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

  • 4
    $\begingroup$ There's nothing informal about using words. Words are great. $\endgroup$ Commented Jan 8, 2019 at 20:48
  • $\begingroup$ @MishaLavrov Sorry, I meant formal notation. I will revise my wording. $\endgroup$ Commented Jan 8, 2019 at 20:50
  • 3
    $\begingroup$ I would use parentheses a little differently but you have the basic idea: $\lnot (\exists x P(x))$ $\endgroup$
    – hardmath
    Commented Jan 8, 2019 at 20:52
  • 4
    $\begingroup$ $\not \exists x \mid P(x)$ $\endgroup$
    – Kuifje
    Commented Jan 8, 2019 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
    Commented Jan 8, 2019 at 22:02

1 Answer 1


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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