THE REAL BEYOND THE VOID:
THE BEGINNING/THE POWER BODY
THE REAL VOID^{1} — FINITE DIFFERENCE OF X 
Product Set 
Product Set: X × Y = {(x,y)  x X, y Y} 
Power Set 
Power Set: p(α) = 2^{α} 
p(x) = 2^{1} = {{x},
Ø} 

THE REAL BEYOND THE VOID — INFINITE DIFFERENCE
OF X^{2} 
Definitions^{3} 
Real Trinary Logic Digital Values: 
Product/Power Body Operational Values: 

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

Power Body 
Where X = finite (1), Y = infinite
(1), x = something (0), y = something else (), 
p
x
= 2^{1} = x, 1 = x, X 
p
x,y
= 2^{2} = x, y, xy, 1 = x,
y, X, Y p 0, = 2^{2} = 0, , 0, 1 = 0, , 1, 1 
p
x,y,z
= 2^{3} = x, y, z, xy, yz,
xz, xyz, 1 = x, y, (X),
X, (x), (y), (X), Y p 0,,1 = 2^{3} = 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 beginning^{4} 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 Cornerstone^{5} 
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
^{
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 Lefthanded 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, 1.1^{1/2}, is the body facediagonal ratio of the absolute dead center triplecube (see, on this web, Report on a Dream & Related Matters & the God Particle, Sorted Diagonals, and Maxwell's Constant & the Trinary Logic Triplecube). 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 edgesharing 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) ~ φ^{1/2} (φ = 1.618033989) (see, on this web, The v_{maxwell}^{1/16} × 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 = φ^{1/2}, accurate to 1 part in 1 million. (829.44/784)^{1/256} × φ^{1/1024} = 1.000690257 ~ 1.000692286 = v_{maxwell}/c, accurate to 1 part in 100,000 (ibid., for v_{maxwell}/c). 'Simplicity' in Hebrew is פשׁטות whose integral product (see, on this web, Transdecimal Calculation of Number Identity: A Note on Integral Product & Related Terms) is 8.2944 × 10^{10}. The factors of 82944 are powers of the first primes, 2^{10} and 3^{4}. 82944^{214} = v_{maxwell}/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.