Previously: Part 8. Next: Part 10. It’s the penultimate week of the course, and up until now we’ve abstained from using the axiom of choice. But this week we gorged on it. The section I most enjoyed ...

every family of well ordered sets has a least member — informally, “the well ordered sets are well ordered”; ...

for all infinite sets X X and Y Y. Proving this required most of the concepts and results from the second half of the course: well ordered sets, the Cantor–Bernstein theorem, the Hartogs theorem, Zorn ...

Thurston gave a concrete procedure to construct triangulations of the 2-sphere where 5 or 6 triangles meet at each vertex. How can you get the icosahedron using this procedure? Gerard Westendorp has a ...

This is the homepage for the UT Geometry and Quantum Field Theory Seminar. At the organizational meeting we will flesh out the details of our plans for the semester. Below are some suggestions to get ...

Nov 6, 2024 17:32 The photo shows a hexagonal antiprism. The diagram in the photo has two red vertices (or rather, a red vertex ...

Nov 7, 2024 00:45 Here’s a way to argue that Gerard’s solution to my puzzle is correct. Thurston showed that any star of the ...