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A Non-Commutative, Associative Operation on the Reals

Published online by Cambridge University Press:  03 November 2016

F. J. Budden
F. J. Budden*
Affiliation:
15 Westfield Avenue, Gosforth, Newcastle-upon-Tyne 3.
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Extract

At the Cambridge Conference, 1969, I proposed the following problem to several members:

Find a binary operation on the reals which is associative but not commutative.

Type
Research Article
Information
The Mathematical Gazette , Volume 54 , Issue 390 , December 1970 , pp. 368 - 372
Copyright
Copyright © Mathematical Association 1970

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References

page 369 note † Or should it be deceptively easy?

page 371 note #x2020; Nobody hates this sort of jargon more than I do [except the Editor; E.A.M.], but it has the advantages of being concise, meaningful, communication-orientated, and euphonistically modish.

page 371 note #x2021; In what follows it is understood that zero is excluded from the set of reals.