Is it a correct way to define image of a subset? $$ f : A \to B\ \text{ function} \\ S\subseteq A \\ f(S)= \left\{b ∈ B ∣ S\cap f^{-1}(\left\{b\right\})≠∅\right\} $$
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1It looks sound to me – Daniel C. Dec 11 '23 at 20:48
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1It's mathematically correct, but what's wrong with $f(S) = { f(a) \mid a\in S}$? – Greg Martin Dec 11 '23 at 21:37
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1I would say that Greg Martin has given the correct definition of the image of $f$, and your expression is an easily proved theorem about it. But that is a personal preference, not some requirement. – Paul Sinclair Dec 12 '23 at 15:29