Division by zero
Since at the latest Newton mankind is kean on the divison by zero. Even in physics you reach borders where the answer would be very helpful. I could not solve the problem completely. Even a virus destroyed my proof on my computer in 1999. Even he destroyed a beginning essay on the constitution of space, too.
Shortly: the proof
I got to do the proof even once more. Hopefully in my basement I have a print of the proof, but here I want to commit the basic truths of the proof. Instead of the old real numbers r (old), we assume the new real numbers r (new). As with the complexe numbers, there are two dimensions added. So we have:
r(new) = vector(r(old) * 0, r(old) * 1, r(old) * infinity) Then you go through the axioms of realsnaumbers and examine whether they are working. An old friend (Schaper) told off a bloated set, but the proof passes and the uniqueness of the numbers is given. So I would not talk about a bloated set, but of a contribution to research epsilon, the set used for deduction. More simple you can use the numbers as 0(1), that would be 1 * 0.
So 0 / 0 = 1 (0 is no longer a number, but a set of numbers)
0(1) / 0(1) = (1 / 1) * (0 / 0) = 1 * 1 = 1
0(r) / 0(r) = 1
0(3) / 0(1) = 3
Therefore the old falsification of division by zero is no longer true, as you cannot say: 0 * r = 0, so there is no uniqueness.
So you do not need complicated limit calculations. (In school I hated that, but I wasn't heard).
There for example the derivation of y = 3x would be:
f´ = (3 * 0) / (1 * 0) = 0(3) / 0(1) = 3
Maybe one day I will solve this problem completely, as it is great, for example:
0(0) / 0(0) = (0 / 0) * (0 / 0) = 1.
So you see that you have to define the real numbers as vector(product(r(old)) * 0, product(r(old)) * 1, product(r(old)) * infinty). The proof would pass through either.
Division by zero and complex numbers
So you know law of derivation. It is delta(y) / delta(x). Normally you take epsilon for derivation. f(x + epsilon) - f(x) / epsilon And epsilon is a number not part of real numbers. It is lower than any real number > 0 but it is for itself > 0 I say the normal way is bullshit. If you substitute epsilon by i you can derive as good So if we take f(x) = 4x^2. so you have ( 4(x + i)^2 – 4x^2) / i
1 / i = -i
So you have (8xi - 1) * i. See both 4x^2 vanish Sorry (8xi - 1) * - i So you get 8x + i. And real part is derivation. Whole thing is better derivation. And now you see you can substitute epsilon or even zero by i.