Okay, so I've read a few different meanings for the exclamation point in a statement. For example: $$!\exists x \in O \ni 2x < 5$$
The only question I have is about the Exclamation point in front of the "there exists" symbol. I know it's also used in permutations, but that's a slightly different concept (I think)
Any clarification would be fantastic, thank you
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$\begingroup$When the exclamation point is "used in permutations", as you put it, it signifies a factorial.
When the exclamation point is used with a "there exists" symbol $\exists$, it means "there exists a unique..." (Wikipedia link) However, it should go in the order $\exists!$, not $!\exists$ like you've written.
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