In the traditional mathematics, every point on the number line represents a number. The algebra or arithmetic deals the relationship among numbers. Thus far, there is no internal structure for every single number in the traditional mathematics. Yet, I have discussed that there are different nothingness in the article “Nothingness Smack down, http://tienzen.blogspot.com/2012/05/nothingness-smack-down.html “. They are different at least ontologically. Then, are they also different mathematically? Are the following two zeros different?
1. 0(c) = 1/countable infinity
2. 0(u) = 1/uncountable
Is 0(c) and 0(u) the same entity? Again, they are obviously different ontologically. Yet, are they different mathematically? The answer is Yes. I will discuss this in detail in the future post.
In general, the validity of mathematics relies not on any correspondence to a reality. But, the reverse is not true. A physics which is not mathematically valid cannot be a valid physics.
Today, the LHC has ruled out the hardcore of most of the SUSY theories and of most of the String theories. The only viable physics remaining is the “Prequark Chromodynamics, http://www.prequark.org/ “. Yet, this “Prequark Chromodynamics” is the direct consequence of the fact that zero (0) has a very rich internal structure. That is, this new mathematics does have a correspondence on the physical reality.
In the book “Super Unified Theory (ISBN 0-916713-02-4, Copyright # TX 1-323-231, Library of Congress Catalog Card Number 84-90325)”, there are three chapters discussing this issue of zero’s internal structure.
Chapter 7 --- Colored numbers (page 53 – 61)
Chapter 8 --- Chromology (page 62 – 69)
Chapter 9 --- Unilogy (page 70 – 74)