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Exercise 5.4.1 (Basic properties of positive reals)

Prove Proposition 5.4.4.

Proposition 5.4.4. For every real number $x$ , exactly one of the following three statements is true: (a) $x$ is zero; (b) $x$ is positive; (c) $x$ is negative. A real number $x$ is negative if and only if $- x$ is positive. If $x$ and $y$ are positive, then so are $x + y$ and $xy$ .

Exercise 5.4.1 (Basic properties of positive reals)

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