THE REAL BEYOND THE VOID:
THE BEGINNING/THE POWER BODY

 

THE REAL VOID1 — FINITE DIFFERENCE OF X
 

Product Set

Product Set: X Y = {(x,y) | x X, y Y}

 

Power Set

Power Set: p(α) = 2α

p(x) = 21 = {{x}, }
p(y) = 21 = {{y}, }
p(x,y) = 22 = {{x}, {y}, {x,y}, }
p(x,y,z) = 23 = {{x}, {y}, {z}, {x,y}, {y,z}, {x,z}, {x,y,z}, }

 

THE REAL BEYOND THE VOID — INFINITE DIFFERENCE OF X2
 

Definitions3

Real Trinary Logic Digital Values:
0 = not nothing (absolute singularity)
= not not nothing (absolute placedness)
1 = finite (absolute particularity)
1 = infinite (absolute simplicity)

 

Product/Power Body Operational Values:
= embodied in
(,) = identical with
(/) = identically

 

Product Body

Where X = finite (1), Y = infinite (1), x = something (0), y = something else (),
Product Body, X Y, = x,y | x/X, y/Y

X Y = 0, | 0/1, /1 = 0, | ,0
X Y = 0, | 0/1, /1 = 0, | 0,/1,1

 

Simplicity of Existence

,0 = something else(,)something
0,/1,1 = something(,)something else (/) finite(,)infinite

 

Power Body

Where X = finite (1), Y = infinite (1), x = something (0), y = something else (),
Power Body, p α, = 2α

p x = 21 = x, 1 = x, X
p
0 = 21 = 0, 1 = 0, 1
p y = 21 = y, 1 = y, Y
p = 21 = , 1 = , 1

p x,y = 22 = x, y, xy, 1 = x, y, X, Y
p 0, = 22 = 0, , 0, 1 = 0, , 1, 1
p x,y,z = 23 = x, y, z, xy, yz, xz, xyz, 1 = x, y, (X), X, (x), (y), (X), Y
p 0,,1 = 23 = 0, , 1, 0, 1, 01, 01, 1 = 0, , (1), 1, (0), (), (1), 1
 

Simplicity of Existence

Where α > 1, embodied in α the absolute repetition of beginning4
Beyond the void the foundation of ordinary mathematics for the first time
 
0, 1 = 0, 1, 0, , 1, 1 = 0, 1, 0, , 1, 1, 0, , (1), 1, (0), (), (1), 1 =
, 1 = , 1, 0, , 1, 1 = , 1, 0, , 1, 1, 0, , (1), 1, (0), (), (1), 1 = 0
 
The Cornerstone5
1, 1, 1, 1, (1), 1, (1), (1), 1 = ,0 (/) 0,/1,1


 



Notes

1  For Alain Badiou and the void as ontological real, see, on this web, Beyond the Good: Not Hither the Good (& Not Hither Beyond the Good).  For set theory, cf. T. Jech, "Set Theory," The Stanford Encyclopedia of Philosophy (Fall 2002 Edition), ed. E. N. Zalta.  Online.  Available at http://plato.stanford.edu/entries/set-theory.  May 2006.
2  For the absolute dead center cube as the mathematical instantiation par excellence of the relation of the infinite difference of x to the finite difference of x, see, on this web,
The Deep Epidermal Surface: The Cornerstone Construction Order, Minimum Order Tetrahedron Hypercube, & Absolute Dead Center Hypercube, Theorem & Proof: The Uniqueness of the Absolute Dead Center Cube, Measure Beyond Beyond Reach, The Magnitude of Being, and Epidermal Immunity Structure & the Absolute Dead Center Hypercube Volume/Boundary Ratio.
3  For real trinary logic, cf. D.G. Leahy, Foundation: Matter the Body Itself (Albany, 1996), Section III.1, et passim, and D.G. Leahy, Faith and Philosophy: The Historical Impact (Aldershot and Burlington, 2003), Chapter 7, et passim.  See also, on this web, Note to Faith and Philosophy Further to the Ontology of Real Trinary Logic, Real Trinary Logic Geometric Series Matrix of the Numeric Geometric Series & the Series of Perfect Numbers, and Quantum Gravitational vs. Quantum Logic: Virtually Left-handed Real Trinary Logic.  For singularity, placedness, particularity, and simplicity, see, on this web, The Simplicity & Syntax of the Concepts, Immediacy, Mediation, Omnipotence, & Beginning.
4  Matthew 18:20.
5
  The Cornerstone
ninefold [111,(1)(1)(1),111], the blueprint for its construction, the product/power body, 1(,)1 (see, on this web, The Simplicity & Syntax of the Concepts, Immediacy, Mediation, Omnipotence, & Beginning), the finite identical with the infinite (cf., above, n. 2, real trinary logic references).  The transcendental deduction of the order of construction of the cornerstone is accomplished by starting with the power body analogue of the power set (above, this table), substituting the real trinary logic digits for x, y, X, and Y (ibid.), marking the rightward displacement of 2 power body variables by parenthesizing the places newly occupied by 3 power elements that were formerly occupied by 2 power elements (ibid.), and, recognizing that the threefold real trinary logic power body series exists (ibid.), by reducing the 3 power body series initially containing the three 1's to the series containing 3 each of 1's, (1)'s, and 1's as follows,

  , 1, 0, , 1, 1, 0, , (1), 1, (0), (), (1), 1 = 0

  1, 0, , 1, 1, 0, , (1), 1, (0), (), (1), 1 = 0

  1,   1,   1, 1,   1,   (1), 1,    (1),    (1), 1 = 0

   1,      1,    1,   1,   (1), 1,    (1),    (1), 1 = 0,

whereupon the cornerstone is constructed by placing the digits on the left side of the last equation, each in order, successively in the leftmost topmost appropriate and unoccupied cornerstone subsquare.  Thus, following the Beginning/Power Body sequence, 1, 1, 1, 1, (1), 1, (1), (1), 1, the cornerstone is constructed in the order here illustrated,
 

,
 

where the sum of the corners of each of the alternate diagonals = 10, the sum of each of the center vertical and horizontal poles = 11, and the square root of the ratio of the latter to the former, 1.11/2, is the body- face-diagonal ratio of the absolute dead center triple-cube (see, on this web, Report on a Dream & Related Matters & the God Particle, Sorted Diagonals, and Maxwell's Constant & the Trinary Logic Triple-cube).  The ratio of the rational product of the sums of the squares on the successive diagonals beginning with 1 and ending with 9 to that of the sums of the squares on the successive diagonals beginning with 8 and ending with 2 in the Beginning/Power Body ordered cornerstone,

[1/(4+5) (8+3+2)/(6+7) 9]/[8/(4+6) (1+3+9)/(5+7) 2] = ,

(1/9 13/13 9)/(8/10 13/12 2) = ,

the ratio at infinity of the total arithmetic value of the edge-sharing triangles to the total arithmetic value of the whole infinitely expanding triangle of digits produced by the iterative sequential summing of the real trinary logic geometric series (see, on this web, Real Trinary Logic Geometric Series Matrix of the Numeric Geometric Series & the Series of Perfect Numbers).  The ratio of the rational product of the sums of the rows top to bottom to that of the sums of the columns left to right (13/14 18)/(8/14 23) ~ φ1/2 (φ = 1.618033989) (see, on this web, The vmaxwell1/16 1 s/m Cube, Human Body Surface & BSA, & the Infinitely Flat Structure of the Universe).  (13/14 18)/(8/14 23) (829.44/784)1/256 (ibid., for 829.44/784, on this web, passim) = 1.272019052 ~ 1.27201965 = φ1/2, accurate to 1 part in 1 million.  (829.44/784)1/256 φ1/1024 = 1.000690257 ~ 1.000692286 = vmaxwell/c, accurate to 1 part in 100,000 (ibid., for vmaxwell/c).  'Simplicity' in Hebrew is פטות whose integral product (see, on this web, Transdecimal Calculation of Number Identity: A Note on Integral Product & Related Terms) is 8.2944 1010.  The factors of 82944 are powers of the first primes, 210 and 34.  829442-14 = vmaxwell/c accurate to 1 part in 1 million.  For more on the cornerstone construction order, see, on this web, The Deep Epidermal Surface: The Cornerstone Construction Order, Minimum Order Tetrahedron Hypercube, & Absolute Dead Center Hypercube and Power Body Cornerstone Construction Order: Absolute Dead Center Hypercube: The Three Unique Transdecimal Number Identities.


 


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