If there is one thing this pandemic has taught us, then it is that few people truly understand exponential growth. This post is an attempt to explore this magical function with minimal prerequisites.

Probability theory is best understood through the lense of “the expected value”. We are fundamentally trying to understand what we can expect so the expected value is a great place to start

Linear functions define matrix multiplication and make matrices and linear functions effectively interchangeable.

Let’s say we want to approximate a function $f$. In an area around $a$ the value $f(a)$ is probably a decent approximation for $f(x)$.

We want to find $a_1$ and $a_2$ using only $p$ and $q$

While most programming languages use 0-based indexing some people are not convinced that this is a good thing and not just the legacy of the language C. They argue that starting to index with one is more intuitive than starting to index with zero, and that there is no good reason to use 0-based indices besides pointer arithmetic which should not be of concern to higher level programming.

And to be fair, proponents of zero based indexing have mostly failed to provide a convincing argument for their preference (Dijkstra’s range argument aside). To remedy this, I am going to present 5 arguments for 0-based indexing and address the intuition argument of 1-based indexing.