Evaluate numerically:

Complex number inputs:

Single-argument Ceiling always returns an exact result:

The two-argument form tracks the precision of the second argument:

Evaluate efficiently at high precision:

Ceiling threads elementwise over lists:

Ceiling can deal with real‐valued intervals:

Values of Ceiling at fixed points:

Value at zero:

Value at Infinity:

Evaluate symbolically:

Manipulate Ceiling symbolically:

Find a value of x for which the Ceiling[x]=2:

Plot the Ceiling function:

Visualize the two-argument form:

Plot Ceiling in three dimensions:

Visualize Ceiling in the complex plane:

Ceiling is defined for all real and complex inputs:

Ceiling can produce infinitely large and small results:

Ceiling is not an analytic function:

It has both singularities and discontinuities:

Ceiling is nondecreasing:

Ceiling is not injective:

Ceiling is not surjective:

Ceiling is neither non-negative nor non-positive:

Ceiling is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to x:

First derivative with respect to a:

Definite integrals of Ceiling:

Series expansion: