14 posts with this tag
If you cast your mind back to the blog post on relations, you might remember a concept called equivalence classes. These are a consequence of when we have an equivalence relation of a set, and they partition the set into mutually exclusive subsets. A …
In the last blog post, we talked about divisibility and the greatest common divisor, or $\gcd$. You might have been wondering already in that post what happens when two integers don't have any common divisors? Well, in this case, as 1 divides every …
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 …
