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) = is the largest integer not greater than x and ceiling(x) = is the smallest integer not less than x.

Notation

Carl Friedrich Gauss introduced the square bracket notation 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 and in his 1962 book A Programming Language. Both notations are now used in mathematics; this article follows Iverson.

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 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 .

Hotel Ceiling

"Hotel Ceiling" is a song performed by English pop band Rixton, issued as the third single from their debut studio album Let the Road.

Music video

The official music video for the song was filmed in London and directed by Clarence Fuller. It features a couple (Alice Eve, Billy Huxley) who initially appear happy, but the relationship becomes violent throughout the course of the video. Eventually the man becomes a missing person; and the video then displays scenes of the woman's distress interspersed with flashback scenes of the couple during happier times. The video ends with the woman calmly waiting for the police after having murdered the man.

None of the members of Rixton appear in the video.

Critical reception

Although the song received positive reviews, the music video received middling reviews. Marian Wyman of The Heights noted that the ending was "subtly creepy"; while Maggie Malach of PopCrush suggested that audiences wouldn't be prepared for the video's content. Dusty Baxter-Wright of Sugarscape.com called the video "disturbing". Rixton lead singer Jake Roche called the video "very depressing" himself, a sentiment that MTV's Christina Garibaldi called "an understatement"; although she also suggested that viewers would still want to re-watch it.