Philosophical and Mathematical Foundations of a Number Generating System: The Lu-Number System

This work sets out to theoretically construct a platform for allowing for the systematic generation of numbers (in any base) from physical or non-physical entropy sources --- ultimately, the purpose is to support the generation of numbers conforming to some preferable distribution, especially the uniform distribution, and thus random numbers. The core of this platform is based on a means of reading raw information from the source of entropy, and then encoding it using an abstract number system we call the Lu-Number System (LNS). Then, starting from that basic LNS number generator --- which shall produce numbers in the LNS base --- lu-Base, more sophisticated generators can then be built atop that --- like those meant to generate higher-order numbers or numbers in common bases such as binary, decimal or base-36. We can then be able to leverage LNS to implement more useful generators such as Random Bit Generators (RBGs), True Random Number Generators (TRNGs) as well as Cryptographically Secure RNGs (CSRNGs) among others. At the moment, this is the condensed edition of that work; thus prepared so it can readily be applicable/usable in theoretical and practical contexts across mathematics, philosophy, but also in various sciences and mathematical disciplines --- especially in Computer Science, its originally intended audience.