floored

Floored is the past participle of the verb floor and is used in several senses. As a verb, to floor someone means to knock them to the ground, as in a boxing match. In figurative usage, being floored describes being overwhelmed or astonished by something. The word can also describe a surface that has been covered with flooring material, for example a room floored with oak planks.

In mathematics, floored refers to the floor function. For any real number x, the floor of x, written floor(x) or ⌊x⌋, is the greatest integer less than or equal to x. Examples include floor(3.7) = 3 and floor(-2.1) = -3. The floor function is a non-decreasing, discontinuous function that satisfies floor(x) ≤ x < floor(x) + 1. It is widely used to round down numbers, to compute discrete indices, and to model quantities that are counted in whole units.

In programming, floor is provided by standard libraries in most languages; applying floor often yields a value that is said to be floored. It differs from truncation toward zero on negative numbers. Beyond mathematics and computing, floored appears in everyday language and journalism as a metaphor for being overwhelmed or impressed by an event.