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Let sn be a Cauchy sequence such that ∀n > 1, n ∈ N, ∃m...

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Advance Math

Let sn be a Cauchy sequence such that ∀n > 1, n ∈ N, ∃m >1, m ∈ N such that |sn − m| = 1/3 (this says that every term of thesequence is an integer plus or minus 1/3 ). Show that the sequencesn is eventually constant, i.e. after a point all terms of thesequence are the same

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