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Exercise 1.1.1

Prove Lemma 1.1.1.

Let ${(x_{n})}_{n = m}^{\infty}$ be a sequence of real numbers, and let $x$ be another real number. Then ${(x_{n})}_{n = m}^{\infty}$ converges to $x$ if and only if $li m_{n \to \infty} d (x_{n}, x) = 0$ .

Exercise 1.1.1

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