Definition and Properties
In the following formulas, x and y are real numbers, k, m, and n are integers, and is the set of integers (positive, negative, and zero).
Floor and ceiling may be defined by the set equations
Since there is exactly one integer in a half-open interval of length one, for any real x there are unique integers m and n satisfying
Then and may also be taken as the definition of floor and ceiling.
Read more about this topic: Floor And Ceiling Functions
Famous quotes containing the words definition and/or properties:
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)