# what a system is

**What a formal system is**

A system is a rulebook with two parts: a starting list of statements accepted without proof (axioms, like “every number has a next number”), and rules for deriving new statements from old ones. A proof is a chain of steps from the axioms using only those rules.

The standard system for numbers is called Peano arithmetic.

Connects to:
- [primes: provable](https://mapideas.org/i/s_primes)
- [the conditions](https://mapideas.org/i/th_cond)
- [Gödel](https://mapideas.org/i/godel)

Source: https://mapideas.org/i/s_sys · open on the map: https://mapideas.org/#s_sys