Where does floor collide?

The floor of a real number is the greatest whole number that does not exceed it, so the floor of 3.7 is 3 and the floor of -1.2 is -2. Gauss introduced the square-bracket notation for this quantity in his 1808 Theorematis arithmetici demonstratio nova, writing [x] for the greatest integer not larger than x. Iverson's 1962 book A Programming Language gave it the modern angled-bracket symbol and paired the floor with the ceiling, the smallest integer not smaller than x. The referent is a mathematical operation that rounds a number down to an integer, and it has nothing to do with a legally set minimum price or the solid bed beneath the ocean.[1][2]

Unit

An integer: the number x rounded down to the nearest whole number

Recovery means

Not applicable

Measured by

Computed directly from x as the largest integer that is less than or equal to it

A price floor is a legal lower limit on the price that may be paid for a good or service, set above what an open market would otherwise reach, with the minimum wage as its most familiar case. Webb's 1912 The Economic Theory of a Legal Minimum Wage argued that a legally fixed wage floor need not cost jobs and could raise the productivity of low-paid labour. Stigler's 1946 The Economics of Minimum Wage Legislation made the opposing standard case, that a floor held above the market wage produces unemployment among the least productive workers. The referent is a policy limit on a money price, and it is unrelated to the solid ground beneath the ocean or the rounding of a number to an integer.[3][4]

Unit

A minimum lawful price, in currency per unit of the good or per hour of labour

Recovery means

Not applicable

Measured by

Assessed by comparing the floor with the market-clearing price and the surplus or unemployment that follows