endgroup$ – NetherGranite Jan 8 '19 at 20:50
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    $\begingroup$ I would use parentheses a little differently but you have the basic idea: $\lnot (\exists x P(x))$ $\endgroup$ – hardmath Jan 8 '19 at 20:52
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    $\begingroup$ $\not \exists x \mid P(x)$ $\endgroup$ – Kuifje Jan 8 '19 at 20:55
  • $\begingroup$ In boolean algebra, wouldn't this just be "For all $x$, $P(x)=0$"? (I mean if it were a logic circuit, you'd just take the $P(x)$ signal directly from the OV supply raill . . .) $\endgroup$ – timtfj Jan 8 '19 at 22:02
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There's no established symbol analogous to $\forall$ or $\exists$, no. You can write either $\neg \exists x. P(x)$ or $\forall x. \neg P(x)$.

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