Exercise 3.25

Question

\def\ints{\mathbb{Z}}
Exercise 25:
    Let $X$ be the metric space whose points are the rational numbers, with the metric $d(x,y)=|x-y|$. What is the completion of this space?

Dan Whitman · Accepted Answer

\def\rats{\mathbb{Q}}

The completion of $\rats$ in the manner described in Exercise~3.24 results in the real numbers.
    In fact this is one way to define the real numbers.

Exercise 3.25

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Exercise 3.25

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