Ceiling and Floor Function NotationDate: 11/16/2002 at 04:57:28 From: Jonson Au Subject: Notation for integer round-up Just a very simple question on notation. What is the symbol (Greek?) to replace "integer round-up" below? Examples: integer round-up(16/5) = 4 integer round-up(10/9) = 2 ? (17/3) = 6 If it is not convenient to type from the keyboard using Courier font, what is the usual short form for it? "integer round-up" looks awkward. Thank you, Jonson Date: 11/16/2002 at 12:31:36 From: Doctor Fenton Subject: Re: Notation for integer round-up Hi Jonson, This function is called the "ceiling" function. The standard notation is like a bracket [ ], but with the little "flange" on the bottom missing: _ _ | 10 | | -- | = 2 , for example. | 9 | If you don't have a word processor with mathematical symbols, you can just write its name, ceiling(10/9) = 2, or the short form ceil(10/9)=2 . The function "floor" rounds down, and "fix" rounds towards 0. I think that "nint" is sometimes used to denote the "nearest integer," and I've seen this written {x} also. "Floor" used to be denoted with brackets, [x], but now it has a notation similar to the ceiling function, a bracket with the upper flange missing. I hope this helps. If you have any questions, please write back. - Doctor Fenton, The Math Forum http://mathforum.org/dr.math/ Date: 11/16/2002 at 20:57:41 From: Jonson Au Subject: Thank you (Notation for integer round-up) Thanks. I 've tried to enter the notation in a html file, but found that fonts that support the Unicode character encoding to display the notation are not common at all. The font is not even already installed in a relatively new computer. As I want my reader to be able to see the notation in a browser, I'd better use simply "ceiling(xxx)." Thanks again. Date: 10/14/2004 at 23:47:31 From: Cristian Subject: Additional comments Note that floor has a dual notation, because it can be used to pair-up with two different things: x = [x] + {x} to reflect the separation of the integer and (positive) fractional part of a real number x, and respectively |_x_| <= x <= ceil(x) to reflect the greatest integer less or equal to the real number x and the smallest integer greater than or equal to the real number x, noted as: _ _ | \ / | | X | | / \ | -Cristian |
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