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Question 5055: Normalized Finite Set Enumeration

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

R0009-05055 · q-20261008-advance-20261011-r04-set-0005

Original question and givens

The raw integer list is entries=[4, -4, 0, 4]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.

  • G001 — The raw integer list is entries=[4, -4, 0, 4]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.

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

raw integer list=[4, -4, 0, 4]

After

extensional set=[-4, 0, 4]

Conditions: none

A set depends on its elements;deduplication and numeric ordering do not change membership.The original list is retained as source.

Step identifiers and dependencies

Rule: set_extensionality_normalization · Uses: G001

S002 · implies

Before

[-4, 0, 4]

After

one occurrence per element;empty set stays[]

Conditions: none

Repeating an element does not create more elements,and input order is not a set property.The empty list represents the empty set.

Step identifiers and dependencies

Rule: duplicate_order_invariance · Uses: G001, S001

Reverse checks

  • S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

[-4, 0, 4]

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: e9101aa5b4f1faafc765e085d556cfb6ea10fd5595d1d43f892a64b12f21f047
  • candidate record SHA-256: ad0be0890a51c5ab6db13bf6c20623e93141acc1331bfdf1d90214c7c9992f45
  • semantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56
  • question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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