In this blog post, we're going to explore some properties of division of integers, and more specifically, a concept called the greatest common divisor. The greatest common divisor, or $\gcd$, is the largest positive integer that divides a pair of …
In this blog post, we're going to talk about a very interesting application of functions called the piegonhole principle. The underlying idea is very simple. Imagine we have some quantity of letters $m$, and a number of pigeonholes $n$. If the number …
You're probably familiar with what a function is: it's a formula or rule that describes a relationship between one number and another. For example, the function $f(x) = |x| + 1$ describes the relationship between a number and its absolute value plus …
An important way of thinking about a set is seeing how the elements are related to each other. For example, some elements of a set might be less than others, some might be equal, and some might belong together because they are even. For example, …
This blog post caps off our series on mathematical induction by discussing another type of induction: proof by strong induction. This is a type of induction that we need to use it doesn't make sense to start from our base case. Instead, we have to …
