Floor Function/Examples/Floor of One Half

Theorem

$\floor {\dfrac 1 2} = 0$

where $\floor x$ denotes the floor of $x$.

Proof

We have that:

$0 \le \dfrac 1 2$

and:

$1 = \dfrac 2 2 > \dfrac 1 2$

Hence $0$ is the floor of $\dfrac 1 2$ by definition.

$\blacksquare$

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory