# Ceiling function

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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.