If $h$ belongs to the set of functions from $X$ to $X$, why is $h$ injective if and only if, for any functions $f$ and $g$ in that set, if $h \circ f = h \circ g$, then $f=g$?
I'm trying to understand this question about set theory. I'm studying Halmos's Naive Set Theory book. I'll post my progress later (if any :/)
So, h composite f means the domain of h equals the range of f. h composite g means the domain of h equals the range of g. then the range of f and g are the same.