I contend that there is a third category of number (in addition to positive and negative numbers), which are neutral.
For the sake of expression, let us call these numbers neutral numbers. Zero, for example, is a neutral number.
The reason I believe this is as a mathematical extension of philosophical dialetheism: the belief that that some statements can be true and untrue simultaneously (such as a: (a) is false).
The square root of $-1$ is $i$. $i$ squared is $-1$.
$i$ is an "imaginary" number because we cannot place it on our number line. No number on the number line squared gives $-1$. Nevertheless, we know that (humour me) the value of $i$ is 1, since $1/1$ or $1\cdot 1$ or $-1\cdot 1$ etc. always gives plus or minus 1.
The only number with "value 1" which when squared gives $-1$ would be a number which is neither positive nor negative, in such a way that $i^2 = 1\cdot(-1)$, or rather $(\pm 1)\cdot (\pm 1)$.
I propose that where the $x$-axis shows positive and negative number beside $0$, there is also a $z$-axis that shows neutral numbers in such a way that $i = \pm 1$.
I know that this appears as a crazy idea, but I came to it though philosophy not mathematics. Despite how crazy it is, is this possible mathematically?