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The Probability of a Given Error Being Exceeded in Approximate Computation*

Published online by Cambridge University Press:  03 November 2016

S. Inman
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Extract

I will illustrate the kind of problem I am going to discuss by showing how it applies to the case of addition. Suppose we add a series of numbers, each correct to the nearest unit ; this may be tenths, hundredths or any other unit. The maximum error in the sum of n such numbers is ½n units. The argument, almost universally applied, is that as the maximum error is ½n units, the answer is unreliable to that extent. This is bad logic. Let us take an analogy from electricity. When a current is switched on the maximum current is reached only after a time which is infinity. Actually, after a very short time, the difference of the current from the maximum is negligible. Likewise to argue that the sum of n items is unreliable to the extent of ½n units is not merely bad logic, it is completely wide of the truth.

Type
Research Article
Information
The Mathematical Gazette , Volume 34 , Issue 308 , May 1950 , pp. 99 - 113
Copyright
Copyright © The Mathematical Association 1950

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Footnotes

*

A paper read before the London Branch of the Mathematical Association, 22nd February, 1947.

References

* A paper read before the London Branch of the Mathematical Association, 22nd February, 1947.