# “nothing” in boolean algebra

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

• There's nothing informal about using words. Words are great. – Misha Lavrov Jan 8 '19 at 20:48
• @MishaLavrov Sorry, I meant formal notation. I will revise my wording. – NetherGranite Jan 8 '19 at 20:50
• I would use parentheses a little differently but you have the basic idea: $\lnot (\exists x P(x))$ – hardmath Jan 8 '19 at 20:52
• $\not \exists x \mid P(x)$ – Kuifje Jan 8 '19 at 20:55
• 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 . . .) – 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 $$\forall x. \neg P(x)$$.