Graceli sequential infinitesimal calculus . And analytic function .

Author : Luiz Ancelmo Graceli .
A] [ [ Fg1log x / x ... n ] =
B ] [ [ Fg1log x / x ] . . R . PP [ real, or high potency and progressions numbers ] .
C ] [ [ Fg1log x / x ... n ] + [ [ Fg2log x / x ... n ] + [ [ Fg3log x / x ... n ] + [ [ Fg4log x / x ... n ] . n ...
Where X can be any number or infinitesimal variable within variables.

D ] [ [ Fg1log x / x ] . R . PP + [ [ Fg log 2 y / y ] . R . PP + [ [ FG3 log / g ] . R . PP +
[ [ FG4 log p / p ] . R . PP + [ [ Fgn ... log a / a ] . R . PP n ...

For different variables . Ie we have a single function many variables [ or size ] with changes as each is in process and transformation , or change in position or shape .

By this way and function is more comprehensive and easier to find variables and modifications of the differential and integral calculus .


Analytical calculation Graceli .
A] Log x / x n ... with power y . g / 1 = 0 ................

B ] log x / x + . [ power ] [ prog . ] Y / g power k.0 = 0 , ..............

C ] K Power x y . g - [1] = 0

D ] Log x / x n ... + . prog . * Power * x with i = 0 1

E] [ 1 - ] [ x / log x with power 0 . x ] = 0

F ] [ 1 / [ x * y power of progression from 2 to infinity ] ] n ...

G] [ 1 / [ x * y power of progression of R * [ log x / x n ... ] ] N ...

H ] [ Log x / x ] / [ x power y . i] / = 1



Graceli theory of sequential and infinitesimal numbers less than 1 and greater than zero.

The numbers are usually divided into positive , negative , the worthless [ zero ] , the cousins ​​, the value of [ one] on functions of exponent 0 , and infinitesimal infinitesimal and sequential .
And it is the latter that graceli develops through its functions so you can have coverage in quantum physics, statistics , sequential , and uncertainty , or even infinitesimal intervals between series. In transformative and infinitesimal geometry, and even the oscillatory matrices variational values ​​.

Graceli comprehensive theory of numbers - shapes, variations , transformations , structures , statistics . Infinitesimal .

The objective of graceli functions are approximate or even intervals between values ​​of infinitesimal sequences series results .

[ [ Fg1 [ x / log x ... n ] / [ c / t ] + [ [ Fg2 [ x / log x ... n ] / [ c / t ] + [ [ FG3 [ x / log x n . .. ] / [ c / t ] + [ [ FG4 [ x / log x ... n ] / [ c / t ] + + fgaâfo [ cc ] n ... . [ far ] + + + + fgie fgei fgr + + + FGMF fgfccâe ] n .... / [ C / t ]


+ N ... [ [ Fg1 [ x / log x ... n ] / [ c / t ] + [ [ Fg2 [ x / log x ... n ] / [ c / t ] + [ [ FG3 [ x / log x n . .. ] / [ c / t ] + [ [ FG4 [ x / log x ... n ] / [ c / t ] + + fgaâfo [ cc ] n ... . [ far ] + + + + fgie fgei fgr + + + FGMF fgfccâe ] n .... / [ C / t ] .

However , if placed in terms of infinitesimal variations have sequential tangential curves with negligible variation.
Example .
[ [ Fg1 [ x / log x ... n ] / [ c / t ] .

However , the case is not being attacked here , since the goal is the infinitesimal infinitesimal and sequential .

Where we do not have absolute final results , but always change by infinitesimal sequence in question to be found .

Ie , the result depends on the purpose to be found according to the type and number of infinitesimal sequence to be found .




Graceli function to growth and degrowth of bodies and particles .

Fg1 + FG2 = streams of pulses and progressive growth or snapshots and quantum .
[ [ Fg1 [ x / log x [ + - . / } [ R ] ... n ] / [ py to x / log x ] / [ c / t ] [ + ]
 [ [ Fg2 [ x / log x [ + - / } [ R ] ... n ] . . [ py to x / log x ] / [ c / t ] =
Divided by y power , or potential multiplied by y


Infinitesimal for sequential or non-sequential numbers, or sequential or interleaved series Graceli function.

[ [ Fg1 [ x / log x [ + - . / } [ R ] ... n ] / [ c / t ] =
More or less , division or multiplication of a real number , fractional or not . Where to find repetitive sequences or growing , or less non-sequential infinitesimal numbers.

Sequential and relativistic and infinitesimal uncertainty Graceli function. Or even statistics. That may have use in quantum , mechanics, thermodynamics, relativity and cosmology, and chemistry .

The Graceli functions do not deal with end results , but at intervals between zero and and least one more , just one has to know the sequence or repeated or sequential sequence enésimos of logarithms , or decimal number that is either the result of higher of 0 , 1 and lower the tiniest infinitesimal n ... . Or even higher infinitesimal numbers 1 . That is, the result is not zero , but always greater than 0 and less than 1. And because the end result and a range of numbers that can be logarithmic in any sequence , then we have a calculation function infinitesimal relativistic with various results.

Or even higher infinitesimal numbers 1 .


And Graceli functions are not two-dimensional , but n- dimensional , and not just treat the external forms , but also the variations of the density , structure , degree of evolution , transformations , flows oscillating and unstable pulses during acceleration and expansion, etc. .

Ie , does not form a Cartesian graph , but latitudes , longitudes , time , time, structures and densities , energy and dilation , pulse flows and flares and shortenings . And other dimensions . And it raised the [ x / log x ... n ] [ x divided by x infinitely often log ] , and the speed of light divided by the time we have a tiny universe inside other universes smallest numbers. And variations within variations.

And we differentials in integrals, differentials and integrals inside , and have infinitesimal infinitesimal within .

Function universal infinitesimal Graceli .





[[Fg1 [x / log x n...] / [c/t] + [[Fg2 [x / log x n...] / [c/t] + [[Fg3 [x / log x n...] / [c/t] + [[Fg4 [x / log x n...] / [c/t] + + fgaâfo [cc] n...  . [far] + + fgie+ + fgei + fgr + fgmf + fgfccâe] n.... / [c /t]


+ n...  [[Fg1 [x / log x n...] / [c/t] + [[Fg2 [x / log x n...] / [c/t] + [[Fg3 [x / log x n...] / [c/t] + [[Fg4 [x / log x n...] / [c/t] + + fgaâfo [cc] n...  . [far] + + fgie+ + fgei + fgr + fgmf + fgfccâe] n.... / [c /t] .



Where x can be a point , a particle, a straight , a link , an interaction, a concave or convex curve , one radian degree , a POI, an extension , an oscillation , one flow structure density of a transformation, a as in chemical processing and isotopes decays , etc. .

And that when divided by him even log nth times have sequences retained numbers, not repeated or increasing sequences .



Universal infinitesimal calculus and Graceli .

Universal function Graceli . [ infinitesimals within infinitesimals , and variations on variations ] .

Author : Luiz Ancelmo graceli .

[ [ Fg1 [ x / log x ... n ] / [ c / t ] n ...

This logarithm function we have the series of numbers repeated [ 0,33 and others] , and the series of progressive sequences [ 1,2,3,4,5,6,7,8,9 and others] .


The universal Graceli function is not measured from the Cartesian graph , but in relation to dimensions of latitude , longitude , height , flow and vibration of his own body in motion , rotational acceleration, and translation relative to the east, west, north and south, and other dimensions. Ie is n -dimensional . What about the speed of light by the time [ c / t ]

And having as parameter divided by the size of the smallest dimensions own level [ ... n ] log , so we have an infinitesimal mathematical universe , and without reference to Cartesian graph .

With this we have not only a function with respect to [ x, y ] , but on many dimensions and in relation to physical and astronomical references .

With this we have to measure the quantum universe , transquímico [ and isotopes decays and other phenomena ] , structures and shapes , densities and intensities both the macro and micro level as the smallest level .

And it has the function not only geometrical , but also the transformation function and structures and even evolutionary potential , and statistical and quantum uncertainty .


One of the key points of this system is that the result will not be the limit to 0 [ zero ] , but will always be between 0 and 1 [ zero -one] , ie , it will always be an infinitesimal . For it will always be a statistical and uncertainty as in physics and quantum phenomena of infinite variations .

Even a point or particle it will always be to be divided infinitely . Or even infinite relationships between parties and movements and accelerations kinking .

We see that the system of graceli function is not the limit , and not the tangent line , but within the infinitesimal infinitesimal , or the end result will never be found . And where there are processes in relation to the tangent line , but in relation to many variables involving a movement , deformation , structures , transformations and evolutions , revolutions and flows in a single function.


We will never have an end result , but always infinitesimal and always between two numbers . For, in this case the functions Graceli is not the end result , but intervals between results , and intermediate results in multiple scales and sequences series .

Universal function Graceli .

In general function measuring all variables and an infinitesimal ococrrer phenomena which can even movements and variations in curves, quantum flow and radiation angle accelerations , latitudes and longitudes and heights , shapes , densities , and structures intensities , disintegration and integration , links and endless interconnections , isotopes and radioactive decay , and various other phenomena , as well as statistics and uncertainties , relativism in relation to references, and variable arrays . And geometric variables , structures , phenomena and transformations .

In this case the variables are not related to time but with respect to the speed of light in relation to time [c / t].

[[Fg1 [x / log x n...] / [c/t] + [[Fg2 [x / log x n...] / [c/t] + [[Fg3 [x / log x n...] / [c/t] + [[Fg4 [x / log x n...] / [c/t] + + fgaâfo [cc] n...  . [far] + + fgie+ + fgei + fgr + fgmf + fgfccâe] n.... / [c /t] 

+ n...  [[Fg1 [x / log x n...] / [c/t] + [[Fg2 [x / log x n...] / [c/t] + [[Fg3 [x / log x n...] / [c/t] + [[Fg4 [x / log x n...] / [c/t] + + fgaâfo [cc] n...  . [far] + + fgie+ + fgei + fgr + fgmf + fgfccâe] n.... / [c /t] .

Graceli is not in infinitesimal curves in relation to time.

But endless tiny or no variations in other variations , and these infinitesimal variations from the shapes of flows in the plans , the concave and convex in heels and rotations , and links entanglement and how we cohesions , delays oscillation and vibration , and internal flows . And other phenomena .

And relates the world of statistics , uncertainties , oscillatory matrices and infinitesimal and changing geometries in a single system .

So we have several variables in one function. Or even variables on variables .

And it approaches the quantum .

And if the function is carried out with exponent result we have between infinitesimal less than 1 and greater than 0.

And if it is raised to the exponent 0 , we have the result to equal 1 .

And relates to observers , or becomes relativistic and uncertainty of forms and variations.

One of the key points of the infinitesimal system is graceli that are not derived with respect to time .

However , it can be . But overall is in relation to algebraic , geometrical , or even in relation to space , or even for algebraic functions as infinitesimal compared to x / log x [ n ... ] .

Graceli function to infinitesimal infinitesimal .

Author : Luiz Ancelmo graceli .

It is the method of infinitesimal variations on infinitesimal changes .

Ie , can be fully differential , or a set of variations that occur in one time and space. As variations in ocean waves that burst in the sand .

But it may be infinitesimal infinitesimal within . [ infinitesimal infinitesimal ] .

How tiny tiny variations within variations .

[[Fg1 [âa / log âa n...] + [[Fg2 [âa / log âa n...] + [[Fg3 [âa / log âa n...] + [[Fg4 [âa / log âa n...]  + fgaâfo [cc] n...  . [far] + + fgie+ + fgei + fgr + fgmf + fgfccâe] n.... / [c /t] 

 + [[Fg1 [âa / log âa n...] + [[Fg2 [âa / log âa n...] + [[Fg3 [âa / log âa n...] + [[Fg4 [âa / log âa n...]  + fgaâfo [cc] n...  . [far] + + fgie+ + fgei + fgr + fgmf + fgfccâe] n.... / [c /t].

Here the sums of series and sequences Graceli infinitesimal .

Imagine a glowing sphere that has infinite electrons with intense vibration and oscillation of vibration and vibration flows , and within each other vibration happens less and less intense in proportion.

What we have in this example is integral differential - the set of variations on a whole block variation.

And each electron with variations within variations , or infinitesimal infinitesimal .

[ cc ] = Concave and convex .

Fgâa = Graceli of angles and accelerations of varying flows function.