| Containership Property of Space Space structure: 4 dimensional (the presence of matter established time, the 4th dimension) Space Capacity: unlimited Boundary Condition: unbounded Internal Risk: inherent risk in the number space is negligible External Risk: negligible Purpose: to provide a quantitative representation of quantities, directions and distances and a general foundation for the numerical analysis of phenomena. Identity of Occupants: numbers Numbers is the name given to specific symbols that have been mapped onto quantities via a one-to-one correspondence. Numbers were created by the configured energy of human thought . The concept of nothing is estalished and mapped onto a symbol ( in the decimal number system, the symbol is 0). The concept of a unit quantity is established and mapped onto a symbol ( in the decimal number system, the symbol is 1). Specific forces then act on these concepts to populate the number space. Forces Addition (incremental force) Subtraction (decremental force) Multiplication (serial incremental force) Division (serial decremental force). |
| Motions Motions in the number space are representations of motions in a priori space continuum. In other words, there is a one-to-one mapping between numbers and positions in space. There are various graphical representations of a number geometry. The rectangular or cartesian form of representation, represents practical 3-dimensional space with 3 perpendicular axes: X, Y and Z. The plane formed by the X and Y axes ( X-Y plane) represents ground zero while the Z-X plane and the Z-Y plane represent the spaces above and beneath ground zero. The point where the X, Y and Z axes intersect is called the origin and is represented as the point (0,0,0). In figure NG1, the point O is the origin. In general, a cartesian point A relative to the origin in a 3-dimentional space is represented as (x, y, z). This representation is called the cartesian coordinates of the point A |
| and it means that we can get to the point A by moving x units along the X axis, then Y units along a line parallel to the Y axis and then z units along a line parallel to the Z axis.
So, implicit in the number space are the concepts of direction and distance. Therefore, Quantity,
Direction and Distance (QDD) are fundamental concepts of number geometry.
The reference point does not always have to be the origin. It can be any point (a,b,c) in the number space. When this is the case,
the axes are said to be translated and the general point (x,y,z) becomes (x-a, y-b, z-c). The notion of direction and distance in a number space implies that there is a theoretical straight line (a ray) that can be drawn from the reference point to any other point in the space, and that this straight line makes an angle with the horizontal line through the reference point (horizontal inclination). The ray and its horizontal inclination are used to establish other forms of coordinate representations in the number space. The coordinates of the points on the suface of a sphere (spherical coordinates) are established using the radii of the sphere, and their horizontal inclinations. These other forms of coordinate representations can be translated to cartesian coordinates. Change A number space is changeable only by a redefinition of the mapping that established it. |
| An efficient number space is defined such that it is structurally fixed and able to accomodate the dynamism of the space it represents. Interactions /Groupings The number line which has Zero as its mid-point, connects all numbers. Its positive segment which contains numbers greater than zero extends to infinity (an exceedingly large number). Its negative segment which contains numbers less than zero extends to negative infinity. Numbers interact when the incremental and decremental forces are applied to them. The numbers of the number line can be grouped in many ways. Some of the important groups are: Integers or whole numbers , fractions, even numbers, prime numbers, rational numbers, irrational numbers and complex numbers. The axes X, Y and Z are number lines. Equilibrium A well-defined number space is stable. |
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