We were supposed to write about three "How to..." blog posts. I have some ideas, but they remain nebulous now: I could write a "How to..." post on "How to Be Good at Math at Any Level," or "How to Cope with Bipolar Disorder," or "How to Read a Person Like a Book." Of these three, the reading a person like a book will be the hardest for me. Indeed, such a post will likely be full of irony, since I read books better than people. So, without further ado, I present

How to Be Good at Math at Any Level

Introduction

Mathematics is a discipline; indeed, it is the discipline, since the word mathematics comes from the Greek mathein, or "to discipline." So, in order to be good at math, one needs to be a good disciple. We need to be able to listen or otherwise receive teaching, whether it be from a teacher or from nature itself. Humility is very important in mathematics, because we are bound to make mistakes. This is in contrast to the popular perception of math, in which everything has to be precise and, dare we say it, correct. Nothing can be further from the truth, for mathematics rests on nothing.

We begin with the empty set { }. Is the set something, or is it not? We assume that it contains nothing, so if there's nothing to talk about, then we are done. However, if the empty set is something, then we can construct another set containing it: {{}}, and from there another set with different elements, {{},{{}}}, and so forth. It is possible this way to construct the entire set of natural numbers N={0,1,2,3...}, and from the set of natural (counting) numbers N to construct the set of real numbers R. Obviously, the latter approach has more describing power than the former, but there is no way to truly distinguish between the two approaches, because we could just as easily say that nothing can contain nothing, and say that something is nothing.

Personally, I don't like such a nihilistic approach to mathematics, so I prefer to make distinctions between something and nothing, or make a distinction between a bag and its contents.

How do we become good at math? We need make as few assumptions as possible, so that we can maximize the number of propositions. This is every bit as true in the field of math as it is in real life. Preconceived notions more often than not hold us back.