Ceiling Function/Examples/Ceiling of Minus One Half

Theorem

$\ceiling {-\dfrac 1 2} = 0$

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

Proof

We have:

$0 \ge -\dfrac 1 2$

and:

$-1 = -\dfrac 2 2 < -\dfrac 1 2$

Hence $0$ is the ceiling 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