In this entry, we establish more results about ordinals, including proving that every well-ordered set has the order type of an ordinal. We introduce transfinite induction, Cardinality, and use the Axiom of Choice to prove that every set can be well-ordered, among other results.

In this article we introduce and discuss all of the axioms of ZFC. We introduce Cartesian products, linear and well-orders, and ordinals.

In the previous entry, we introduced Rings and Fields. In this entry we continue our investigation. We will investigate structures that can be built on top of them. This entry will mostly involve grinding through fundamental proofs that are necessary for more interesting results which will come later.

In this entry we introduce rings and fields. We establish some of their basic properties.

In this article we combine some Linear Algebra with a bit of geometry to make some real-world calculations about finding the nearest line to two or more points on a map. We’ve also implemented a tool that uses those calculations to fit a great circle to two or more points on the globe. Check it out!