**Other Possible Foundational Ideas: The Implied Continuity of Quasifinte Prime Numbers**

*07 July, 2012*

**L. Edgar Otto***The case is one of nonnecessity where a number in its role as a class or instance of primacy is established in intelligible isolation where we can define fundamental secessor to a number, or of mathematical induction of a series of such numbers or of the concept of cause as dynamic or just a fortious path by random higher ordinal succession. In this sense just as successors in ordinal transfinite orgins may not have a direct route to any one predicessor, so too in the quasifinite case of the intrinsic patterns and constants that involve quasication of natural structures and numbers- that these too are a state of nonnecessity or ateleological that is a teleology by sign inversion logical statement with the path defined then as the exception paradox that some state is possible as if necessary.

*A collection of such numbers may intelligibly form into patterns and implied orderings as classes of classes of which the structure may be coherent, isolated, and of predictive expression at any original choice of actualization.

*A creative particle may decay into several creative particles before the actual observation of energetic paths in quasic space before its actualization (materialization) into an intelligible systems of particle (and momenta) path count. From this view the structure may in a sense be nonnecessary as to the idea of some creative particle as assumed to be a unity or a multiplicity.

*(This conception may apply to political systems that holds the general context above the individual and unique balance of culture and inheritence in the persuit of theories of Liberty in an imperfect world of theory and its application to universals.)

*A number may be used as an alphabetic code regardless of the given sequence (beyond the usual ideas of ordinality) yet can be so ordered in a set of numbers based in the independence of the digits (to any base) in the reading and its direction and sub-loops and directions. As such it is a unified general philosophy of science in that ideas of a metalanguage are thus unique and intelligible as if the alphanumerics can be divided into that of creative number patterns in context and that context creative fields to which we find the simple idea of distinctions as to what is consciousness.

*In that we define place holders, the zero as in a sense independent and thus unique in its primal influence of nonnecessity, as algebraic... we can distinguish what is a number as the cooefficients or variable in the same alphanumeric interdimensional bases as intelligible. The level of function or the generator of function reflects this continuation of the basic evolving of these distinguished and unified in the quasifinite properties of number.

*As structure, actual or virtual, exact or representational, we can adjust as if in systems or contexts of useful numerical information models of entropy visualized in a directed system or logic of geometry as a purely numerical counting process.

*An arbitary sequence of digits so encoding or capable of various interpretations is nevertheless numerically unique and from this follows other foundational fundamental mathematical laws as they appear to evolve or be discovered in hierarchies we order as the number line names of such numbers. Such uniqueness can be experienced or observed in the physical actualities of nonnecessary space.

*With the natural laws of arithmetic and the exceptional axioms of the continuum hypothesis and that of choice we can see these as one set of axioms in vacuum and matter structure- even if not necessarily complete yet of a unique and independent sense of primacy as a fundamental law of the level of mathematics in question.

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