### Brave New World

The operations we defined in **Σ** (union and cartesian product, corresponding to addition and multiplication), extend to
**S**, and we get a new number system lying **behind** the integers:
Collapsing each path component of **S** to a point gives a map

**S**-> **Z**
This map is pitifully forgetful: it forgets everything about a set except how many elements it had.
The mathematics over **Z** is rich, exciting and has a history spanning over millenia. The mathematics over **S** is richer, more exciting, and history has just begun!

Bjørn Ian Dundas
2017-07-21 14:40:56 UTC