six faces of numbers

[AntonioLao]

The set of real whole numbers is {0,1,2,3,4,5,6,7,8,…,∞}. Minus the number 1 the set becomes a proper subset called the sieve of Diophantus. However, the proper subset {0,1,2,3,4,5} can be used to designate the six faces of a cube, a regular polyhedron which according to Euler’s formula V-E+F=2 satisfying the following given values: E=12, V=8, and F=6 or 8-12+6=2. E is the number of edges, V is the number of vertices, and F is the number of faces. In a game of chance, {0,1,2,3,4,5} can be used to mark the six faces of a six sided dice such that all opposite sides always add up to 5. There are three distinct pairs: (0,5), (1,4), and (2,3). Normally, as found in the casinos, 1 is added to the components of each pair and the opposite sums always add up to 7. The pairs are (1,6), (2,5), (3,4). It can be noted that the markings of a pair is independent of the marking of the other remaining 2 pairs. Arbitrarily, for the purpose of giving directional invariance properties, these pairs can be replaced with (left, right), (up,down), and (forward, backward) or (L,R), (U,D), and (F,B). Then the following eight directional invariance properties can be created such that both opposites never appear simultaneously in each directional property: LUF, LUB, LDF, LDB, RUF, RUB, RDF, and RDB. These comprise the eight directional invariance properties of physical reality. However, they do not specify their magnitudes. Magnitude can be specified by using again the three pairs: (0,5), (1,4), and (2,3). It is the minimum set whose opposite sums always add up to 5. Adding 1, give (1,6), (2,5), and (3,4) opposite sums always add up to 7. Continuous additions of unity give the sequence of odd numbers: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, to infinity. These define the infinite number of proper subset of the six faces of numbers

[Profpat]

Adding 1, give (1,6), (2,5), and (3,4) opposite sums always add up to 7.

Hi Antonio;

This is true in my Venn Diagram model why are those numbers opposite? I know they are opposite sides of dice.




You can see the opposites very easily using the I Ching trigrams, but I didn't know the arabic numbers were also opposite.

Best,

Pat

[AntonioLao]

why are those numbers opposite?

I think it has to do with spontaneous broken symmetry of left and right or top and bottom or forward and backward and the reason why time only flows in one direction in the space-time continuum of the universe.