i is the square root of -1. For a long time, roots of negative numbers were considered undefined, until you went there and simply said that the root of -1 was i, the imaginary number. Even modern pocket calculators sometimes show an error with negative roots. With i you could continue to calculate and quickly develop the complex numbers. The complex numbers have a real and an imaginary part. A complex number c1 is equal to (r * i, s). So you no longer have simple numbers, but a vector. The complex numbers form a body with regard to addition and multiplication, but according to the previous view this is not ordered. The order properties fail, it is believed, because i would be neither positive nor negative, so that a relation like <or> would not be applicable.
The absolute theory and the complex numbers
So far it's just an idea and almost pure speculation: The numbers that I defined for the Division by Zero always played a life of their own. Recently I've been discovering that it is possible that they are not as different from complex numbers as I always thought. The assumption is 0 * 0 = -1, i.e. i = 0. On the one hand, this results from the consideration that infinitely times 0 comes close to 1 and can also be referred to as epsilon, the number that is greater than 0 , but smaller than any real number so far. According to the field axioms, 1 * 0 would be exactly the zero element and everything <1 * 0 would then go into the imaginary area, i.e. in particular 0 * 0 = -1. It should be noted that by 1 I always mean the ones element, i.e. the smallest possible non-imaginary number in the number set. This can be illustrated physically using the quantization. On the other hand, the assumption arises that i would be equal to 0 in the sense of my newly defined zero elements from physics. After the anti-proportionality of locomotion and mass the energy for faster than light speed moves into the area of the zero elements, but according to Einstein and Minkowski it moves into the imaginary area. For a long time I thought that was a contradiction, but as always it was only an apparent one that leads to a greater truth.
It would also result from this that the complex numbers would be an ordered field, because i = 0 = + 0 and n * i> = 0, with n * i> m * i for n> m. This is how you could order the numbers. Unfortunately, there are also new contradictions with this idea, for example 1 / i = -i, which would mean that 1/0 = -0. And that brings me completely into the devil's kitchen, because then the difference between 0 and infinity, and also the difference between positive and negative values in these two areas, could disappear. Let's see what greater truth is behind it.
Further development of this idea via the complex numbers
In the meantime, I don't think it's so improbable that 1/0 = -0 in the sense that 1 / i = -i. With that one would of course have to give up the idea that infinity is the reciprocal of 0. But that too can result from the logical formulation. If we define all times as infinite, and something happens once, then it happened and not zero. The phrase "once is never" would then not apply. I already have a good formulation for 0 * 0 = -1, but in the form 1 * 0 * 1 * 0 = -1 <=> 0 (1) * 0 (1) = -1. If you don't have something this one time, then you have something this one time, i.e. 1. Then there is the new problem that something would be 1 and not -1, but I think with a little time I'll get that too solved. For Multiply by zero, I also omit the relevant reference.
Complex numbers and derivatives
A nice connection that would result from this idea is the calculation of the abilities. So f (x + i) / i = f (x + i) * -i in the real part is the first derivative of f (x), namely f '(x). Here there is a problem with cubic equations that i ^ 4 would no longer be +1. This is difficult to determine on the number line because I always equate 0 with +0. As a result, the jump from -0 to 1 can be too far, and this also applies to the derivatives. You would then always have to calculate the power of i according to your own power rules, because then it does not apply that i ^ 4 = i² * i² = -1 * -1 = +1. But here I have come to the last question of all body axioms. Namely, it makes sense to distinguish between + and -, male and female, positive and negative, and how, if so, do you do it correctly.