Feedback on hw 6


This one was well-understood. Notice that you really need a to be nonzero to have f bijective. Also, once you have proven that f is bijective, it is enough to say that g must also be bijective, since it has exactly the same form.


A lot of you proved part (a) by showing the contrapositive. This is perfectly okay, but is not needed: the same proof will work to give the result directly.

In part (b), drawing a picture is very helpful, but you should always write down your counter-examples symbolically as well (and check it works): pictures can be misleading.

Also, when you define a function f from A to B, make sure that it really maps to B, e.g. f(x) = x - 1 is not a function from the naturals to the naturals (why ?).


This is actually a special case of 4.34 (a), so there was no need to prove it again.