Monotone subsequence via ultrapower
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🧮 math.CA
math.LO
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monotonesubsequenceinfiniteultrapowerapplicationsapplyarguedcalculus
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An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite subsequence, and give other applications. Keywords: ordered structures; monotone subsequence; ultrapower; saturation; compactness
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