Floor Function/Examples/Floor of Minus One Half

Theorem

 * $\left\lfloor{-\dfrac 1 2}\right\rfloor = -1$

where $\left\lfloor{x}\right\rfloor$ denotes the floor of $x$.

Proof
We have that:
 * $-1 = -\dfrac 2 2 \le -\dfrac 1 2$

and:
 * $0 > -\dfrac 1 2$

Hence $-1$ is the floor of $-\dfrac 1 2$ by definition.