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Playing Diffy with real sequences

Published online by Cambridge University Press:  01 August 2016

K. Robin McLean
K. Robin McLean*
Affiliation:
Department of Education, PO Box 147, University of Liverpool L69 3BX
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Extract

The offer of real money is a powerful inducement to work at a problem. So when Sir Bryan Thwaites put £100 behind his conjecture about what happens when we repeatedly take positive differences of a sequence of rational numbers, I could not resist his challenge. My solution may not have been the first to reach him, nor the most elegant, but it was fun to do. In showing that any sequence of 2n such numbers would eventually reach a string of zeros, my argument (and the one given in) depended heavily on the fact that they were rational numbers. I couldn’t help wondering what would happen if we started with a sequence of real numbers.

Type
Articles
Information
The Mathematical Gazette , Volume 83 , Issue 496 , March 1999 , pp. 58 - 68
Copyright
Copyright © The Mathematical Association 1999

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References

1. Thwaites, B., Two conjectures or how to win £1100, Math. Gaz. 80 (March 1996) pp. 35–36.Google Scholar
2. Thwaites, B., Letter to the Editor, Math. Gaz. 80 (July 1996) p. 420.Google Scholar
3. Pompili, F., Evolution of finite sequences of integers, Math. Gaz. 80 (July 1996) pp. 322–332.Google Scholar
4. Ciamberlini, C. and Marengoni, A., Su una interessante curiosita numerica, Periodiche di Matematiche 17 (1937) pp. 25–30.Google Scholar
5. Rogers, D.G., Letter to the Editor, Math. Gaz. 81 (March 1997) p. 127.Google Scholar