What is Set Theory?

Set Theory · Axiom Academy

Discover the fundamental language of mathematics by collecting objects into groups. Step 1: Collecting Things Together Click on items below to add them to your collection. What happens when you group objects together? Now let's explore the most fundamental question in set theory: does an element belong to a set? Given the set B = , , , , click items to test membership: Step 3: Sets Can Contain Anything! Explore different types of sets. Click each button to see what kinds of elements sets can contain. Click a button above to explore Add or remove elements and watch the size of the set change. What patterns do you notice? You've discovered the fundamental concepts that make set theory the foundation of all mathematics! Any well-defined collection of distinct objects forms a set. We write sets using curly braces: elements The relation "x ∈ A" (x belongs to A) is the most basic concept. Everything in set theory builds from this. The notation |A| counts how many elements are in set A. This leads to deep questions about infinity. The set with no elements, written ∅ or , is a valid and important set in mathematics.

This is the written version of the interactive lesson above. See the full Set Theory course.