B.5.TC:4.3 - Work the same case and align the answers

Choose a small case that exercises the disputed operation or distinction. Give each account the corresponding inputs, derive its answer, and express the answers in the terms of the working question. Explain the correspondence when the inputs or outputs have different forms.

For a mathematical application, compare the retained distinctions and operations. C.29.1 supplies the preservation argument when a result is to be transferred. For a physical application, keep the phenomenon, operating conditions and meaning of the predicted quantity aligned. For a computation, separate the mathematical formulation from approximation, numerical tolerance and execution.

Begin with an understood case so a transcription or implementation error can be found. Then use a changed case that exercises the claimed difference: a shared resource, a constraint, an intervention or another relevant variation. Derive a general relation when the intended conclusion ranges beyond the cases. A finite example establishes its own result; a counterexample can refute a general assertion whose premises it satisfies.

Agreement of reported numbers is informative only after their meanings and conditions are aligned. Conversely, different intermediate objects can lead to the same answer through an explained correspondence. Record only the derivation or explanation the receiving use needs; the comparison does not require a standard table or separate report.