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Nate Hayes wrote:
>>When restricted to bounded intervals, the Level 1 arithmetic is >>closed and cancellative for addition, subtraction, multiplication >>and division with 0 not in the denominator. > >This is not the definition of a closed arithmetic. If you can get >an interval as a result, say [0,1], you mustn't remove it from the >possible inputs of an operation. At Level 2 its not.Do you mean that you have an operation at Level 2 with no corresponding operation at Level 1? This doesn't make sense.Sure it does. It all depends on the underlying axioms and definitions.
BTW, in the current P1788 model, the midpoint operation is a prefect example of this because it is not defined at Level 1!
Nate