I am learning from this video: https://www.youtube.com/watch?v=eHZifpgyH_4 at 21:17 he talks about his definition of NP-Hard.
The definition is: X is NP-Hard if every problem y which belongs to NP reduces to X.
I watched that part of the video several times but don't understand it. In particular, here's one thing I don't get:
P is also a part of NP so when we say every problem y which belongs to NP we are saying we can take a problem in P and reduce to some X. Then X is NP-Hard? That would mean that y we just converted would have an NP-Hard solution but it is actually polynomial? Sorry if this is confusing. I hope I can word it better but it to me that definition only makes sense if they talk about NP problems that are not part of P