MMP.10:2 - Problem

A convenient variable can leave out the possibility that matters. A single interval cannot represent an activity that may pause. A membership bit cannot record repeated membership. Coefficients of a straight line cannot describe every continuous curve. These restrictions may be useful, but they change which cases the formulation can answer for.

Representation can also add possibilities. A table intended to describe a function can allow two values for one argument unless its conditions exclude that case. Extra fields can create several records of the same object. A calculation over those records can then answer a different counting or probability question.

The difficulty is to construct the mathematical expression of the intended possibilities, including their joint restrictions and the requested result. Solving the resulting equations addresses the problem only after that construction has been made.