Knowlpedia

Definition

Ceiling function

The least integer not less than a real number.

For a real number xx, its ceiling ⌈x⌉\lceil x\rceil is the unique integer satisfying

⌈x⌉−1<x≤⌈x⌉.\lceil x\rceil-1<x\le\lceil x\rceil.

Equivalently, ⌈x⌉=−⌊−x⌋\lceil x\rceil=-\lfloor-x\rfloor, where the brackets on the right denote the .

Scale comparison

For x≥1x\ge1,

x≤⌈x⌉<x+1≤2x.x\le\lceil x\rceil<x+1\le2x.

Thus replacing a positive real frequency scale by its ceiling gives an integer scale with comparable size. For example, ⌈2.3⌉=3\lceil2.3\rceil=3 and ⌈−2.3⌉=−2\lceil-2.3\rceil=-2.