Is there a shorthand for 'for some x'?

Question

'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 $y$".

Answer 1

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

Answer 2

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

Answer 3

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