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R0070-35620 · q-20260913-natural-number-membership-0005
Under this OCME entry's convention that N includes 0, does 10 belong to N?
G001 — Under this OCME entry's convention that N includes 0, does 10 belong to N?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
source roles = [qf-natural-number-membership, [scenario, value]]
After
derived = [natural, null, null]
Conditions: none
Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules.
Rule: R70_SOURCE_bank_specific_interface · Uses: G001
Before
source roles = [10, int]
After
derived = [Yes, Yes, Yes]
Conditions: none
THIS entry’s N includes0.Check actual numeric type,integrality and nonnegativity.Zero belongs;negative,fractional and textual values do not.A noninteger is a LEGAL No,not an input to discard before classification.
Rule: Natural_membership_NUMERIC_integrality_not_string_regex · Uses: G001, S001
Before
source roles = [Yes, Yes]
After
derived = [Yes]
Conditions: none
N={0,1,2,...}is EXACTLY the nonnegative integers.BOTH conditions must hold;neither scenario metadata nor integer-looking strings determine membership.
Rule: Natural_membership_INTERSECTION_integer_AND_nonnegative · Uses: G001, S002
S003 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S002 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.Yes
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: e44aed3b91aa75abbf94a5e8af605eb22e5fb51663afe288567b704ab80f52c3candidate record SHA-256: 089701b0dcc7d8ebf0c0a958a45d23df84a65a345216a948e4b87b38de384751semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dabLean: NOT_RUN · human review: NOT_PERFORMED