This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Ceiling

 Ceiling[x]gives the smallest integer greater than or equal to x. Ceilinggives the smallest multiple of a greater than or equal to x.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• 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.
Round up to the nearest integer:
Round up to the nearest multiple of 10:
Round up to the nearest integer:
 Out[1]=
 Out[2]=
 Out[3]=

Round up to the nearest multiple of 10:
 Out[1]=
 Out[2]=
 Scope   (6)
Use exact numeric quantities:
Round up to the nearest multiple of :
Manipulate Ceiling symbolically:
Evaluate an integral:
Evaluate for complex numbers:
Ceiling can deal with real-valued intervals:
Infinite arguments give symbolic results:
Series expansion:
Use Esc lc Esc and Esc rc Esc to enter a short notation for Ceiling:
 Applications   (4)
Self-counting sequence:
Minimal number of elements in a box according to the pigeonhole principle:
Negative numbers round up to the nearest integer above:
Convert Ceiling to Piecewise:
De-nest Ceiling functions:
Reduce equations containing Ceiling:
Ceiling function in the complex plane:
Ceiling does not automatically resolve the value:
Convergence of the Fourier series of Ceiling: