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:
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“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)