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Article Title

Dominance Over ℵ

Abstract

This paper provides an overview of the b-dominance order over the natural numbers, ℵ, using the base b expansion of natural numbers. The b-dominance order is an accessible partially-ordered set that is less complex than the divisor relation but more complex than ≤; thus, it supplies a good medium through which an undergraduate can be exposed to the subject of order theory. Here we discuss many ideas in order theory, including the Poincare polynomial and the Mobius function.

Author Bio

Tyler Ball graduated from Pacific Lutheran University with a B.S. in Mathematics in May of 2013. He is currently working toward a Master's degree in Education at PLU, where he will graduate in June of 2014. He plans on working in the education field, but is still considering the possibility of a Master's or Ph.D. program for Mathematics in the distant future.

Daniel Juda graduated from Pacific Lutheran University with a B.S. in Mathematics in May of 2013. He is currently working towards a Ph.D. in Mathematics at the University of Arkansas and hopes to pursue a career in research.

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