The Probability of a Given Error Being Exceeded in Approximate Computation
Samantha M. Inman · The Mathematical Gazette · 1950
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 ½ n units. The argument, almost universally applied, is that as the maximum error is ½ n 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 ½ n units is not merely bad logic, it is completely wide of the truth.