The **Cantor set** is a fractal that is obtained by repeatedly removing the middle third of a segment. Start with the closed interval . Remove the open interval to obtain , i.e. two disjoint closed segments. Remove the middle thirds of those two segments, and you end up with four disjoint segments. After infinitely many steps, the result is called the **Cantor set**. The diagram below is only an approximation after a finite number of steps.

# #3: Rings

The point of this post is to provide examples and non-examples for the following ring classes:

**Ring****Commutative Ring****Integral Domain****Integrally Closed Domain****Unique Factorization Domain (UFD)****Principal Ideal Domain (PID)****Euclidean Domain****Field**

# #2: Epic Morphisms

Given that the name of this site is **Epic Math**, I felt I should write about a topic where the word **epic** is a technical term! It is hardly surprising that such a term exists, as many otherwise non-mathematical words such as **almost**, **simple**, **open**, **connected**, **regular**, **normal**, **field**, **ring**, **onto**, **map**, **twin**, **lucky**, and even **sexy** have technical definitions.

**Category Theory**

The term **epic** is found in **category theory**, which is an extremely abstract branch of mathematics that formally deals with many other fields of math. It is so strange that some mathematicians have labeled it “abstract nonsense.”

# #1: De Bruijn Sequences

**Sequences of 0’s and 1’s**

Suppose I want to write a sequence of 0’s and 1’s that contains every possible 2-letter subsequence. This means somewhere in my sequence I need 01, 10, 00, and 11.

Obviously, gluing them all together gives a valid sequence:

**01100011**