Progress in Mathematics: Trans-Finite Primer Part II.

I think I found a math system where 0/0 actually equals zero, unlike the current system, where it equals 1, and then divided by zero again, equals infinity, etc.

Mathematicians treat this as a simple conventionality, but it is a large thing to overlook, in my opinion.

In the new theory, 1 / infinity = infinity / 1 as usual (I think), since infinity = infinity = infinity...

However, 2 infinity would equal 0, as well as all other even numbered infinities.

The result is a system in which 2 infinity / 2 infinity = 0 instead of 1.

However, all the other discrepancies appear to be overcome, with the possible exception that there is a kind of quantum flux or uncertainty to the process of counting infinities...

I have used my variation on trans-finite numbers to calculate the types of deductions possible in larger category sets. The following matrix is produced for the first three charts of modulus 4 (some of the values are left unsolved as I have heard is common with trans-finites).



A = infinity,  1/infinity,  3 infinity,  1 / 3 infinity
BCD = 3 infinity, 1/3infinity, (1 inf. + 2 inf. = ) infinity, 1/ infinity
[-------------------------------------------------------]
ABCD = 4 infinity, 1/ 4 infinity, 12 infinity, 1 / 12 infinity
EFGHIJKLMNOP = 12 infinity, 1/12 infinity, ( (4/infinity) * inf. ^2)=) 4 infinity, 1/4 infinity
[-------------------------------------------------------]
{1 to 16} = 16 infinity, 1/16 infinity, 48 infinity, 1/48 infinity
{17 to 64} = 48 infinity, 1/48 infinity, (((4/inf. * 4/inf) inf. ^2) =) 16 inf., (1/1/2inf. =) 1/16 inf.

The point being that 2 infinity from the first square results in 2 deductions, the 2 or sixteen infinity from the second square results in sixteen parts split over a duality, and the end result of (4 (4 / inf. * 4 / inf. ) inf ^ 2 = 4) for the third square results in four minimal deductions for the sixty-four square diagram, again split into dualities.