In the paradigm of the TOTAL Universe, we can now divide by zero!

In the paradigm of cyclical numbers (that is also the paradigm of equivalence), any number ω satisfies the equality (and precisely the equivalence) : 0 = ω. Therefore, we call this the Cycle ω.

In the Cycle ω, we simply have :
1/0 = ω et 1/ω = 0.
And also, the equality of the cycle, namely 0 = ω, leads to this amazing result : 1/0 = 0.

For example, in the cycle 4 that is written 0 = 4, we have : 1/0 = 4 et 1/4 = 0.
And in the cycle 564725 that is written 0 = 564725, we have : 1/0 = 564725 et 1/564725 = 0.

We must also notice that in the paradigm of Cycle, the notions of infinity and of variable (or unknown) are the same notion.

For example, let us consider this equation :
X = X + X

In the classical algebra (non cyclical algebra), solving this equation leads to the solution :
X = 0
and we were usually saying that the single solution of that équation is 0.

But in the cyclical algebra, the variable (or unknown) X is also an infinite number, we can call ω. So in fact we have (at least) two solutions for that equations, 0 and ω. In other words, we have two extreme numbers that satisfy this kind of equality :
X = X + X .
First we have 0 :
0 = 0 + 0
and at the other extreme we have the infinity ω:
ω = ω + ω.

In other words, the result X = 0 is simply the expresiion of the cycle X, namely 0 = X. In the cyclical algebra, we directly solve equations with the infinite number ω. So we solve this :
ω = ω + ω
and we get this result : ω = 0 or 0 = ω, that is simple expression of Cycle ω.