proposition-no-smallest-positive-real-numbers-can-exist_202508160041

Proposition

Notice that if $a\in \mathbb{P}$, and since $\frac{1}{2}>0$, we have

$$0<\frac{1}{2}a<a$$

Thus if it is claimed that $a$ is the smallest real positive number, we can obtain a smaller positive number $\frac{1}{2}a$.