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. $\endgroup$ – 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
  • 3
    $\begingroup$ 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
  • 4
    $\begingroup$ $\not \exists x \mid P(x)$ $\endgroup$ – 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

There's no established symbol analogous to $\forall$ or $\exists$, no. You can write either $\neg \exists x. P(x)$ or $\forall x. \neg P(x)$.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.