Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

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)*

Offline

**Sekky****Member**- Registered: 2007-01-12
- Posts: 181

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)

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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

Offline

**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

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

The Beginning Of All Things To End.

The End Of All Things To Come.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

luca-deltodesco wrote:

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.

Offline

**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

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

The Beginning Of All Things To End.

The End Of All Things To Come.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

luca-deltodesco wrote:

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.

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Ricky wrote:

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

)

IPBLE: Increasing Performance By Lowering Expectations.

Offline

Pages: **1**