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Question 34087: Minimum and Maximum of a Finite Real Set

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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R0067-34087 · q-20261005-advance-20261006-r01-order-relation-0037

Original question and givens

Under the usual real order, the explicit finite nonempty set has elements {-11, 0, 13}. Give (minimum, maximum).

  • G001 — Under the usual real order, the explicit finite nonempty set has elements {-11, 0, 13}. Give (minimum, maximum).

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-order-finite-extrema, [operation, values]]

After

derived = [finite_extrema, no-invented-domain]

Conditions: none

Check THIS bank’s keys/operation/domain:legacy table underscores,MOD50 local hyphens;permissive BASE data acquires no unknown-field restriction.Keep Number.isInteger and SAFE source guards distinct,while preserving ORIGINAL JSON number representations.

Step identifiers and dependencies

Rule: R67_SOURCE_specific_keys_operation_domain_and_numeric_bank · Uses: G001

S002 · implies

Before

source roles = [[-11, 0, 13]]

After

derived = [[-11, 0, 13], [[-11, Yes], [0, Yes], [13, Yes]], -11, 13]

Conditions: none

This is a NONEMPTY finite SET of at most100 DISTINCT elements,not an observation multiset.Audit min≤x≤max for EVERY element and attainment at both endpoints.A singleton has equal extrema;the empty set is outside THIS protocol.

Step identifiers and dependencies

Rule: Order_FINITE_nonempty_DISTINCT_set_ALL_extrema_bounds · Uses: G001, S001

Reverse checks

  • S002 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
  • S001 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.

Result

(-11, 13)

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: 37001e74fd3b9fa3c4ba2a1c7fb06b8320530072dba40f3ffaa9dd17bebab496
  • candidate record SHA-256: 0432d639a76297ce577828c71d1a5f7adedd31c3b11709c70faed612c7fe6d1e
  • semantic review receipt SHA-256: c89efa383b67bb2cf25bcf16160b9f5f614bbe5e5e791f4d7f58234d17a3371c
  • question-first witness SHA-256: 12766d451c5375842b4fc2843ae94807ec55f15763a916558026912a13873d57
  • Lean: NOT_RUN · human review: NOT_PERFORMED
Same-source full JSON