- A 2 Marks Let Be An Arbitrary Order Translate In Mathematical Language The Quoted Statement Has Mc B 2 Ma 1 (60.48 KiB) Viewed 35 times
(a) (2 MARKS ) Let
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(a) (2 MARKS ) Let
(a) (2 MARKS ) Let <be an arbitrary order. Translate in MATHEMATICAL language the quoted statement: "<has MC". (b) (2 MARKS ) Does the usual < on the integers Z = {...,-2, -1, 0, 1, 2,...} have MC? = Justify your answer. (c) (5 MARKS) Now suppose that some < which is NOT THE USUAL ONE on N- indeed has MC. Prove that there is NO infinite (enumerable) sequence of objects ai —these are NOT NECESSARILY NUMBERS, for which the "infinite descending (by size) chain" below represents a true statement about the aj: ... <di+1 <a;<...< a2 < 01 <00 (1) Hint. If we do have the truth of (1) for some "well-chosen" ai, then consider the set {..., dj+1, Qi, ..., 22,21,20} (2) and take it from here. WHY is (2) a "SET"?
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