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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?

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

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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College Definitions
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