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Mathematical Induction: A Recurring Theme

Published online by Cambridge University Press:  22 September 2016

Paul Ernest*
Affiliation:
Bedford College of Higher Education, Bedford

Extract

The great mathematician Henri Poincare [1] described the method of proof by mathematical induction as mathematical reasoning par excellence. Induction is, undoubtedly, a method of great significance for mathematics. Unfortunately, induction is also a rather complicated form of proof. Furthermore, it is taught in schools at sixth form level. In fact, it is probably the only method of proof explicitly taught in British schools. Perhaps it is not surprising that some students find the method difficult to apply. In view of the importance and difficulty of the method, mathematical induction is worthy of further attention. In this article, the history and equivalents of mathematical induction are discussed.

Type
Research Article
Copyright
Copyright © Mathematical Association 1982

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References

1. Poincaré, H., Science and hypothesis. Dover (1952).Google Scholar
2. Heath, T. L., The thirteen books of Euclid’s elements (2nd ed.). CUP (1926).Google Scholar
3. Boyer, C. B., A history of mathematics. Wiley (1968).Google Scholar
4. Edwards, H. M., Fermat’s last theorem. Springer (1977).CrossRefGoogle Scholar
5. Smith, D. E., A source book in mathematics, volume 1. Dover (t1959).Google Scholar
6. Dedekind, R., Was sind und was sollen die Zahlen? Brunswick (1888).Google Scholar
7. Peano, G., Arithmeticesprincipia, nova methodo exposita. Turin (1889).Google Scholar
8. Woodall, D. R., Inductio ad absurdam? Mathl. Gaz. 59, 6470 (1975).Google Scholar