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Commuting and Noncommuting Infinitesimals
Mikhail G. Katz and Eric Leichtnam
The American Mathematical Monthly
Vol. 120, No. 7 (August–September 2013), pp. 631-641
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.07.631
Page Count: 11
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Abstract Infinitesimals are natural products of the human imagination. Their history goes back to Greek antiquity. Their role in the calculus and analysis has seen dramatic ups and downs; they have stimulated strong opinions and even vitriol. Edwin Hewitt developed hyperreal fields in the 1940s. Abraham Robinson’s infinitesimals date from the 1960s. A noncommutative version of infinitesimals, due to Alain Connes, has been in use since the 1990s. We review some of the hyperreal concepts, and compare them with some of the concepts underlying noncommutative geometry.
Copyright the Mathematical Association of America 2013