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It's only 0 as far as statisticians and cheap calculators are concerned. The number of N-digit numbers without 9s in them is much higher than the number of sim
by redthrowaway 15y ago
It's only 0 as far as statisticians and cheap calculators are concerned. The number of N-digit numbers without 9s in them is much higher than the number of similar (N-1)-digit numbers, it's just the proportion that falls. The probability isn't 0, it just asymptotically approaches 0, as the number of non-9-containing numbers approaches infinity.
In essence, the cardinality of the set of all numbers that do not contain 9 is infinity; the cardinality of the set of all numbers is infinitier. This despite the fact that both sets are countably infinite.
- neutronicus 15y agoCardinality is not the term you want to be using.
- redthrowaway 15y agoI can see how it's imprecise, but I'm struggling to find a better descriptor. "Size" doesn't really work.
- Dylan16807 15y agoThe way an infinitely unlikely but theoretically possible event is described is in fact 'probability 0'. Sure, in a specific finite range the chance is a specific positive number, but the overall chance is 0.