Question: 7. Prove that the two definitions given for Cauchy sequence in (5.10) and (5.11) are equivalent. (Hint: That (5.10) ) (5.11) is true follows by

7. Prove that the two definitions given for Cauchy sequence in (5.10) and (5.11) are equivalent. (Hint: That (5.10) ) (5.11) is true follows by definition. For the reverse implication, express dðxn; xmÞ using the triangle inequality.)

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