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Question 32544: Integer Membership

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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R0064-32544 · q-20260919-integer-membership-0019

Original question and givens

Does 18 belong to the integer set Z?

  • G001 — Does 18 belong to the integer set Z?

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-integer-membership, no-required-operation, no-required-domain, []]

After

derived = [[mathematical_membership_YesNo_STRING]]

Conditions: none

Legacy banks enforce their exact source keys/operation/domain.BASE integers retain metadata without treating it as an oracle.Distinguish NUMBER,string,fraction pair and vector equality formats;retain original bilingual data/AST/status.

Step identifiers and dependencies

Rule: R64_SOURCE_exact_legacy_interface_BASE_metadata_AND_output_roles · Uses: G001

S002 · implies

Before

source roles = [18, Yes]

After

derived = [Yes, 18/1, Yes]

Conditions: none

FIRST verify the raw string and Boolean flag against the declared ASCII syntax,THEN classify the exact value.The frozen No cases are genuine half-integers.A parser rejecting string1.0 does NOT prove real1.0 is outside Z.Ambiguous out-of-slice cases are not false mathematical No answers.

Step identifiers and dependencies

Rule: Integer_RAW_ASCII_syntax_flag_verified_SEPARATE_exact_numeric_value · Uses: G001, S001

S003 · implies

Before

source roles = [18, 18/1]

After

derived = [18, Yes]

Conditions: none

A reduced denominator1 means the value IS the integer n.Positive integers,zero and negative integers all belong to Z.This is not an appearance guess or a rewrite of original raw data.

Step identifiers and dependencies

Rule: Integer_EXACT_value_has_denominator1_signed_integer_definition · Uses: G001, S002

Reverse checks

  • S003 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S002 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S001 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.

Result

Yes

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: ed3bed92a1f4fe4a51c4cb262542cc6ef105d790b9bb3f40fba8839409dd5b9f
  • candidate record SHA-256: e70a4f8d57d73a6c85207197f0ea7fed9ab694a64ebd765afc0a0f364184acdc
  • semantic review receipt SHA-256: 8b9ea3ddfab468e9e3f0a0fc0f7682987d5e030be0d7c8860fd85df19cbe183b
  • question-first witness SHA-256: 066bfeab8fc279706861faade71b9a18a61a25235fc48700092f0488d2a6da6a
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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