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Unformatted text preview: (b) Is there a least element? A greatest element? (c) Find a lower bound for 60 , 72. (d) Find all upper bounds for 2 , 9 (e) Is this a lattice? 5. A poset is called well-founded if there is no inﬁnite descending chain of elements. A poset is called well-ordered if every non-empty subset has a least element. Consider the poset Z , ± given by x ≺ y iﬀ | x | < | y | (a) Show that this is a poset (b) Show that it is well-founded, but not well-ordered. 6. Show that the lexicographic order on the product of two well-founded posets is well-founded. 7. Show that the lexicographic order on the product of two well-ordered posets is a well-ordering....
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This note was uploaded on 09/10/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.
- Summer '08