While the ED symmetry breaking can be explained with the concept of having more than one zero at the “point” zero, how does the GD symmetry breaking arise (from a singularity point to a loop or a line)? Why should the split of zeros turn into a loop?

Again, you might guess it; the loop is the intrinsic nature of the singular geometric point. Yet, how can such a loop be defined mathematically?

The geometric point on a number line is defined with and by a number; that is, every point in the number line has one and only one number according to the current Math. However, I will show this issue in a different view.

1. 1/3 = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + 1/128 - 1/256 + 1/512 - 1/1024 + 1/2048 -... +...

= .33349 - ... + ... = .3333333333333.....

= .33349 - ... + ... = .3333333333333.....

2. pi / 4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ... + ... (with "countable" infinity steps)

For 1/3 (with an odd number as the denominator), it can only be “reached” with the sum of a sequence of numbers with only the even numbers as the denominators.

For pi (an irrational number), it can only be “reached” with a set of numbers which have the old numbers as the denominators and by multiplying with an even number 4.

Thus, for the entire number set, there are three “types” of numbers, the odd, the even and the irrational. Yet, these three different types are not separated as complements but are deeply entangled.

The odd (frictional) number can only be reached by a set of even frictional numbers. That is, the odd frictional number is permanently confined in (or glued onto) the even frictional numbers.

On the same token, all irrational frictional numbers are permanently confined by both groups, the odd frictional and the even frictional numbers.

This concept of permanent confinement is one of the central point of the Linguistics Manifesto (http://www.chinese-word-roots.org/cwy.htm ).

This kind of entanglement among different type groups gives rise to loops. Yet, how is a loop defined in this new number theory?

Tienzen (Jeh-Tween) Gong

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