Explore related knowledge and questions →
← Question derivation index · Original question batch
R0009-05401 · q-20261008-advance-20261012-r01-mathematical-induction-0026
N is indexed from 0; this is an explicitly finite induction protocol, not a universal proof. a(0)=-2, a(k+1)=a(k)+(99), through=0. List a(0) through a(through), inclusive.
G001 — N is indexed from 0; this is an explicitly finite induction protocol, not a universal proof. a(0)=-2, a(k+1)=a(k)+(99), through=0. List a(0) through a(through), inclusive.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.
Before
natural indices start at0;finite induction protocol
After
index bookkeeping and finite values are not proofs of all P(n)
Conditions: none
Natural indices do not require nonnegative sequence values.Checking a finite range or a successor index does not supply proposition truth or an induction proof over all naturals.
Rule: finite_induction_claim_boundary · Uses: G001
Before
a(0)=-2;through=0
After
[-2]
Conditions: none
Start with the supplied initial value;through=0 retains only it.
Rule: recurrence_prefix_base · Uses: G001, S001
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.[-2]
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 2f4849764c6e263239583423d8d31d95db30402f3dda167e4e3f5be3d11a6258candidate record SHA-256: 9298aa01c30e3d611a7b44653c1fce4aae391c76a8a01a9a6c80f3b7efec6600semantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462Lean: NOT_RUN · human review: NOT_PERFORMED