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R0070-35519 · q-20260914-arithmetic-domain-boundary-0019
In the number system N, including 0, how should the result of 9/0 be classified?
G001 — In the number system N, including 0, how should the result of 9/0 be classified?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-arithmetic-domain-boundary, [a, b, number_system, operator, state]]
After
derived = [arithmetic, 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 = [9, 0, /]
After
derived = [N={0,1,2,...}]Conditions: none
FIRST fix THIS question’s N={0,1,2,...} and nonnegative integral operands.The question asks for a value WITHIN this system,not a silent change to integers/rationals.
Rule: Natural_arithmetic_GIVEN_N_includes0_and_operands · Uses: G001, S001
Before
source roles = [9, 0]
After
derived = [zero_divisor, zero divisor，no ordinary numerical result]
Conditions: none
Zero has no multiplicative inverse:0x=a has no solution for a≠0 and is nonunique for a=0.Thus even0/0 has no ordinary unique quotient;NO division is evaluated in this branch.
Rule: Division_ZERO_never_evaluate_including0over0 · Uses: G001, S002
Before
source roles = [zero_divisor, zero_divisor]
After
derived = [zero divisor，no ordinary numerical result]
Conditions: none
Check state metadata ONLY AFTER deriving the result;never use it instead of calculation.Keep zero divisor,nonclosure and N-valued result distinct.
Rule: Arithmetic_STATE_checked_AFTER_derivation · Uses: G001, S003
S004 · 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.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.Zero divisor; no ordinary numerical result
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: d488892ced7d0258d2bbc7c2a7e35aca45867a9465922ca138d4f1d05448d3accandidate record SHA-256: bec418ce03f6bf1c8b9d66eec9d947edf8258ce9d80e2d094abcfcceac687052semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dabLean: NOT_RUN · human review: NOT_PERFORMED