Directed Sets

A directed set is a collection of elements with a special property: for any two elements, there is a third one that "comes after" or "follows" both of them. Think of it as a set where, no matter which two items you pick, you can always find a bigger or more advanced item that relates to both. This concept helps in advanced mathematics to analyze structures that grow or develop over time, providing a framework to understand limits and convergence without relying solely on sequences.