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16101977 No.16101977 [Reply] [Original]

What do you guys think of my new number system?
does anyone want to prove some theorems?

>> No.16102002

coal

>> No.16102005

coal

>> No.16102054

>>16102005
>>16102002
Huh? Did you mean cool? Why did you pay the same thing twice?

>> No.16102117

>>16101977

i is defined as the algebraic number satisfying x2 +1 = 0. Its usefulness comes from the fact that you can create a quadratic extension of IR called IR(i) = C
This degree-2-extension allows us to find many exiting results.

In your system, i2 = j2. Hence, they are the same algebraic number, both equivalent in creating a 2-degree complex vectorial space which includes IR.

Easy way to prove that :

j2 = -0.999... = A

10j2 = 10A = -9.999... <-> 10A = -9 + A <-> A = -1 = j2 = i2

All right, since C is defined as a commutative-body which is also a quadratic extension of IR, it's homogeneous to IR[X]/X2+1. That polynomial form is satisfied using either i or j.

I don't see where we can go with such system.