Among researchers who study number theories, “dividing by 0”, “infinity” and “infinitesimal” are the taboo topics, because historically, students of “number theories” had the natural tendency to refuse treating “number theory” as part of the “group theory”. Numbers in number theories often reflect projections of numbers from multi-dimensional groups interacting in universes which possesses far more dimensions than 1 or 2. When a number is divided by 0, much like how -1 was taken a square-root by mathematicians hundreds of years ago, numbers in one dimension are logically and rigorously associated with numbers in another dimension. Only after realizing this from the perspective of multi-dimensional space-time, can we appreciate the improvements and significance of “dividing by 0”, as being of such great contributions to the further perfection of the number theories.
The following equations form a list of important ingredients and necessities, sorely missed in today’s number theories.
x / 0 = y (electromagnetic or other forms of “inductions”: for instance, electrical current induce magnetic fields in a shifted reference frame-set)
0 / 0 = h (because h*0=0; uncertainty principle; history “h” always has a certain percentage of lies)
1 / 0 = 0.5h, -0.5h (setting the unit for the “history number” as “h”, and set quantum gap for natural number to be 0.5h, like 1/2 spin in quantum theory)
-1 / 0 = -0.5h, 0.5h (same as above)
A ≡ A (a number is identical to itself in the same dimension)
Ａ ≢ B (two numbers can not be identical when dimensions or reference frames are different)
With the above equations，the number theory has just become much more mature and more reflective of the multidimensional nature of our universe. With “infinity” and “infinitesimal” better depicted and within our scope of study，many of the conjectures of the past centuries，such as: Riemann Hypothesis，Goldbach’s conjecture, twin prime conjecture…can be easily proven.
Now let’s look at how x / 0 = y is deducted:
Now let’s look at how the unit of “history number” is established. Because this dimension “y” is merged from two opposite directions, the unit “1h” is split by the real value “0” in the middle.
The establishment and evolution of the above unit “h” for “history number” is the proof of Riemann hypothesis. Because the original Riemann hypothesis was observed between the 2 dimensions of “real number” and “complex numbers”. Now when we can witness the same relationship between the 2 dimensions of “real number” and “history number”, then the inter-dimensional relationship defined in the hypothesis is “confirmed”, a.k.a. “proven”. An additional reminder to support such claim is: among inter-dimensional observations, there is no difference in status among “reference frame-set” or “dimensions”. All dimensions (real number vs. complex number; real number vs. history number) are interchangeable, no matter in the Cartesian xyz coordinate system or Einstein’s xyz-t coordinate system, in abstract algebra.
Like in the numbering system of “complex number”, there are “real part” and “imaginary part”, if we make “history number” to equivalently possess “real part” and “story part”, then Goldbach’s Conjecture becomes to prove numbers in the groups of “history number”, the following equation is true “1+ah = 0.5+bh + 0.5+ch” in “real part”. That is to prove “1=0.5+0.5”, need I say more? It is as proven as being “self-evident”.
Aha, don’t forget about the “infinite twin prime conjecture” here either. Since Euclid has already proven there are infinite amount of prime numbers thousands of years ago, and now we have observed in the multiple dimensional space-time, (for prime numbers >3) the minimum prime number gap is “1h” in history number, or a projection of “2” in real number. “1h” or “2” are the dimensions module that can be used to solve modulus to determine prime number among nature numbers. Therefore it is proven, there has to be infinite twin prime numbers among natural numbers, or otherwise we would have been 1) disputing with Euclid; 2) letting second part of natural number changing the dimensions of minimal gap module “1h” or “2” for the first part of the natural numbers. 1) and 2) would both be irrational.