gives the smallest integer greater than or equal to x.
gives the smallest multiple of a greater than or equal to x.
- Mathematical function, suitable for both symbolic and numerical manipulation.
- Ceiling[x] can be entered in StandardForm and InputForm as ⌈x⌉, lc rc or
- Ceiling[x] returns an integer when is any numeric quantity, whether or not it is an explicit number.
- For exact numeric quantities, Ceiling internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.
- Ceiling applies separately to real and imaginary parts of complex numbers.
- Ceiling automatically threads over lists.
Examplesopen allclose all
Basic Examples (3)
Numerical Evaluation (6)
Specific Values (6)
Function Properties (4)
Differentiation and Integration (4)
Definite integrals of Ceiling:
Minimal number of elements in a box according to the pigeonhole principle:
Properties & Relations (9)
Denest Ceiling functions:
Reduce equations containing Ceiling:
Ceiling function in the complex plane:
The generating function for Ceiling:
The exponential generating function for Ceiling:
Possible Issues (1)
Ceiling does not automatically resolve the value:
Neat Examples (1)
Convergence of the Fourier series of Ceiling: