(a) (2 MARKS ) Let < be an arbitrary order. Translate in MATHEMATICAL language the quoted statement: "

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A 2 Marks Let Be An Arbitrary Order Translate In Mathematical Language The Quoted Statement Has Mc B 2 M 1 (36.35 KiB) Viewed 43 times

(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 a; these are NOT NECESSARILY NUMBERS- for which the "infinite descending (by size) chain" below represents a true statement about the q;: ... <0;+1 <Q; <... <a2 <a <a (1) Hint. If we do have the truth of (1) for some "well-chosen" di, then consider the set {....4+1,2,...,12,01,20} and take it from here. WHY is (2) a "SET"?