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

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?

• 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. – Prototank Oct 11 '18 at 14:11
• 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 ? – Mauro ALLEGRANZA Oct 11 '18 at 14:11
• You might as well ask, "Is $0/0$ green?" – TonyK Oct 11 '18 at 15:11
• It's still open to interpretation... "0/0 is not green because it's not a color, therefore 0/0 is not green == true" – Kerooker Oct 11 '18 at 16:19
• Do you know any reference for this kind of assertion? – Kerooker Oct 11 '18 at 16:20

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