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.