Since reading Paul Ormerod’s Why Things Fall Apart I have been thinking a bit more about this
Price points offer a good day to day example of how a number may take only one of an ill-defined set of values – ill-defined that is in the sense that one might list them, but not state any mathematical formula by which one could determine if a number is a member of the set. With the possible exception of all numbers whose last 2 digits are 99
In some areas the membership rule is not rigid, but there is a distinct bias towards some numbers. When the British population census used to ask merely for a respondent’s age numbers ending in 0 or, to a lesser extent, 5 were over-represented
Others that have been reported include a bias towards even numbers in estimates of gestational age, towards numbers ending in 5 for blood pressure, & I once read a passionate denunciation of the practice of choosing from only certain numbers of μg or mg for dosages of pharmaceutical drugs once they reach the market
Some of these do not matter at the level of the individual, but could potentially affect the calculations of statistical relationships, in a way that could mislead. Then changes in the technology of measurement - eg new electronic blood pressure monitors - could upset things all over again
Most of the time, especially in these days of computers, we proceed quite happily assuming that all numbers are real & continuous, all our equations & techniques valid. Even when we know they are not, or learn the hard way, mostly we just settle for a pragmatic solution to the practical problem which faces us: What is the log of zero?
Once upon a time, maybe still, statisticians were advised to keep a test data set which could be run through any new computer software to check for unforeseen problems – or at least to find out about its bad habits – a bit like testing a new calculator for how it handles 1÷3x3
But there are holes in our number lines, planes or n-dimensional spaces which we cheerfully jump or fly over, hoping for the best
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