Positive Real Numbers not Closed under Subtraction

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Theorem

The set $\R_{>0}$ of strictly positive real numbers is not closed under subtraction.


Proof

Proof by Counterexample

Let $a = 1$ and $b = 2$.

Then:

$a - b = -1$

but $-1$ is not a (strictly) positive real number.

$\blacksquare$


Sources