10
Numbers, Sequences, and Series
”It’s like asking why is Ludwig van Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.”
— Paul Erdős
When I was about to take my first mathematical analysis course at the university, coming straight from high school, I wondered why we would spend several lectures on real numbers. At the time, I was confident in my knowledge and thought that I knew what numbers were. This was my first painful encounter with the Dunning–Kruger effect: the less you know, the more confident you are. Suffice to say, after a few classes, I was left confused about numbers, taking a while to finally understand them.
If you look at numbers under a magnifying glass, they become extremely complex. In this chapter, we are going to make sense of them. To look ahead and keep machine learning in our sights, consider...
