A Theory of Number

For denumerability N of elements n, the probability P(a(f)) = a/n = 0 
for finite a. The problems also pertain at P(sub-N) = n/(n + n) = 1.
The issue is addition, where n + n = n, etc. Part of the paradox is
representational. High symmetry allows radial proximity, so that
@ = 2 is a circle, etc. The representation forces a limit function of
increasing density, with @2 expressible within any trigonometric arc, 
mod@. Transfinite numbers define orders of mapping. To 
conceptualize choice from sets @(N), points are assigned infinite sets, 
numerical universes multiplying to the touch, pointwise. The point 
itself cannot be chosen, since a finite choice cannot exhaust an infinite 
set. P(a(f)), for finite a and infinite sample space, is satisfactorily 0.
Each number a is renamable as @(N)-{a}: the universe less itself 
(a characteristic way of negatively reconstructing a mathematical
object) . We represent numbers as holes in an otherwise continuous 
mapping, as point discontinuities of @ fields. What are the properties
of such a mapping? Most telling is its probability theory, above: 
P(a) = 0, for all a, due to the fractallic density of the field. The object 
remains spatially opaque--the boundary condition of objecthood. Note: 
The opacity is perspective, by which numbers are characterized. The 
form of the distribution is combinatorial, so that the point appears
independent of its surroundings, projecting identity. The universe @(N) 
maps to every point, i.e. each element is deletable, by which it is