tags : Math

95% of the numbers that you use were invented to solve equations. Probably the least important property of these things, mathematically at least, is their decimal expansion. Their corresponding equations are infinitely more vital.

I believe the fundamental problem (or confusion) here is that OP finds it difficult to believe that a rational number, which is a ratio of two finite integers, can have a representation which is infinite. This confusion is primarily due to the fact that most people try to think of a number and its representation as one and the same thing. However the concept of a number is different from the concept of representing it.

## Primitives

### Axioms

- Minimum necessary subset of rules
- Greek axioma, âthat which is self evidentâ

### Theorems

- We can call the derived rules theorems
- Greek theorema, âa proposition to be provedâ

### Symbols

- Symbols used in math are contextual
- Eg.
`0x20`

means 32 in Hex, but space in ASCII - So Symbols without the rules/context mean almost nothing.

## Peano

### Peanoâs Axioms

- 1st Axioms were given by Peano. (
`S`

is Successor Function)