Exercise 2.6.1

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Prove every convergent sequence is a Cauchy sequence. (Theorem 2.6.2)

Ulisse Mini · Accepted Answer

Suppose $(x_n)$ is convergent, we must show that for $m,n > N$ we have $|x_n - x_m| < \epsilon$ Set $|x_n - x| < \epsilon/2$ for $n > N$. We get $|x_n - x_m| \le |x_n - x| + |x - x_m| \le \epsilon/2 + \epsilon/2 = \epsilon$

Exercise 2.6.1

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Exercise 2.6.1

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