# Neither positive nor negative ?

1. Sep 13, 2010

### phya

If we require that the north is positive number,For example +10Km,South for the negative number,For example -10Km,So, what is the number of 10 km east then?

I think there are other neither positive nor negative，Not only 0 is neither positive nor negative .

Therefore, a number of absolute value is not positive number，Is neither positive nor negative.

For example,|-2|= 2,|+4|= 4
2 and 4 are neither positive nor negative.

Distance should not be a positive number.Distance should be neither positive nor negative.

Last edited: Sep 14, 2010
2. Sep 14, 2010

### Staff: Mentor

What are you saying here?
No, 0 is the only real number that is neither positive nor negative. All other real numbers are either positive or negative.
Baloney. Any real number that is less than 0 is negative; any real number that is greater than 0 is positive. -2 is negative, since - 2 < 0. 4 is positive, since 4 > 0.

Distance is typically nonnegative, but directed distance (e.g. 5 units forward or 8 units backward) can have a connotation of sign.

3. Sep 14, 2010

### Mentallic

There is a reason why it is called a number line. If you want to involve 2 dimensions then you need a coordinate system that has two real numbers (x,y) to describe every point in the system.
So, 10km East breaks away from the 1 dimensional line that the numbers lie on that are representing North and South which means 10km East cannot be represented by a number in the typical sense if 10km North = 10 and 10km South = -10.

4. Sep 14, 2010

### phya

If the distance is only the size, then there being no sign.If the distance is typically nonnegative,Then the distance is a direction.

5. Sep 14, 2010

### Staff: Mentor

Sure.
???

6. Sep 14, 2010

### phya

So，Distance should be neither positive nor negative.

7. Sep 14, 2010

### phya

directed distance .

8. Sep 14, 2010

### phya

If we require that the female is positive number,For example +10,Male for the negative number,For example -10,So, what is the number of 10 Asexual then?

9. Sep 14, 2010

### Staff: Mentor

No, distance is nonnegative: either positive or zero.

10. Sep 14, 2010

### phya

phya: If the distance is only the size, then there being no sign.
Mark44: Sure.
phya: So，Distance should be neither positive nor negative.

This is the correct logic.

11. Sep 14, 2010

### Staff: Mentor

This doesn't work. You are trying to measure three attributes but have only two directions. You need another dimension.

It's the same thing with your first example. If going east is considered the positive direction, then going west would be considered the negative direction. For example, + 8 would mean 8 units to the east, and -4 would be 4 units to the west. You can't work in another direction in this simple system, as Mentallic already mentioned.

It seems to me that you have a fundamental misunderstanding of how numbers work. A number such as 6 is positive. It could be written as +6, but that + sign is not needed, since 6 is already positive. The sign has to be present for negative numbers, though, such as -5.

12. Sep 14, 2010

### phya

You do not understand.If we require that the female is positive number,For example +10 man,Male for the negative number,For example -10 woman,So, what is the number of 10 person (neither female nor male )then?

13. Sep 14, 2010

### phya

Abstract person.

14. Sep 14, 2010

### Mentallic

Why are these males and females given the value 10? We used 10 for north because it was 10km north, our unit being the kilometre. What is the unit for the values representing the people?
However, introducing an abstract concept like this into the mathematics of magnitudes, there most likely won't be any reasonable answer since it is not a reasonable question.

In my garden, each apple I have is given the value +1 while each orange I have is given the value -1. When you introduce bananas into the problem then it becomes meaningless.

15. Sep 14, 2010

### JeSuisConf

I'm not 100% sure what you're asking, but presumably you're looking at using complex valued numbers (the standard way to represent direction and distance), and the 2-norm for distance.

16. Sep 14, 2010

### Staff: Mentor

Well, that's an apples to oranges (+ bananas) comparison.

17. Sep 14, 2010

### Staff: Mentor

The simplistic system you have set up does not allow for neuter persons.

You have two pieces of information: a sign (+ for women and - for men) and a number. You have not clearly defined what the number represents. Is it how many men or women we're talking about?

If that's the case, then

+4 (or 4) means 4 men
-6 means 6 women
0 means no people

You can't extend this system to include genderless persons.

18. Sep 14, 2010

### Mute

Your notions are incorrect. In Euclidean space distances are postive; we simply don't write the + sign because everything is positive by assumption.

In Minkowski space (which is what special relativity's spacetime is), however, it is possible for distances to be negative. Just because we do not have negative distances in Euclidean space does not mean the distances have no sign.

19. Sep 14, 2010

### phya

The amount of positive and negative numbers are opposite, but Apple's content is contrary to what?

20. Sep 14, 2010

### phya

Three men, +3, three woman, -3,Three people,3.

21. Sep 15, 2010

### Mentallic

Contrary to how you brought neuter people into the equation. Females are positive, males are negative, and that's all you can say. Bringing in neutral people does not make sense in your setup and I gave you another example of such with the apples and oranges.

This is like saying 3km north +3, 3km south -3, 3km in either direction (assuming the 3 people are all the same gender because we can't be certain without more information). We would equate this as |x|=3 which means absolute value of x is 3 or in other words $x=\pm 3$. Now if you try introduce something completely different into this system like neuter people or old people or whatever you want, you need to define what their value is in the system you've shown (i.e. a neutral person can have value 0 and an old female can have value 1/2 etc.)
But this isn't like the north east south example because East is already well defined as a direction perpendicular to the north-south line. This means we need 2 dimensions to describe a point in that plane.

22. Sep 15, 2010

### jgens

Basically, it looks like the OP is looking for a nice way to order the elements of $\mathbb{R}^2$, which AFAIK doesn't have a standard ordering. At the very least, it's certainly not possible to impose an ordering over $\mathbb{R}^2$ which satisfies the axioms for an ordered field.

23. Sep 15, 2010

### Staff: Mentor

This makes no sense at all.

24. Sep 15, 2010

### Staff: Mentor

As already stated, 3 and +3 are considered to be the same number.

You could define an encoding system that used +,-,<blank> together with a number to represent the number of men, women, or neuters, but it would have to be understood by all who used this system that it bears little relation to the way numbers are traditionally represented. In particular, +n $\neq$ n.

25. Sep 15, 2010

### phya

Outflow volume, negative，Volume of inflows, positive，Flow，Flow is only the size.North is negative, the South is positive, the absolute value of only size,absolute value is neither positive nor negative.