摘要：Theirnumber of factors, factor density, rate of change, and bifractal values ​play exactly the opposite roles.

"Five Chapters"

Continuing from "Section 5,5,"

The accumulation of the value-added coefficient qxz of the highest full-form fraction , and the characteristics of the anti-high shrinkage coefficient fgsx

Similarities between qxz accumulation and fgsx accumulation

They are all the cumulative products of single factors of the corresponding order contained in the fraction . They are all the products of the ratios between the prime order of the corresponding order: sx andy its constant n value . They all respectively represent the change factors caused by the order level of the calculated fraction , the distance between it and the starting number of natural numbers: 1.

The difference between qxz accumulation and fgsx accumulation

Their number of factors, factor density, rate of change, and bifractal values ​play exactly the opposite roles .

qxz accumulates , the higher the order and series of the fraction , the more factors qxz >1 , and the greater the cumulative increase . In the order calculation , because the end point fraction has the highest order , its value-added accumulation is the largest .

Among the total fractions of each order , the qxz accumulation of the highest total fraction is, because it has the highest order , so its qxz accumulation factor is the largest and the qxz accumulation quantity is the largest .

The lower the order number of the fraction , the fewer factors qxz >1 of the fraction . Below the 1st order, 3rd order, 5th order, 7th order of the 11th order fraction , among the four starting conjoined order fractions , because the 1st order, 3rd order, 5th order, Their odd-numbered coefficients , n y =1, cannot form an increment coefficient greater than 1 , and they have no order increment .

In nature, due to the positioning effect of the odd composite number 1 y of the 3rd order prime number , for every sister prime order of ny=1 , there is at least one order fraction of ny≥2 , so that The order ny=1 cannot be continuous . Therefore, the order value-added coefficient qxz , which uses the ny value of the fractional order as a step, grows by leaps and bounds , resulting in a cumulative factor chain.

And fxsx is a continuous cumulative factor product of fxsx factors that reduces the amount of single factor reduction step by step in an orderly manner.

For each fraction of the order formula, the lower its order, the more fxsx single factor accumulation factors, and the greater the reduction. The higher the order of the fraction, the smaller the single factor reduction of fxsx and the fewer accumulated factors. Entering the highest full-form fraction of the order formula, the fxsx accumulation all becomes the fgsx accumulation . Among the various full-form fractions, the highest full-form fraction has the smallest number of factors, and sometimes there are none.

For qxz and fgsx in the highest full-form fraction , comparison of their single-order increase and decrease rates

Among the highest full-form fractions, those with orders lower than 11 , qxz , and fgsx , have no added value because their single increment rate is qxz=1 .

And their fgsx reduction amount is less than 1 . So below the 11th order , 1, 3, 5, 7 , the increase and shrinkage rates of the four orders , they are all, qxz accumulation

The highest full-form fraction , after ≥11th order ,

qxz is tired and fgsx is tired , because,

Average single-stage value-added rate of ≥11 stages :

qxz (single-order lowest average): ≥+(ny -1)/(sx-2ny)

fgsx single-order (average) reduction rate : ≤-1/(sx+2ny+2ny1)

So there is,

The ratio of the average single-order value-added rate qxz to the average single-order reduction rate fxsx is :

│+(ny-1)/(sx-2ny)│ // │-1/(sx+2ny+2ny1)│

(ny-1)/(sx -2ny) // 1/(sx+2ny+2ny1)

Compare the two fractions of the above equation

Because the fraction, after ≥11th order , has n y values ​​with increment , they are all integers of ≥2 ,

Therefore, it can be concluded that after the fraction ≥ 11th order ,

qxz and fxsx , their molecular parts,

有，(ny-1)≥1

Then compare the denominator ,

Because, ny≥1

Therefore, it can be concluded that the denominators of the two equations are,

(sx+2ny+2ny1)>(sx-2ny)

Since the smaller the denominator of a fraction is, the larger its fractional value is.

Get the fraction,

│(ny-1)/(sx-2ny)│>│-1/(sx+2ny+2ny1)│

The calculation results prove that the fraction, after ≥11th order

Comparison results of average single-order growth and contraction rates:

│qxz│>│fgsx│

Due to the sister order , the density among natural numbers becomes increasingly sparse . Some two adjacent prime numbers contain more and more odd and composite numbers , so their n y values ​​become larger and larger. Therefore, the average value-added amount of qxz is much greater than this minimum average value .

The reduction rate of fxsx is still decreasing step by step.

It follows that

"Part Two", Chapter Five,

Conclusion 5.

After the highest full-form fraction, ≥11 orders, the average single-order value-added rate of qxz is greater than the average single-order reduction rate of his fgsx .

The qxz accumulation in the highest full-form fraction , compared with the increase and contraction rate of the fgsx accumulation

because,

The fxsx accumulation that enters the highest full-form fraction becomes the fgsx accumulation .

The anti-high shrinkage fgsx accumulation factors that form a reduction effect on the highest full-form fraction are just the anti-high shrinkage coefficients fgsx covered in the vertical equivalent position in the terminal order field .

And because there is,

Two even-numbered positive and negative bidirectional number axis segments have the relationship (√2X)/(√X)=(√2),

So it follows that,

The number of anti-high shrinkage fgsx accumulation factors is ≤1/(√2) of the n y value of the end point (√X) order .

The qxz accumulation of the highest total fraction is the highest-order qxz accumulation of total fractions among all total fractions . Its cumulative quantity of qxz is the largest and has the largest cumulative quantity among all full-form fractions . And it also includes the single-factor accumulation of all total fractions with qxz≥1 ;

The fgsx accumulation of the highest full-form fraction is composed of the inverse high-shrinking fgsx order reduction factor that is 2 orders higher than the highest full-form fraction . Moreover, it is only the end point order field, the reduction factor formed by the anti-high shrinkage fgsx order covered in the vertical position. They also have, " The number of anti-high-shrinking fgsx accumulation factors, ≤ 1/(√2) of the ny value of the end point (√X) order) ", between columns and in the same position, covering the anti-high-shrinking fgsx Order, the accumulation of reduced factors . ( "Part 2", Chapter 5, Presumption 5, ).

From the position in the order formula ,

The qxz accumulation of the highest total fraction , the number of factors is at the position with the most qxz factors among the total fractions of each order ;

The fgsx accumulation of the highest total fraction is the position with the smallest fgsx factor and the smallest reduction among the total fractions of each order (sometimes there is none).

Therefore, it is concluded that

Highest full form fraction , ≥ after 11th order

The number of his qxz accumulation factors, > the number of his anti-high shrinkage fgsx order reduction factors.

And because,

The highest full-form fraction, after ≥ 11th order , qxz accumulation and fgsx accumulation , their average single factors are compared,

│qxz│>│fgsx│

The number of factors accumulated by qxz , ≥ the number of factors accumulated by fgsx ;

It follows that

"Part 2" Chapter 5, Conclusion 6,

End of paragraph 63 .

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