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Exercise 6.1.6 (Formal limits are genuine limits)

Prove Proposition 6.1.15, using the following outline.

Proposition 6.1.15. Suppose that ${(a_{n})}_{n = 1}^{\infty}$ is a Cauchy sequence of rational numbers. Then ${(a_{n})}_{n = 1}^{\infty}$ converges to ${LIM}_{n \to \infty} a_{n}$ , i.e.

{LIM}_{n \to \infty} a_{n} = \lim_{n \to \infty} a_{n} .

Exercise 6.1.6 (Formal limits are genuine limits)

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