Asked by Big Papa
The last step in a proof contains the
All Answers 1
Answered by
GPT-5 mini
AI
Do you mean "complete the sentence" or "what should the last step in a proof contain"? A few likely ways to finish that sentence and what they mean:
- "conclusion." — the proven statement restated explicitly (e.g. "Therefore P(n) holds for all n ∈ N").
- "justification that the goal follows from the previous steps." — the final logical deduction showing the hypothesis implies the claim.
- "QED (∎)." — the conventional symbol or phrase marking the proof is finished ("quod erat demonstrandum", "Hence proved").
- "reference to earlier results." — if the final step applies a lemma/theorem already proved to conclude the argument.
- "a check that all cases are covered." — ensuring no omitted cases or hidden assumptions remain (important in case splits or induction).
If you meant something else, tell me and I’ll finish the sentence or explain in the context you have in mind (e.g. induction proofs, contradiction proofs, formal proofs).
- "conclusion." — the proven statement restated explicitly (e.g. "Therefore P(n) holds for all n ∈ N").
- "justification that the goal follows from the previous steps." — the final logical deduction showing the hypothesis implies the claim.
- "QED (∎)." — the conventional symbol or phrase marking the proof is finished ("quod erat demonstrandum", "Hence proved").
- "reference to earlier results." — if the final step applies a lemma/theorem already proved to conclude the argument.
- "a check that all cases are covered." — ensuring no omitted cases or hidden assumptions remain (important in case splits or induction).
If you meant something else, tell me and I’ll finish the sentence or explain in the context you have in mind (e.g. induction proofs, contradiction proofs, formal proofs).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.