If I ask an adult to tell me what *3-5* is, there’s a good chance that they would tell me the answer is 2 without much thought. This kind of arithmetic is simple to us, since we’ve had to do it over and over again through elementary and secondary education. Even if we haven’t used mathematics in a long time, these questions are straightforward.

I remember when I first took a class in linear algebra, and we were talking about vector spaces. In addition to the definition of a vector space, we were also given multiple axioms that define what the structure of a vector space looks like. This included a bunch of boring things, like the fact that if you have a vector *v*, you should have a corresponding vector *-v* such that *v+(-v)=0*, where 0 is the zero vector. There are eight of these axioms, and together they describe exactly what can be called a vector space.