Problem #PRU-5091

Problem

Let’s prove that $1$ is the smallest positive real number: Assume the contrary and let $x$ be the smallest positive real number. If $x>1$ then $1$ is smaller, thus $x$ is not the smallest. If $x<1,$ then $\frac{x}{2}<x$ so $x$ can not be the smallest either. Then $x$ can only be equal to $1$.