I just got home from a 12 hour day "math" work day from the Starbucks on the 2nd level at Horton Plaza Mall, Westfield's on 4th Ave in the heart of the business district of downtown San Diego, California 92101. I was working from where I left off at yesterday, and that is, towards the proof and algorithm for the following: B is found in set {{N}X{P}}, and B is found in set {{N}X{T}}, if and only if B' is found in {N}X{P} when B is found in {{N}X{T}}, while {{N}X{P}} = {{N}X{T}}, but if and only if B and B' are both equal to the binary solution; B = B' = {1,0,1}, that must be proved with binary solution B = B' = {1,0,1}'s developed algorithm such that the binary solution is equal to {{N}X{P}} = {{N}X{T}} = {1,0,1} for both B and B', and that both B and B' are the binary solution for language L, where L is equal to Ax = b and also that the following holds,
Set A is the set of simultaneous polynomial nondeterministic discrete time coefficients solutions' sets' for the decidable array for the elements found in set {{0,1}^n : (n > 0)}.
L the language L such that L is an finite array of nonnegative simultaneous polynomial nondeterministic discrete time coefficients solutions' sets' for the decidable array of the elements found in set {{0,1}^n : (n > 0)} = Ax = b, but if and only if b/A = {x1,...,xij,x(i + 1)(j + 1)}, and if and only if, {x1,...,xij,x(i + 1)(j + 1)} is the finite number of product sums for the binary solutions of [m] finite natural numbers of rows multiples by [n] finite natural number of columns [of which all [m]x[n]'s are only the binary solution equal to [m]x[n] = {1,0,1}]. However this [finite number of product sums for the binary solutions of [m] finite natural numbers of rows multiples by [n] finite natural number of columns of which all [m]x[n]'s are only the binary solution equal to [m]x[n] = {1,0,1}] must equal the matrix w's solution, such that the decidable matrix w = Ax = b only when the following holds,
There must also exist a particular number (r) if and only if (r) > 0, such that |w| + r = {1,0,1}, while w = Ax = b = |w| + r = {1,0,1}.
But however we must also develop the algorithm for w = Ax = b = |w| + r = {1,0,1}, that will be the binary solution for; |w| + r = {1,0,1}, and for w = Ax = b = |w| + r = {1,0,1}. Hence,
B is found in set {{N}X{P}}, and B is found in set {{N}X{T}}, if and only if B' is found in {N}X{P} when B is found in {{N}X{T}}, while {{N}X{P}} = {{N}X{T}}, but if and only if when B and B' are both binary solution {1,0,1} for that can be proved with the binary solution for number developed algorithm such that the binary solution is equal to {{N}X{P}} = {{N}X{T}} = {1,0,1}.
Once I have developed the algorithm from the definition of the following,
[{{N}X{P}} = {{N}X{T}} = {1,0,1}],
that was already defined from the paragraphs contained on this page [only above this paragraph] indeed the following was proved,
the decidable solutions [b] were found in w such that w = Ax = b [are the decidable solutions [b], and are strictly the same decidable solutions [b] that are equal to [b] found in |w| while the following holds,
Let P be the set P such that |w| + r = {1,0,1} = set P. Let T be a set T such that T = w = Ax = b = {1,0,1}, and also that the following holds,
Let N be the set N such that N = Ax = b = |w| + r = {1,0,1}, while {N}X{P} = {N}X{T}, such that if and only if B is the decidable solution for P while set B' is also the decidable solution for P, such that {{N}X{P}} = {{N}X{T} = {1,0,1}}, such that {B = {1,0,1}} = {B' = {1,0,1}}.
It should be obvious [to the reader] that we need the algorithm from the following to be proved,
B = B' = {1,0,1} = {N}X{P} = {N}X{T}.
When I am done completing the proof that verifies that the following supposition [was indeed shown to be proved true],
B = B' = {1,0,1} = {N}X{P} = {N}X{T},
I will then develop the algorithm from the following,
B = B' = {1,0,1} = {N}X{P} = {N}X{T}, from the following that was proved, that is,
B = B' = {1,0,1} = {N}X{P} = {N}X{T}.
When I am done completing everything from all of the paragraphs contained above this paragraph, and when all of my proof and developed algorithm from this proof that was then already checked and verified by two or more qualified math readers to have not more that zero errors contained within both the proof and the developed algorithm from this proof that proved that B = B' = {1,0,1} = {N}X{P} = {N}X{T} is true; defined from the paragraphs found above, then the following event will have 100 percent probability it occurrence causing the following to occur,
I will be awarded $1,000,000.00 U.S. dollars from the Association for the Society of Mathematicians that was founded during the very first year of the Korean War, that both occurred during the year 1951.
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