Orders of ∞

The idea of infinity is easy to look over upon first glance. It can simply be defined as the idea that numbers go on forever and it is easy to end there. However, there are very developed and well-defined notions of infinity suggest that there are different orders and types of infinity which come with various properties. The consideration of all these are vital to our understanding of infinite quantities and especially in set theory. The exploration of these transfinite numbers Read More »

Differential Forms Part 1: Dimensions and Notation

Differential forms is a topic that, in some sense, extends ideas presented in vector calculus with more suggestive notation and geometric intuition into higher dimensions. The distinction may seem small and insignificant especially in the third dimension that we live in but its results and implications are quite elegant and can lead to nice formalization of certain results such as Stokes’ Theorem. Read More »