Math Is Fun Forum

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Natural Number

How do I create equations that will only yield a natural answer number? For instance, how would I change this so that for any value of a or b (as long as b is greater than or equal to 10a), x will be a natural number?

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

Last edited by Toast (2007-03-12 00:14:56)

Sekky

Member

Registered: 2007-01-12

Posts: 181

Re: Natural Number

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)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Natural Number

You can write it as

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−10a)⁄9 to the last integer before it.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Natural 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 -> 0

and then:

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

Last edited by luca-deltodesco (2007-03-12 05:12:46)

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Natural Number

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.

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Natural 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 -> 0

and then:

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

[x] always rounds down, never up.

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

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Natural Number

not according to wikipedia, many other mathematics websites including wolfram mathworld, and ofcourse, LaTeX itself, since the other two i called floor and ceiling, are made with the symbols \lfloor \rfloor \lceil \rceil

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

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krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Natural 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 -> 0

and 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.

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krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Natural Number

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:

is integer, where

are integers.
(that follows from

and

)

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