a) Suppose that {xn) and {yn} converge to the same real number. Prove that xn - yn

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a) Suppose that {xn) and {yn} converge to the same real number. Prove that xn - yn → 0 as n → ∞.
b) Prove that the sequence {n} does not converge.
c) Show that there exist unbounded sequences xn ≠ yn which satisfy the conclusion of part (a).

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 03:55 AM

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a) Suppose that {xn) and {yn} converge to the same real number. Prove that xn - yn

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a Let a be the common limit point Given 0 choose N N such that n N implies x n a and ...View the full answer

An Introduction to Analysis

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