Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Ceiling function

(Redirected from Ceiling)

The ceiling function, also known as the "least integer function," gives the least integer greater than or equal to its argument. The ceiling of $x$ is usually denoted by $\lceil x \rceil$. The action of the function is also described by the phrase "rounding up." On the negative real numbers, this corresponds to the action "dropping everything after the decimal point".

Examples

  • $\lceil 3.14 \rceil = 4$
  • $\lceil 5 \rceil = 5$
  • $\lceil -3.2\rceil = -3$
  • $\lceil 100.2 \rceil = 101$

Relation to the Floor Function

For an integer, the ceiling function is equal to the floor function. For any other number, the ceiling function is the floor function plus one.

See Also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Ceiling_function&oldid=81830"