aquamongoose

Maybe because PhD programs in those fields already are free at every university (in fact, they pay you a stipend).

Axiom of choice assumes that you can always pick the best possible option, however you need to be able to account for your worst possible options as well. All mathematical optimization falls outside of classical logic.

Not sure what you mean here. The axiom of choice just says that the Cartesian product of a set of nonempty sets is nonempty. Can you explain what you mean by "best possible option" and "worst possible options"?

No: (ii) only holds when e1, e2 come from the original vector space (not the product).

His would be: Still much more productive with vi keys!

Yours would be: Still much productive with vi keys!

With regards to (2), this is one way of solving the problem. However, your solution uses O(n) memory (where n is the size of the linked list), and the tortoise-and-hare algorithm uses only O(1) memory. Here's how it works: http://en.wikipedia.org/wiki/Cycle_detection#Tortoise_and_ha...

True, but that's still O(n!), so the overall complexity doesn't change.

I think it's because a lot of his humor is self-deprecating, so many of his jokes are "on" him.