Programmable Database Applying Matinga Probability Theorem

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Diagram 1 Matinga Diagrams Versus Venn Diagrams

The Language All Of Set Theorems,

Sets describe algebraic expression or elements of algebra (language) as they relate to each other. Set theory is relational theory or database theory. All of algebra is related or relational. One element can be used to describe the other via a mathematical or algebraic relationship known as a formula.

Repetition In Matinga Set Theorem

In nuture when an element repeats, we cannot know of its frequency unless its repetitions are recorded in atomised format. Set theory has always omitted repetition while demanding it in statistics. A universal solution is required. It is illustrated below.

n = N, [ natural numbers ]

f = Mo / N

a = [ 1 ; 2 ; 3 ; 3 ; 4 ; 4 ; 4 ; 4 ; 5 ; 6 ]

n ( a ) = 10

Σ a = 34

u = [ Count ; Mo ; f ; n ; ϵ ;

1 ; 1 ; 1/10 ; 1 ; 1 ;

2 ; 1 ; 1/10 ; 2 ; 3 ;

3 ; 2 ; 2/10 ; 4 ; 4 ;

4 ; 4 ; 4/10 ; 8 ; 5 ;

5 ; 1 ; 1/10 ; 9 ; 6 ;

6 ; 1 ; 1/10 ; 10 ; 7 ]

The matrix above represents all metadata of database, including the primary data or event space of elements in column ϵ.

Matinga's Intersection Theorem

The Matinga Intersection is simply the the event space or set where the sampled array or subset intersects with or is placed in the universal set. The reader may test the relationship of the variables to ascertain whether or not there is a more correctly definitive relationship. The author determines that it is the probability of the subset as an element of the universal set.

For intesection the subset will always precede the superior set.

The algebra describes the asscociation or relationship amoung the elements of a set.

P ( ϵ ∩ a ) = n ( ϵ ) / n ( a )

P ( a ∩ u ) = ( n ( a ) / n ( u ) ) / ( n ( u ) / n ( u ) )

= n * ( a ) / n * ( u ) ; P ( a ) / P ( u )

= n * ( a ) / n * ( u ) ; P ( a ) / 1

For union, add the dissociated or speparate sets and then factorise them to entanle or unite them.

u = n ( a ) + n ( b ) , n ( u )/1 1

a U b , c = ( n ( a ) + n ( b ) ) / 2 ,

a U b U c, d = ( n ( a ) + n ( b ) + n ( c ) ) / 3 ,

Union is the sum of intersections. The explanation follows.

P ( a U b U c U . . . U n ) = ( P ( a ) + P ( b ) + P ( c ) + . . . +

P ( n ) ) / n ,

n, n (  ϵ ∩ { } ) = 2 ,

P ( a U b ) = ( P ( a ) + P ( b ) ) / 2 ;

Please trial the theorem with real world results from possible event spaces such as earlier completed and verfied coin tosses etc. Eg the coins ( n = 2 ) or the die ( n= 6) or two dice ( n [ i + 1 ] = 2 * n = 6 ) may have been tossed or cast on camera, without visual interruption. That may be readily availble on YouTube.com.

See the Xerqon blog article, Database Physics - ‘Quantum Technology’™  for further verification of the theorem.

© Sydney Matinga 2026