The thing is that Well-Ordering Principle seems a bit tricky to me...I understand the theorem that every non-empty set has got a least element and all that, but I didn't understand the example of round-robin tournament... Basically because I don't know the rules of a domino tournament, I don't know what happens when a player beats another player and in what order do players play...so I felt lost on that example... :S Sooo today when I was doing my assignment the question# 3 gave me a hard time but in the end I think I understood that by WOP if you can always find an element which is a bit less than the element already in the set it creates a contradiction..Is that right? :)
Everything else is quite clear...
1 comment:
Yes. The most common use of well-ordering here is to create a contradiction. If you want to prove that some subset of N is empty, you assume (for the sake of contradiction) that it isn't. Then well-ordering requires that it have a smallest element, and you (somehow) show it doesn't.
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