User:Average/Mathematics

So Posits and Definitions create the background in which mathematics stays useful and interesting (call this the philosophy of math, or metamathematics). Axioms are the light sources. Theorems are the objects illuminated thereby.

There are an endless and uncountable number of starting points to make an axiom in mathematics. Most aren't interesting. So a review of all axioms would be good, but before we can even go there, we have to define the domain. We do this using posits (read as a position).

Position: there's a quantitative and qualitative difference between spatial math (geometry) and analytical math (arithemetic). Note that this is before we even start talking about axoims, because we need to define our metamathematics before number and symbols make any analytical sense.

We will define the domain for arithemetic as Q, and geometry A. The reason for choosing Q, instead of N or Z will be explained later. These are so basic and core that they should be taught and the curriculum perfected for elementary gradeschool.

There's a solid metaphysics foundation on which to build a more defined mathematics. STUB

...and begin: