Atoms in Mathematics and Science, Part 3: Power Series

We’ve been talking about reductionism in the past couple of posts, and we’ll continue the story by discussing power series in this post. The idea behind reductionism in mathematics is to identify some elementary “objects” and to express a complicated “thing” in terms of the elementary things. The intention is either to make it easier … Read more

Atoms in Mathematics and Science, Part 2: Infinite-Dimensional Spaces

In a previous post we began to discuss the idea of a basis in mathematics. The examples given in that post are finite-dimensional vector spaces, and in this post we are going to generalize them by giving some examples of infinite-dimensional vector spaces. But before we do this, let’s play with some motivating examples not … Read more