# Is there a shorthand for 'for some x'?

'For all x' = $\forall x$, but what's a convenient shorthand for 'for some x', or 'atleast one x'? $\exists$ doesn't always seem to fit the context. For example "Find $z$ such that $xz < y$ for some $y$".

∃ does always work: for your example, a rephrasing would be "Find $z$ such that ∃$y:xz<y$".

• Slightly beaten to it; not sure what the etiquette is here. Oct 1, 2014 at 5:48
• Nobody will take any offence whatever you do. Oct 1, 2014 at 5:58
• Ok, thanks. I'm leaving it, since it mentions that ∃ always works. Oct 1, 2014 at 6:05
• Right. And if you want to say "Find $z$ such that $xz\lt y$ for all $y$" you can write "Find $z$ such that $\forall y:xz\lt y$". But please don't write stuff like "Find $z$ such that $xz\lt y\ \forall y$" or "A man's a man $\forall$ that" or "once and $\forall$". That will just annoy people.
– bof
Aug 4, 2015 at 22:16

$\exists$ is fine here: "Find $z$ such that $\exists y \, xz < y$."

There's always "∃!x" for there exists exactly one x" But I don't think there's a official symbol for "for some" at least not one that i have seen: https://en.wikipedia.org/wiki/List_of_logic_symbols

• I think $\exists$ is an official symbol for "for some", e.g. $\exists x[x^2=2]$ means "for some $x$, $x^2=2$".
– bof
Aug 4, 2015 at 22:20