The title indicates the content of this capsule. Among all finite semigroups, the set of probabilities that two elements commute is dense in [0, 1]. (This is in contrast to the fact that the corresponding probability for a non-Abelian group is never greater than ⅝).
Document Type: Miscellaneous
Publication date: November 1, 2008
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The College Mathematics Journal is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. CMJ publishes articles, short Classroom Capsules, problems, solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years.