Looking for some help with this problem, Thanks ahead of time

. Given the relation defined on N XN by (a, b) "<" (c, d) iffb<d.

(a). Why is the relation well-founded?

(b). What are the minimal elements?

(Rock)

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- Apr 30th 2008, 07:08 PMcrowned1relations
Looking for some help with this problem, Thanks ahead of time

. Given the relation defined on N XN by (*a, b*) "<" (*c, d*) iff*b*<*d*.

(a). Why is the relation well-founded?

(b). What are the minimal elements?

(Rock) - May 1st 2008, 04:21 AMMoo
Hello,

This relation is well-founded if there doesn't exist an infinite sequence ( ) such as

Assuming that it's not well-founded, this means that there will always be such as

If , it's a nonsense since there doesn't exist such an x.

Hence, the relation is well-founded...

Minimal elements will be any elements such as

This means that can be any element in

has to be the element such as ,

So logically, but I think there is a problem (Wait)