NP-hard = harder or equal to, not harder, than NP-complete. He was likely just demonstrating mastery of the subject :)
First, suppose your problem is NP-hard. This means “at least as hard as one of the NP-complete problems, e.g. 3SAT”, in that if you have a poly-time solution to your problem, it can be used to make a poly-time solution to the NP-complete problem.
Now, becoming more specific: what if a P-time solution to one of the NP-complete problems would yield a P-time solution to your problem? Then your problem joins the class of NP-complete problems, which are all P-time reducible to one another.
NP-hard = harder or equal to, not harder, than NP-complete. He was likely just demonstrating mastery of the subject :)
First, suppose your problem is NP-hard. This means “at least as hard as one of the NP-complete problems, e.g. 3SAT”, in that if you have a poly-time solution to your problem, it can be used to make a poly-time solution to the NP-complete problem.
Now, becoming more specific: what if a P-time solution to one of the NP-complete problems would yield a P-time solution to your problem? Then your problem joins the class of NP-complete problems, which are all P-time reducible to one another.