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Question 31826: Exact Factorial Value

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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← Question derivation index · Original question batch

R0062-31826 · q-20260926-factorial-exact-evaluation-0001

Original question and givens

Compute n! for the natural number n=0; give the answer as a decimal integer string.

  • G001 — Compute n! for the natural number n=0; 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.

Step-by-step derivation

S001 · implies

Before

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 dependencies

Rule: R62_EXACT_source_keys_domain_operation_form_AND_output_types · Uses: G001

S002 · implies

Before

source roles = [Factorial requested n, 0]

After

derived = [1]

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 dependencies

Rule: Factorial_COMPLETE_product_EMPTY0and1_are1_not_input_n64_cap · Uses: G001, S001

Reverse checks

  • S002 · 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.
  • 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

1

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: a88441b3e2b988b7b3c4d9542fb1d3f2ecb7f0899c73f065b0b30ddac2cd8dde
  • candidate record SHA-256: 393f70657d492aab3b9dff7224b845b40785200b5fbe15e6afa2d9381b710c28
  • semantic review receipt SHA-256: 963099ffc9f754069fdce6792949a85ed350472465eaceb3038fa8011cf672bd
  • question-first witness SHA-256: d7655324c5d11528e1af90b757384cebd3313e19dc5f6f5b9b8ea7624fb06f6f
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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