Greatest integer function: Learn about the Greatest Integer Function (⌊x⌋)

Learn about the Greatest Integer Function (⌊x⌋), its definition, graph, properties, and solved examples. Understand how it works with step-by-step illustrations. Efficiently compute the greatest integer function (⌊x⌋) with our online calculator. Get accurate results for any real number. The greatest integer function of a number is the greatest integer less than or equal to the number. i.e., the input of the function can be any real number whereas its output is always an integer. Thus, its domain is ℝ and its range is ℤ. The greatest integer function, also called step function, is a piecewise function whose graph looks like the steps of a staircase. The greatest integer function is denoted by f (x) = [x] and is defined as the greatest integer less or equal to x.