Set theory is the field of study surrounding sets, and in this particular development, the study of sets as they relate to the foundation of mathematics and the construction from sets of a workable substitute for the concept of number. This work builds a theory of cardinal numbers using nothing but basic logical operations along with the primitive notions of set and membership. This is accomplished in four parts: the development the Zermelo-Fraenkel Axioms of set theory; the introduction of fundamental concepts regarding sets and the construction of the ordinal numbers using the axioms introduced; the development of three additional fundamental concepts in set theory; and the description of the concept of cardinal numbers as a construction analogous to natural numbers along with the development of basic arithmetical operations on both the ordinal and cardinal numbers.
Sizek, Philip H., "Set Theory: Building Numbers From Nothing" (2015). Senior Independent Study Theses. Paper 6560.
Set Theory, Zermelo-Fraenkel, Ordinals, Cardinals
Bachelor of Arts
Senior Independent Study Thesis
© Copyright 2015 Philip H. Sizek