Web Reference: Mar 24, 2026 · Learn what a step function is, how floor and ceiling functions work, and where step functions appear in calculus, signal processing, and machine learning. In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less than or equal to x, written ⌊x⌋ or floor (x). Similarly, the ceiling function returns the least integer greater than or equal to x, written ⌈x⌉ or ceil (x). [1] The Floor Function is this curious "step" function (like an infinite staircase): A solid dot means " including " and an open dot means " not including ". Example: at x=2 we meet: so the answer is y=2. And this is the Ceiling Function: The Ceiling Function.
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