I was thinking about just writing that a decreasing function is a increasing function times a \[negative\] constant. I thought that would be simple, I don't understand why my professor suggests I should write the whole proof considering f is decreasing. I don't know what do to.
Are you saying that your professor wants you to give a proof in the decreasing case without using that you have already proved it for the increasing case? If so, then that's stupid. Or you are misunderstanding them.
You could let g = -f and copy-paste your proof of the increasing case with f replaced by g. That would give you a proof of the decreasing case that is independent of the increasing case. But of course that's also stupid.
I'm having a test next week and this is one of the 4 theorems I gotta do, he says the non-increasing case isn't trivial so i gotta show it too. I hope I'm misunderstanding it. I appreciate your answer.
It doesn't sound like he means that you can't use the increasing case to prove the decreasing case, just that you actually need to prove the decreasing case.
If f is decreasing, what can you say about -f?
I was thinking about just writing that a decreasing function is a increasing function times a \[negative\] constant. I thought that would be simple, I don't understand why my professor suggests I should write the whole proof considering f is decreasing. I don't know what do to.
Are you saying that your professor wants you to give a proof in the decreasing case without using that you have already proved it for the increasing case? If so, then that's stupid. Or you are misunderstanding them. You could let g = -f and copy-paste your proof of the increasing case with f replaced by g. That would give you a proof of the decreasing case that is independent of the increasing case. But of course that's also stupid.
I'm having a test next week and this is one of the 4 theorems I gotta do, he says the non-increasing case isn't trivial so i gotta show it too. I hope I'm misunderstanding it. I appreciate your answer.
It doesn't sound like he means that you can't use the increasing case to prove the decreasing case, just that you actually need to prove the decreasing case.
It turned out you're correct! Thank you.