# Least Integer Function

## Least Integer Function

A function f of $$\mathbb{R}$$ in $$\mathbb{R}$$ is a function of the least integer that is greater than or equal to x if and only if: ∀x ∈ [n, n + 1] : x → ⌈x⌉ = n + 1 where n ∈ $$\mathbb{Z}$$ and n ≤ x ≤ n + 1.

A least integer function that is greater than or equal to a number returns a rounded up value of the real value of the number.

### Notation

The least integer function greater than or equal to x is noted as ⌈x⌉ and is read as “integral value greater than x”.

We use the notation ⌈x⌉ to refer to the “least integer that is greater than or equal to” in opposition to the notation ⌊x⌋ to refer to the greatest integer that is less than or equal to.

### Example

If we want to find out how many dozen eggs we will need to buy to serve one egg to each person in a group of x friends, the number of dozens is given by the least integer function that is greater than or equal to x defined by f(x) = ⌈x⌉.

Therefore, to serve 27 people, we will need to buy 3 dozen eggs, because ⌈27 ÷ 12⌉ = ⌈2.25⌉ = 3, since 3 is the least integer greater than 2.25.