The Helpful Mathematics
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Article 11 — Appendix A.38

ceil — ceiling function

Category. Mathematics.

Abstract. Ceiling: definition, graph and properties.

References. This article is a part of scientific calculator Li-Lc and scientific calculator Li-Xc products.

See also. Floor function.

1. Definition

Ceiling is the nearest integer to the righ — smallest integer greater than or equal to the argument.

2. Plot

Ceiling function defined everywhere on real axis — so, its domain is (−∞, +∞). Its stair-like plot is depicted below — fig. 1.

y = ceil x Fig. 1. Plot of the ceiling function y = ceilx.

Function codomain is the set of integer numbers.

3. Properties

When using the function be aware, that in general case:

ceil(x) + ceil(y) ≠ ceil(x + y)
ceil(x) − ceil(y) ≠ ceil(xy)
ceil(x) ceil(y) ≠ ceil(x y)
ceil(x) /ceil(y) ≠ ceil(x /y)

4. Support

Ceiling function of the complex argument ceil is supported in:

5. How to use

To calculate ceiling of the number:

ceil(-1.8);

To calculate ceiling of the current result:

ceil(Rslt);

To calculate ceiling of the number x in memory:

ceil(Mem[x]);