# Question 31828: Exact Factorial Value

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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.

R0062-31828 · q-20260926-factorial-exact-evaluation-0003



## Original question and givens

Compute n! for the natural number n=2; give the answer as a decimal integer string.


- G001 — Compute n! for the natural number n=2; give the answer as a decimal integer string.





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





## Step-by-step derivation

S001 · impliesBefore

source roles = [qf-factorial-exact-evaluation, no-domain-field, exact_factorial, no-form-field]

After

derived = [[exact_integer_STRING]]

Conditions: none

Check THIS bank interface:BASE equations use form/domain;BASE events/complement have no operation;factorials have no domain.ext18 uses local hyphens,other legacy operations underscores.Do not force every answer into a tuple or fraction.

Step identifiers and dependenciesRule: R62_EXACT_source_keys_domain_operation_form_AND_output_types · Uses: G001





S002 · calculationBefore

Factorial requested n ORIGINAL factorial factor2 := mul(1, 2)

After

Factorial requested n ORIGINAL factorial factor2 = 2

Conditions: none

Use ORIGINAL operands and declared order for exact integer/rational arithmetic,not floats.Bounds are family-specific:do not revalidate derived values as RAW inputs or add blanket SAFE/n64 caps to BASE families.

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





S003 · impliesBefore

source roles = [Factorial requested n, 2]

After

derived = [2]

Conditions: none

Factorial multiplies the COMPLETE2..n factors;at n0/1 the empty product is1.Use arbitrary-precision integers,not Number/scientific notation or another family n64 cap.

Step identifiers and dependenciesRule: Factorial_COMPLETE_product_EMPTY0and1_are1_not_input_n64_cap · Uses: G001, S002









## Reverse checks


- S003 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
- S002 · premise_and_result_audit — Recompute Factorial requested n ORIGINAL factorial factor2 with exact rational arithmetic, not rounded decimals.
- S001 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.





## Result

2

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: 068133ae7c3beb03a9ac3ac44bf026541711fc09ea15cba3dd5174380bbd386c
- candidate record SHA-256: b51679253a668ab04f46510c91c78c2d8668e4c5a7520d8fd35a71f4e733a940
- semantic review receipt SHA-256: 963099ffc9f754069fdce6792949a85ed350472465eaceb3038fa8011cf672bd
- question-first witness SHA-256: d7655324c5d11528e1af90b757384cebd3313e19dc5f6f5b9b8ea7624fb06f6f
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260926-factorial-exact-evaluation-0003.json)