Can I assert if an undefined number is not positive or not negative?

Question

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?

Answer 1

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.

Answer 2

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