Search results
Results From The WOW.Com Content Network
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
The "ceiling effect" is one type of scale attenuation effect; [1] the other scale attenuation effect is the "floor effect".The ceiling effect is observed when an independent variable no longer has an effect on a dependent variable, or the level above which variance in an independent variable is no longer measurable. [2]
The floor function = ⌊ ⌋, which returns the greatest integer less than or equal to a given real number , is everywhere upper semicontinuous. Similarly, the ceiling function f ( x ) = ⌈ x ⌉ {\displaystyle f(x)=\lceil x\rceil } is lower semicontinuous.
In mathematics, an integer-valued function is a function whose values are integers.In other words, it is a function that assigns an integer to each member of its domain.. The floor and ceiling functions are examples of integer-valued functions of a real variable, but on real numbers and, generally, on (non-disconnected) topological spaces integer-valued functions are not especially useful.
The book popularized some mathematical notation: the Iverson bracket, floor and ceiling functions, and notation for rising and falling factorials. Typography
the floor, ceiling and fractional part functions are idempotent; the real part function () of a complex number, is idempotent. the subgroup generated function from the power set of a group to itself is idempotent; the convex hull function from the power set of an affine space over the reals to itself is idempotent;
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
However, for negative numbers truncation does not round in the same direction as the floor function: truncation always rounds toward zero, the function rounds towards negative infinity. For a given number x ∈ R − {\displaystyle x\in \mathbb {R} _{-}} , the function ceil {\displaystyle \operatorname {ceil} } is used instead