CHAPTERSELECT | In the first two sections we developed various numeration systems and naming schemes to provide guide posts across the infinitely vast field of finite numbers. This already allowed us to go way beyond any numbers we would need for practical purposes and was really no more than an exercise in how to construct number systems for their own sake. Despite this, it was found that continuing in an ad hoc manner leads to a great deal of confusion, making the way forward increasingly difficult and potentially meaningless.To move forward we must begin again with an eye towards generalization and pattern recognition. In this chapter we will begin to develop a "theory of recursive functions" which will allow us, in fairly short order to break free and completely transcend all of the numbers discussed in the previous two sections !!! Articles3.1.1 - Constructed Set of NWe learn about finite sets, infinite sets, and constructed sets. We then apply this theory to the notion of Natural Numbers to create a new theoretical framework from which to begin. 3.1.2 - The Fundamental FunctionsNext we define the four fundamental functions and apply this to our theory of constructed sets. 3.1.3 - Building basic operationsHere we'll build some basic operations from scratch. This will strictly be in the domain of Natural Numbers 3.1.1Alt - A New Paradigm (ON HIATUS)3.1.2Alt - Introduction to Functions (ON HIATUS)3.1.3Alt - Functions of a Single-Variable (ON HIATUS) 3.1.4Alt - Multi-Variable Functions, Arrays, and Higher Structures (ON HIATUS)3.1.5Alt - Generating New functions (ON HIATUS) 3.1.6Alt - Introduction to the Primitive Recursion (ON HIATUS) 3.1.7Alt - The Diagonal Method (ON HIATUS)3.1.8Alt - Instruction Tables and General Recursion (ON HIATUS)3.1.9Alt - Replicator Notations (ON HIATUS) |

home >