Suppose you have a calculator on which the only working keys are 3,6,+ and the decimal point. prove that the only numbers you can make this calculator display are of the form
3k/(10^p) for k ? z, p ? n; that is, show that the only numbers you can display are multiples of three with a decimal point inserted somewhere. hint: use the well-ordering principle. what set might it be useful to define a well-ordering on?