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Author Topic:  New Theory of Super-Real and Complex-Complex Numbers and Aleph-Null  (Read 698 times)

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Offline M8W

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I had tried to develop A new complex-complex number theory in a Gaussian Integral youtube video in the comments but now - as this can apply to fractals more so then normal Maths I will continue the discourse here (if you let me).  The video is simple and my comments are interesting concerning the (x,i;y,j) complex by complex ordered pairs in a four space mapping.


My assertion is that in the x+i, y+j define 2 complex planes were i and j are complex components of the x and y values respectfully.  The idea that i and j, when mapping a power of 2 equation they interact on the x and y values by adding a negative 1 to the real values there of but they do not interact with each other.  I think they do.  It is possible to define on a computer this type of situation using recursion.  I reason that in multiple recursive evaluations of power equations we might have to rephrase a complex number as a complex-complex number such that the complex part of the complex number has an alternate complex - component.  Even when this might be "unproven" as a true theory to complex number theory this may still be useful in fractal design with the recursive elements being developed further in a pseudo idea of number theory for manipulations and assertions in Fractal Maths. 

I think of super-real numbers as powers of infinity I think they are call Aleph Null values but have no relationship to the Real numbers other then being the power of an infinite amount of them.  Super-reals may still have a kind of degeneration to them that causes infinite loop like qualities beyond the Aleph-Null definitions and postulates.

Linkback: https://fractalforums.org/index.php?topic=671.0
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Offline hgjf2

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Re: New Theory of Super-Real and Complex-Complex Numbers and Aleph-Null
« Reply #1 on: January 06, 2018, 08:04:23 AM »
With this method I learnt how doing integral[0;+oo](e^(-(x^3))dx whick is a value of the elliptical integral what equal with
 (iintegral[0;1][0;1]((1-x^3-y^3)^(1/3))dxdy)^(1/3) where "iintegral" mean the double integral whick is volume of solid with a curve surface border.

I keep trying to know what value the complex integral: integral[-oo;0](e^((x^3)+x))dx+integral[0;((-1+sqrt(-3))/2)*oo](e^((x^3)+x))dx that I couldn't compare this solution with other elliptical integrals due is more complicated, but and the program WOLFRAM INTEGRATOR showing "Integrator couldn't find formula for 'integral(e^((x^3)+x))dx' "

The regions of function integral(e^((x^3)+x))dx at infinity give complex numbers at only 3 regions separated with the complex lines (0+ri);
((sqrt(3)-ri)/2) and (((-sqrt(3)-ri)/2))
« Last Edit: January 06, 2018, 10:06:32 AM by hgjf2, Reason: complete »
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Offline M8W

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Re: New Theory of Super-Real and Complex-Complex Numbers and Aleph-Null
« Reply #2 on: January 06, 2018, 08:40:15 AM »
With this method I learnt how doing integral[0;+oo](e^(-(x^3))dx whick is a value of the elliptical integral what equal with
 iintegral[0;1][0;1]((1-x^3-y^3)^(1/3))dxdy where "iintegral" mean the double integral whick is volume of solid with a curve surface border.

I keep trying to know what value the complex integral: integral[-oo;0](e^(x^3+x))dx+integral[0;((-1+sqrt(-3))/2)*oo](e^(x^3+x))dx that I couldn't compare this solution with other elliptical integrals due is more complicated, but and the program WOLFRAM INTEGRATOR showing "Integrator couldn't find formula for 'integral(e^(x^3+x))dx' "


thank you for replying.

What are you saying here has me confused maybe? e^ (x to the power (3) plus x) or e^ (x to the power (3 plus x))?

So from a geometric point of view of the actual elliptic might have a perpendicular that could be put there for a parameter variation that would solve the problem when integrating for the volume using hyperbolic integrations.  I know if slicing a cylinder with a flat plane leaves the contact points in elliptically ordered...--- but also related = it can be solved when dropping perpendiculars into the ellipsis and then the sin - cos rules would apply.

I fined with a power of 3 the sin and cos... are quite altered by the corresponding line definitions .. - for length along a line or area of the surface or volume of the solid.

On the side of this is of course the integrals between one integral and two integral and three integral as say one and one half integral values being examples on a continuous field of Banach equations having a C constant Matrix variable for the integral value a kind of eigenvalue variable but as well these too can be solved by fractal maths with between the whole value dimensions -but normal maths this would not be as easy.


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