[computer-science] What are the differences between NP, NP-Complete and NP-Hard?

As I understand it, an np-hard problem is not "harder" than an np-complete problem. In fact, by definition, every np-complete problem is:

  1. in NP
  2. np-hard

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-- Intro. to Algorithms (3ed) by Cormen, Leiserson, Rivest, and Stein, pg 1069