How to prove that $\frac{x}{2}$ is smaller than $x$ for positive $x$

Question

Could someone provide me a valid proof that $\frac{x}{2}$ is smaller than $x$. It seems obvious but i cannot think of a proof. Or just prove that $x+x$ is larger than $x$ for positive $x$.

Answer 1

$$ \begin{aligned} x \phantom{\:+0} &= x \\ 0 &< \phantom{x+\:} x \\ x + 0&< x + x \\ x/2 &< x/2 + x/2 \\ x/2 &< x \end{aligned} $$

Answer 2

Note that if:

$$x>0$$

Then add $x$ to both sides:

$$x+x>0+x$$

Or

$$2x>x$$

Then we may divide by $2$

$$x>\frac{x}{2}$$