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MATH.23:4.3 - State the proposed law and its answer form

Give the objects, domains, allowed operations, assumptions and proposed conclusion. In particular, make the quantifiers distinguishable. These statements ask different questions:

  • For each input, some construction has the property.
  • One construction works for every input.
  • Every admitted construction has the property.

A finite pattern of results can suggest a formula. Derive it from the generating operation, a recurrence, an invariant or another mathematical relation when possible. If that derivation is missing, retain the formula as a conjecture and identify the step that would establish it.

Say what would resolve the present question. An explicit construction, a characterization of all admissible cases, a bound, or a counterexample can open different next uses. A conjectured optimal construction needs both an attainable value and an argument excluding better ones when optimality is the required conclusion.

Check whether the proposed law is already a known result under another description. MATH.18 can compare representations. An available theorem can close this question and expose a more useful next one.