- published: 28 Oct 2014
- views: 52220
Floor and ceiling functions
In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively. More precisely, floor(x) = Failed to parse (Missing texvc executable; please see math/README to configure.): \lfloor x\rfloor
Carl Friedrich Gauss introduced the square bracket notation [x] for the floor function in his third proof of quadratic reciprocity (1808). This remained the standard in mathematics until Kenneth E. Iverson introduced the names "floor" and "ceiling" and the corresponding notations Failed to parse (Missing texvc executable; please see math/README to configure.): \lfloor xFailed to parse (Missing texvc executable; please see math/README to configure.): \rfloor
xFailed to parse (Missing texvc executable; please see math/README to configure.): \rceil
The floor function is also called the greatest integer or entier (French for "integer") function, and its value at x is called the integral part or integer part of x; for negative values of x the latter terms are sometimes instead taken to be the value of the ceiling function, i.e., the value of x rounded to an integer towards 0. The language APL (programming language) uses ⌊x
; other computer languages commonly use notations like entier(x)
(Algol), INT(x)
(BASIC), or floor(x)
(C, C++, R, and Python). In mathematics, it can also be written with boldface or double brackets Failed to parse (Missing texvc executable; please see math/README to configure.): [\![x]\!] .
Will you be there when the fire turns ardour
Will you be there when the fire turns ardour
'cause it is more than a flame of the night
will you be there when the sun is goin' down for good
will you take care that it's alright
My friends and I were in a party mood
'cause we were sick of all that solitude
I saw you first down in your favourite club
bought you a drink and showed you what I've got
and you loved me till I cried
Will you be there when the fire turns ardour
'cause it is more than a flame of the night
will you be there when the sun is going down for good
will you take care that it's alright
I'm so afraid that you will leave again
my soul was searching for a suchlike man
a one-night-stand was what I had in mind
now my emotions give me difference signs
will you hold me when I cry
Will you be there when the fire turns ardour
'cause it is more than a flame of the night
will you be there when the sun is going down for good
will you take care that it's alright
Will you be there when the fire turns ardour
will you be there when the fire turns ardour
(more than a flame of the night)
Will you be there when the fire turn ardour
('cause it is more than a flame of the night) baby
will you be there when the sun is going down for good
will you take care that it's alright
Will you be there when the fire turns ardour
'cause it is more than a flame of the night
will you be there when the sun is going down for good
will you take care that... will you take care that