### Extensions of number systems

We are used to extensions of number systems
**Z <Q <R <C**.

These number systems are created by adding solutions to increasingly more complicated questions. Today, we're going in the opposite direction: there are number systems **more** fundamental than **Z**. This number scheme contains more concrete information, and hence manipulations become more involved, but encodes problems the integers hardly can speak about.
In order to do this, I must speak about *negative* sets (and * negative dimensional* vector spaces?)

Negative numbers