1. Rounding function

,

where represents the largest integer not exceeding the real number The domain of this function

,

Value range . Function value example:

, , .

　　2. An important property of the rounding function

　　For any real number , we have

.

This inequality is often used in inequality scaling of real numbers and integers .

　　3. Image of rounding function

　　The rounding function is a piecewise function , and its image is as shown in the figure below.

[ Animation ]

　　Note: The graph of the rounding function is shaped like a " step" , and the function whose graph is shaped like a ladder is often called a step-shaped function.