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- Jan 30, 2012

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This statement reminded me another article I saw a long time ago, which said something like, "If there is the youngest river boat captain in this country, it must be ...". Guess what? The set of captain's ages is well-ordered because the order is total and the set is finite. Therefore, if the set of river boat captains in this country is nonempty, then there exists a captain with the smallest age. Now, there is a possibility that there is more than one captain with exactly the same age. However, if ages are measured in hours and minutes and not just days, this is very unlikely. And if by "younger" we mean a non-strict, i.e., reflexive, relation, then this does not even matter. So, there does indeed exist the youngest captain.

Another article that comes to mind is from the wonderful Russian mathematical magazine "Quantum". It talked about another record in a 100 meters dash. All sport commentators were excited and asked: "Is there a limit to human capabilities?" "Poor commentators", said the magazine. "They did not know the monotone convergence theorem!"

Going back to the Armstrong's interview, I am wondering about the precise meaning of that statement. Surely he did not mean that if nobody uses doping, there would be no winner in Tour de France. Then what exactly did he mean, in your opinion?