Neither positive nor negative ?

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SUMMARY

The discussion centers on the classification of numbers as positive, negative, or neutral, particularly in the context of distance and directional values. Participants assert that only zero is neither positive nor negative, while all other real numbers fall into one of the two categories. The concept of directed distance is introduced, emphasizing that distances are typically nonnegative, and the need for a coordinate system to represent multidimensional values is highlighted. The conversation concludes that absolute values are always nonnegative, reinforcing the definitions of positive and negative numbers.

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  • Understanding of real numbers and their classifications
  • Familiarity with absolute value concepts
  • Basic knowledge of Euclidean and Minkowski spaces
  • Awareness of coordinate systems in mathematics
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  • #31
For example -1, the volume is 1, the symbol -. Therefore, the symbols and the volume is not the same thing.
 
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  • #32
If you define a situation where you count -1 for each litre of water in tank A and 1 for each litre in tank B, then when the water is in tank A it will be -1, but the volume of water is still 1 litre. I don't get why this is bothering you so much...
 
  • #33
phya said:
For example -1, the volume is 1, the symbol -. Therefore, the symbols and the volume is not the same thing.
You keep asserting nonsense. Nosense does not become true, or even 'sense' just because you say so. "1" is a number, whether you think of it as a volume, and area or anything else. "-1" is also a number. To assert that "-" is a symbol without saying what you mean by "symbol" is nonsense. If you mean what is normally meant by "symbol", then, yes, "-" is a symbol, but so is "1" so you are still talking nonsense. Symbols by themselves mean nothing. "-1" and "1" are symbols with specific given meanings- in that sense they are both numbers.
 
  • #34
Mentallic said:
If you define a situation where you count -1 for each litre of water in tank A and 1 for each litre in tank B, then when the water is in tank A it will be -1, but the volume of water is still 1 litre. I don't get why this is bothering you so much...

Suppose we require, the men said with a -1, the woman says with a +1, then the three men, that is, 3 * (-1), the three women is 3 * (+1), may I ask, where the third is positive or negative ? Obviously, the three is not positive, not negative.
 
  • #35
phya said:
Suppose we require, the men said with a -1, the woman says with a +1, then the three men, that is, 3 * (-1), the three women is 3 * (+1), may I ask, where the third is positive or negative ? Obviously, the three is not positive, not negative.
It is apparently not obvious to you, but it's obvious to pretty much everyone else that 3 is positive.

As already stated a couple of other times, 3 and +3 represent the same (positive) number.
 
  • #36
phya said:
Suppose we require, the men said with a -1, the woman says with a +1, then the three men, that is, 3 * (-1), the three women is 3 * (+1), may I ask, where the third is positive or negative ? Obviously, the three is not positive, not negative.

Positive numbers are defined to be real number greater than zero. A person is either female or male, you don't know so you can't determine whether it is 1 or -1, but this doesn't mean that it is neither. If you're talking about a neutral person that has no gender, then your example is too simplistic to accommodate for them, unless of course you define neutral people to be equal to... whatever you want.
 
  • #37
Absolute value of a number we have three answers to choose from, be negative, be positive, be neither positive nor negative. Why do we choose a positive number it? This is not injustice it?
 
  • #38
What does "the number be neutral" mean? Please show me on a number line where this "neutral" 3 lies exactly.
 
  • #39
phya said:
Absolute value of a number we have three answers to choose from, be negative,
-n
phya said:
be positive,
+n
phya said:
the number of neutral
Not neutral - zero.

phya said:
- not positive, not negative. Why do we choose a positive number it? This is not injustice it?
Because x*0 = 0, which is not what we want.
And x*-1=-x, which is not what we want.
But x*+1=x, which is what we want.
 
  • #40
phya is simply talking about scalars versus vectors.

+3 on the number line has a magnitude of 3 and a direction of positive.

Magnitude is always positive. phya thinks of magnitude (which has no directional component) as if it should have no directional sign.
 
  • #41
Mentallic said:
Positive numbers are defined to be real number greater than zero. A person is either female or male, you don't know so you can't determine whether it is 1 or -1, but this doesn't mean that it is neither. If you're talking about a neutral person that has no gender, then your example is too simplistic to accommodate for them, unless of course you define neutral people to be equal to... whatever you want.

For a man or a woman, we can say that a person, while a person is neutral.
 
  • #42
This is the abstract.
 
  • #43
phya said:
For a man or a woman, we can say that a person, while a person is neutral.

OK, so there's you answer.

What exactly was the question again?
 
  • #44
phya said:
Absolute value of a number we have three answers to choose from, be negative, be positive, be neither positive nor negative. Why do we choose a positive number it?
Because that's how the absolute value function is defined -- it evaluates to a nonnegative number. The absolute value function maps
  1. negative numbers to their positive opposites.
  2. zero to zero.
  3. positive numbers to themselves.
phya said:
This is not injustice it?
Justice and injustice are totally irrelevant to the concept of absolute value. Why would you even think of it in these terms?
 
  • #45
DaveC426913 said:
OK, so there's you answer.

What exactly was the question again?

Sorry, I do not understand what you mean. Please note from another perspective.
 
  • #46
Mark44 said:
Because that's how the absolute value function is defined -- it evaluates to a nonnegative number. The absolute value function maps
  1. negative numbers to their positive opposites.
  2. zero to zero.
  3. positive numbers to themselves.

Justice and injustice are totally irrelevant to the concept of absolute value. Why would you even think of it in these terms?

The previous provisions may not be correct.
On justice, the world is interconnected.
Newton's absolute space and time corresponding to the past, and Einstein's space-time corresponds to a relatively modern.

Oh. What is the meaning of absolute space and time? What is the meaning of absolute value?
 
  • #47
phya said:
What is the meaning of absolute value?

Absolute value is a mathematical function defined such that each input produces a non-negative output.
 
  • #48
phya said:
The previous provisions may not be correct.
What previous provisions?
phya said:
On justice, the world is interconnected.
This is a non sequitur that has nothing to do with absolute value.
phya said:
Newton's absolute space and time corresponding to the past, and Einstein's space-time corresponds to a relatively modern.
This is irrelevant to our discussion of absolute value.
phya said:
Oh. What is the meaning of absolute space and time?
This is a topic for a philosophy discussion, maybe.
phya said:
What is the meaning of absolute value?
The absolute value of a real number is its distance from zero. This distance is always nonnegative (i.e., positive or zero).
 
  • #49
Mark44 said:
What previous provisions?
This is a non sequitur that has nothing to do with absolute value.
This is irrelevant to our discussion of absolute value.
This is a topic for a philosophy discussion, maybe.

The absolute value of a real number is its distance from zero. This distance is always nonnegative (i.e., positive or zero).

Oh, why a number of non-negative absolute value of it?
 
  • #50
What is absolute?What is absolute value? Which do not contact?
 
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  • #51
phya said:
What is absolute?What is absolute? Which do not contact?
?
 
  • #52
phya said:
Oh, why a number of non-negative absolute value of it?
Please translate this into something that makes sense, preferably English. Be sure to include a verb.
 
  • #53
Mark44 said:
Please translate this into something that makes sense, preferably English. Be sure to include a verb.

Even another language would be better than horribly broken English. Google translator would help me in the first case.

Seriously, phya, why are you so bothered by this?
 
  • #54
phya said:
Oh, why a number of non-negative absolute value of it?

Again, if I may, I think the crux here lies in the fact that phya is seeing that absolute values are magnitudes should thus be unsigned, (since a sign such as + or - indicates a direction.

i.e. magnitude is the unsigned scalar property of a vector.

So, question: does it make sense to have a scalar with a sign, or is it simply an unsigned value?
 
  • #55
Everybody with questions like this should read

Lakoff, Nuñez "Where mathematics come from?"

Great book with a lot of cognitive understanding how things are progressing in mathematics.
 
  • #56
DaveC426913 said:
Again, if I may, I think the crux here lies in the fact that phya is seeing that absolute values are magnitudes should thus be unsigned, (since a sign such as + or - indicates a direction.

i.e. magnitude is the unsigned scalar property of a vector.

So, question: does it make sense to have a scalar with a sign, or is it simply an unsigned value?
Inasmuch as real numbers are scalars, and they can be negative, zero, or positive, yes it makes sense to have a sign with a scalar.
 
  • #57
Mark44 said:
?
Sorry
What is absolute?What is absolute value? Which do not contact?
 
  • #58
What is absolute?What is absolute value?
 
  • #59
phya said:
What is absolute?
See any reasonably comprehensive dictionary.

phya said:
What is absolute value?
This term is precisely defined in mathematics, and the definition has been given numerous times in this thread. Why are you still asking a question that has already been answered?

For a real number x,
|x| = \left\{ \begin{array}{l l}x & \text{if x } > 0\\ 0 & \text{if x } = 0 \\ -x & \text{if x }< 0 \end{array} \right.

Note that +x and x mean the same thing.
 
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  • #60
DaveC is correct, one of phyas problems is confusing scalars with vectors.

As an example, think of it as velocity vs speed:
north = +
south = -

+10mph = 10mph north
-10mph = 10mph south

What phya is doing is removing the direction sign (+/-) and simply looking at what is left, the 10mph. Which is a meaningless magnitude without an assigned direction.

In his case he has the direction which is either positive or negative and then the 'how much' (10, 20, 30 etc). This is where he is confusing things. He is removing the (+/-) and assuming the number left is meaningless, which is incorrect as many have pointed out, a number without a sign is simply positive (or neutral as the case with 0).
 

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