Publication Date

Spring 2017

Document Type


Degree Name

Master of Science



First Advisor

J. Christopher Tweddle, Ph.D.

Second Advisor

Andrius Tamulis, Ph.D.

Third Advisor

Jing Zhang, Ph.D.


Following the literature from the origin of Set Theory in the late 19th century to more current times, an arithmetic of finite and transfinite ordinal numbers is outlined. The concept of a set is outlined and directed to the understanding that an ordinal, a special kind of number, is a particular kind of well-ordered set. From this, the idea of counting ordinals is introduced. With the fundamental notion of counting addressed: then addition, multiplication, and exponentiation are defined and developed by established fundamentals of Set Theory. Many known theorems are based upon this foundation. Ultimately, as part of the conclusion, a table of many simplified results of ordinal arithmetic with these three operations are presented.