MATH.2:4.1 - Specify the carrier, operations and receiving question

Name the set A of objects and the operations to retain. An n-ary total operation f maps every tuple in A^n to an element of A. A partial operation has a stated domain D_f⊆A^n.

When an operation takes inputs from different sets or returns a result in another set, choose an equivalence relation on each participating set. Compare corresponding inputs under their sets’ relations and the resulting outputs under the output set’s relation. A transition on states and concatenation of paths are different operations; choose the one actually used by the proposed identification.

State the receiving question. For example, the receiver may need the parity of a sum, the cost of a continuation, or whether a next step is available. This determines which distinctions a useful quotient can lose.