# Are positive numbers somehow more “fundamental” than negative numbers?

I know this seems like a dumb question, but hear me out. Whenever you multiply a number by itself, you get a positive number, and whenever you divide a number by itself, you also get a positive number.

For some reason, the operations of multiplication and division seem to have some sort of connection to the positive numbers. It seems like there should be some reason for this. I know how multiplication and division work, but I still feel dissatisfied. It seems like there is something special about positive numbers in relation to these operations. Maybe this is more of a philosophical question than anything.

If this still sounds dumb I completely understand. Thanks for any thoughts.

• Positive numbers are closed under multiplication, while negative numbers are not. – Crostul Mar 21 at 16:18
• Building up the number system from scratch starts with $1$ and building up positve integers. Negatives come later. – herb steinberg Mar 21 at 16:20
• It is a worthwhile observation, even if it has a philosophical nature. Leopold Kronecker famously said, "God made the integers, all else is the work of man." One can go beyond this to say that the counting numbers (positive integers) are even more fundamental (since one needs to count in order to verify arithmetic facts and check that formulas are in agreement).. – hardmath Mar 21 at 16:23
• The fact that $(-1,1)$ forms a group under multiplication called $\mathbb{Z}_2$ is probably what you are noticing. That may not mean anything to you if you are not familiar with group theory but the basic idea is that “all the positive numbers” have this “positiveness” propert that makes them act as if they are the “original identity” element of the set of reals, whereas the negative numbers, carry more unusual behavior. – frogeyedpeas Mar 21 at 16:27
• @frogeyedpeas But why do positive numbers have this "original identity" property? Is it just because we defined them first? – Tdonut Mar 21 at 16:44

There is no strictly mathematical answer to this question. It has to do with the long history of mathematics. For thousands of years, negative numbers were not used in mathematics and hence did not exist. All numbers were positive and the positive versus negative number concept did not arise until a few centuries ago. For example, from Wiktionary article positive

Of number, greater than zero. [from the 18th c.]

To state the obvious, when we refer to or write the number seven we write just $$7$$. To refer to the additive inverse we need to use "negative" seven and we need to write $$-7$$ which is strong evidence that the positive numbers are more fundamental than the so called "negative" numbers since we can only refer to them in terms of positive numbers.