MATH.2:1 - Problem frame

Use this pattern when you want to treat several mathematical objects as one because a working question appears not to distinguish them. You still intend to apply operations to the resulting classes. The recurring difficulty is that two apparently interchangeable inputs can produce different classes of output, or permit different next operations.

Start with the proposed identification and one operation the receiver will use. Find two identified inputs and apply that operation. A differing output class, or availability after only one input, is already a useful counterexample. Repair the identification or change the intended use before calculating with the classes.

The method constructs a quotient: a set of equivalence classes with operations inherited from the original objects. You need elementary sets, relations and functions. It applies to specified total operations, and to partial operations under the additional domain condition in :4.3. When individual objects already support the question economically, use them directly.