Here's a challenge of sorts, inspired by some previous discussions. You must choose a random number uniformly on the interval ##[0, 1]##. If the number is rational, someone wins a £1 million prize. If the number is irrational, no prize is won. It is your task to devise the method by which the random number is chosen and checked for rationality. All numbers between ##0## and ##1## must have an equal probability (density) of being chosen. What we know from probability theory is that the probability of a rational number being chosen is 0, but that it is still "possible", in some sense. My belief is that the challenge is impossible, although I am happy to be proved wrong.