Say we have some function $f:X\rightarrow Y$ where $C$ is a subset of $Y$. Can we always state that $f(f^{-1}(C))=C$?
Is this image/preimage statement true?
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elementary-set-theory
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3In http://math.stackexchange.com/questions/78110/ you ask *almost* the same thing. The same example could have been used in this answer (as Zev shows). – 2011-11-11