I believe I have the same professor G as mathgirl13 and the whole class is struggling.
I need to prove the converse of the above:
If f: X Y has a two-sided inverse, prove that it is a bijection.
Given and
T.P.
Now choose . This should prove f is injective, right?
Next T.P.
Choose y=f(x) then
but also
This should prove f is surjective, right?
Thanks for any and all help.