On Double-Entry Bookkeeping: The Mathematical Treatment

21 Pages Posted: 9 Jul 2014

Date Written: July 7, 2014


Double-entry bookkeeping (DEB) implicitly uses a specific mathematical construction, the group of differences using pairs of unsigned numbers ("T-accounts"). That construction was only formulated abstractly in mathematics in the 19th century — even though DEB had been used in the business world for over five centuries. Yet the connection between DEB and the group of differences (here called the "Pacioli group") is still largely unknown both in mathematics and accounting. The precise mathematical treatment of DEB allows clarity on certain conceptual questions and it immediately yields the generalization of the double-entry method to multi-dimensional vectors typically representing the different types of property involved in an enterprise or household.

Keywords: double-entry method, group of differences, Pacioli group, T-accounts, multi-dimensional double-entry bookkeeping

JEL Classification: M4

Suggested Citation

Ellerman, David, On Double-Entry Bookkeeping: The Mathematical Treatment (July 7, 2014). Available at SSRN: https://ssrn.com/abstract=2463442 or http://dx.doi.org/10.2139/ssrn.2463442

David Ellerman (Contact Author)

University of Ljubljana ( email )

School of Social Science
Ljubljana, CA

HOME PAGE: http://www.ellerman.org

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