Question 5461: Finite Coverage and Next Uncovered Index

Original question and givens

N is indexed from 0; this is an explicitly finite induction protocol, not a universal proof. P(0) through P(9) have been checked individually. Give (number of covered P indices, number of adjacent steps, next uncovered target index).

• G001 — N is indexed from 0; this is an explicitly finite induction protocol, not a universal proof. P(0) through P(9) have been checked individually. Give (number of covered P indices, number of adjacent steps, next uncovered target index).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-mathematical-induction

Step-by-step derivation

natural indices start at0;finite induction protocol

index bookkeeping and finite values are not proofs of all P(n)

covered inclusive index count := sum(9, 1)

covered inclusive index count = 10

covered indices0,...,9

9 adjacent steps;next uncovered target=10

Reverse checks

• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Recompute covered inclusive index count with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(10, 9, 10)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.