Sekky wrote:Use the natural numbers as the group you're operating on, and only use operations that will form a group under the naturals

(Silly question)

Is always a natural, even though division won't form a group under the naturals. So you are missing out many of functions by doing as you advised.

There's someting very more general than the binomials:

(that follows from

and

)]]>

i thought

denoted rounding the number, [0.3] = 0, [0.8] = 1, [0.5] = 1 etc.and then:

denotes the floor of the number, 0.3 -> 0, 0.8 -> 0and then:

denotes the ceiling of the number, 0.3 -> 1, 0.8 -> 1

luca and jane, you're not *absolutely* right. The notation [.] is an old floor-notation. Today we use \lfloor ect. , but if you look at some notebooks from the 80's, for example, you'll see there floor is [.] . Now [.] is used for another notation.

It's something like the *natural* number - definition, different in different countries.

and ofcourse everysingle programming language in existance will back me up when i say floor always rounds down, and ceil always rounds up

wikipedia:

http://en.wikipedia.org/wiki/Floor_function

http://en.wikipedia.org/wiki/Nearest_integer_function

wolfram:

http://mathworld.wolfram.com/FloorFunction.html

although, to be fair, it does say on wikipedia, that the [x] notation is sometimes used for the floor function aswell, but proper notation for floor function is the one i listed, with [x] being the normal rounding of the number

]]>i thought

denoted rounding the number, [0.3] = 0, [0.8] = 1, [0.5] = 1 etc.and then:

denotes the floor of the number, 0.3 -> 0, 0.8 -> 0and then:

denotes the ceiling of the number, 0.3 -> 1, 0.8 -> 1

[*x*] always rounds down, never up.

Also note that its not the same as taking the integer part of *x* for *x* < 0: [−0.5] = −1, [−2.3] = −3, etc.

Use the natural numbers as the group you're operating on, and only use operations that will form a group under the naturals

(Silly question)

Is always a natural, even though division won't form a group under the naturals. So you are missing out many of functions by doing as you advised.

]]>and then:

denotes the floor of the number, 0.3 -> 0, 0.8 -> 0and then:

denotes the ceiling of the number, 0.3 -> 1, 0.8 -> 1]]>For each real number *x*, denotes the greatest integer less than or equal to *x*. For example: [0.2] = 0, [3.8] = 3, [5] = 5.

The formula above rounds down the value of (*b*−10*a*)⁄9 to the last integer before it.

(Silly question)

]]>I've seen it done with pythagorean triples, can it be done elsewhere too?

]]>