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Ceiling and Floor Function Notation

Date: 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?


  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,

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 

          _  _
         | 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 

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   |
  |  / \  |

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