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The Method of Infinite Descent and the Method of Mathematical Induction

Published online by Cambridge University Press:  14 March 2022

Harriet F. Montague
Harriet F. Montague*
Affiliation:
University of Buffalo
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Extract

The purpose of this paper may be found in the following quotation. “Whenever an argument can be made to lead to a descending infinitude of natural numbers the hypothesis upon which the argument rests becomes untenable. This method of proof is called the method of infinite descent; .... It would be interesting and valuable to compare this method with the method of mathematical induction.”

Type
Research Article
Information
Philosophy of Science , Volume 11 , Issue 3 , July 1944 , pp. 178 - 185
Copyright
Copyright © The Philosophy of Science Association 1944

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References

1 Dresden, Arnold, An Invitation to Mathematics (New York: Henry Holt and Company, 1936), p. 171.

2 For entire proof see: Reid, Leigh W., Theory of Algebraic Numbers (New York: The Macmillan Company, 1910), pp. 19–20.

3 Smart, Harold R., The Logic of Science (New York: D. Appleton and Company, 1931), p. 103.

4 All historical information given from this point on is taken from Bulletin of the National Research Council, #63, National Academy of Sciences (Washington, D. C., 1928).