# Question 35520: Arithmetic Number-System Boundary

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0070-35520 · q-20260914-arithmetic-domain-boundary-0020



## Original question and givens

In the number system N, including 0, how should the result of 0/0 be classified?


- G001 — In the number system N, including 0, how should the result of 0/0 be classified?





## 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-arithmetic-operations](https://ocme.evemisslab.com/en/mko/mko-arithmetic-operations/)





## Step-by-step derivation

S001 · impliesBefore

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.

Step identifiers and dependenciesRule: R70_SOURCE_bank_specific_interface · Uses: G001





S002 · impliesBefore

source roles = [0, 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.

Step identifiers and dependenciesRule: Natural_arithmetic_GIVEN_N_includes0_and_operands · Uses: G001, S001





S003 · impliesBefore

source roles = [0, 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.

Step identifiers and dependenciesRule: Division_ZERO_never_evaluate_including0over0 · Uses: G001, S002





S004 · impliesBefore

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.

Step identifiers and dependenciesRule: Arithmetic_STATE_checked_AFTER_derivation · Uses: G001, S003









## Reverse checks


- 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.





## Result

Zero divisor; no ordinary numerical result

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.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: d51e4c2c102fe914f20f76abc2a756d7a52c0aa247d67f561aaf22fa09e0b4cc
- candidate record SHA-256: c74a02040eca3f801efd31b84b480206d125de129f8bcced7ed2e739cca48115
- semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80
- question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260914-arithmetic-domain-boundary-0020.json)