Ceiling Function/Examples/Ceiling of Minus One Half
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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