Groupoid Cardinality and Egyptian Fractions

Abstract

SummaryTwo very new questions about the cardinality of groupoids reduce to very old questions concerning the ancient Egyptians’ method for writing fractions. First, the question of whether any positive real number is the groupoid cardinality of some groupoid reduces to the question of whether any positive rational number has an Egyptian fraction decomposition. Second, the question of how many nonequivalent groupoids have a given cardinality can be answered via the number of distinct Egyptian fraction decompositions.