What is the standard notation for “for some number”?

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While $\forall$ means “for all”, there seems to be no symbol which means “for some.” What would be the correct way to generally notate this?

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"For some number n in the naturals, n=10" can be written as $$\exists n\in\mathbb N(n=10)$$

This doesn't specify whether that's the only number equal to 10, but it does specify that there is at least one such number in the set of all natural numbers. Does that answer your question?