The sphere spectrum
BID, Lisboa 2017
  1. Extensions of number systems
2. Negative numbers
3. Briefly on sheep
4. A trade deficit
5. Out in space
6. Ulla and Henriette live in RP
7. Negative sets
8. The sphere spectrum
9. Brave New World

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:

S->ZCollapsing each path component of S to a point gives a map mon cher Einstein

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