The small council

Cute abstract argument for why the hands don't meet 24 times in 24 hours but I think the count done doesn't seem applicable for a very rigorous inquiry way though.

In your count you make the statement that in 12 hours we have always 11 times when the hands coincide but this is true just for the intermediary rotations between the first and the last moment of the periods of 12 hours and depending how you count you can have either the first or the last cycle having 12 hours if you accept the last moment of the last rotation as included in the period of 12 hour or not because the total accumulation of the periods of times when the hands meet is the union of all the repeating times minus the intersections. Therefore it might be said that the intersection of 2 consecutive sets of periods of 12 hours from all the sequences of intersections of such periods includes just the intermediary last moments of sets between the first and last rotations done but not the last meeting in the last of the coincidence for which the 11 times rule doesn't necessary apply though. Therefore the argument works not because in every 12 hours always the number of intersections will be 11 but because you consider a special case in which you conventionally eliminate the last moment of the 12 hours being completed as not part of the interval of time. As such concluding from this sort of characteristic found that there always are a number of 11 meetings between the hands is a little erroneous. Nonetheless such an argument works and is pretty ok but it's not a rigorous abstraction anyway.