# the triangle

**The triangle: checkable, complete, true**

There is one special system that is complete and fully true: take every true statement about numbers as an axiom. It exists, but nobody can write it down or check it, so it is useless as a rulebook.

Gödel says no system can have all three. Pure randomness gives up checkability and truth, and only gets completeness by luck.

Connects to:
- [unchecked system](https://mapideas.org/i/r_none)
- [what escape takes](https://mapideas.org/i/r_escape)
- [what true means](https://mapideas.org/i/tr_true)
- [the conditions](https://mapideas.org/i/th_cond)

Sources:
- [Wikipedia: True arithmetic](https://en.wikipedia.org/wiki/True_arithmetic)

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