[FOM] Question on the number line

[Alasdair Urquhart]

John von Neumann suggested a resolution to these sort of
puzzles, in his paper "Operator Methods in Classical Mechanics",
Annals of Mathematics, Vol. 33 (1932), 587-642.   
The idea is to define an observable in classical mechanics
in terms of a certain algebra.  Operating over R^n,
we define the algebra of observables to be the family 
of Borel sets, but with the identification of sets that 
differ in a set of measure 0.  

This takes care of the Suarez puzzle, and also gets rid of
physically meaningless questions like: "Is the length of
this metal rod a rational number?"