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Some calculations in mathematics cannot be defined as a number. For instance,

$\frac{0}{0}$ is not defined as a number. $\sqrt{-1}$ is also not defined as a number.

For these formulas, if I ask the question

Is this positive?

As in

Is $\frac{0}{0}$ positive?

The answer will be false. $\frac{0}{0}$ is not a number, therefore it is not possible.

But what about the negation of this question?

Is this not positive?

As in

Is $\frac{0}{0}$ not positive?

Note that I'm not asking if it's negative, nor am I asking if it's 0. I'm just asserting that it's not in the definition of positive.

Can I say that something that's not a number is also not positive? Is $\sqrt{-1}$ in the scope of things that are not positive?

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    $\begingroup$ Positivity and negativity refer to a property on the real number line - a number is to the left or to the right of zero. It isn't more interesting than that. So, I don't think it makes sense to "define" these expressions (which aren't real numbers) as positive or negative. $\endgroup$ – Prototank Oct 11 '18 at 14:11
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    $\begingroup$ If "positive" and "negative" are properties of numbers, to ask if something that is not a number is either pos or neg makes little sense ? Is the Moon positive ? Is it negative ? $\endgroup$ – Mauro ALLEGRANZA Oct 11 '18 at 14:11
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    $\begingroup$ You might as well ask, "Is $0/0$ green?" $\endgroup$ – TonyK Oct 11 '18 at 15:11
  • $\begingroup$ It's still open to interpretation... "0/0 is not green because it's not a color, therefore 0/0 is not green == true" $\endgroup$ – Kerooker Oct 11 '18 at 16:19
  • $\begingroup$ Do you know any reference for this kind of assertion? $\endgroup$ – Kerooker Oct 11 '18 at 16:20
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To define what positive and negative means, you need a certain kind of relation, you can read a lot about it on wikipedia.

Note that since positivity is not defined in your example, one could say that YES, the things you mentioned are not positive. To grab something from the comments: The moon isn't positive, since positivity is not defined for the moon. But this does of course not give you anything meaningful.

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Ascribing polarity to objects is always justifiable with the caveat that these attributes have some demonstrable meaning or function.

Consider that, under ordinary circumstances, polarity is not ascribed to '0'. However, when one is dealing with limits, we regularly see just that:

$$\lim_{x \to -0}$$ Or: $$\lim_{x \to +0}$$

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