I've learned some basics about P and NP. Please excuse if the following is not very precise.
I've read that NP-complete problems are the hardest problems in NP. (Is that correct?)
But now I'm wondering if P problems have polynomial runtime, and assuming P=NP for a moment, how can polynomial runtime problems ever have something like a "hardest problem"? How could polynomial runtime problems have a thing like the largest element?
EDIT: I just remembered that the notion of NP-complete being the "hardest" is defined up to polynomial transformations? And the comparability of P problems is a different thing. Is that the answer? Or can the notion of comparing P problems and NP-complete problems being the hardest be made similar?