I’ve been thinking about AI for a while and its gotten to the point where I feel I have something to say about an hypothetical application of it to education in auto-graders etc.

I offer a bleak future in semi-jest and use it to extrapolate some truisms that may hold in the real world.

Smart Pointers, Dumb Idea

Wherein are described the spells of lambdas and overloading.

∫nake goes hssss

Quantales are a type of monoidal complete lattice, I give a class of quantales which are locally (ie. its down-sets are) in that same class – akin to what happens in the case of Locales, which are locally locales.

An interesting but simple consequence of set theory is that the complement of any countable set in any convex set remains path connected. We show this for the plane.

I give an almost complete proof of Gödel’s first incompleteness theorem, and give an idea of how to prove the second from the first.

Continuous functions from products of compact Hausdorf spaces to the real numbers factor through a countable sub-product of them. This is obtained through the Stone-Weierstrass theorem.