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Question 4892: Inclusive Natural Successor Window

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

R0008-04892 · q-20261008-advance-20261011-r01-natural-number-0017

Original question and givens

N includes 0. n=15, k=7. List the complete ordered window beginning at n and applying the successor k times.

  • G001 — N includes 0. n=15, k=7. List the complete ordered window beginning at n and applying the successor k times.

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

N={0,1,2,...}

After

0 belongs;negative and nonintegral rational values do not

Conditions: none

This convention includes0 in N;distinguish membership,rational values,partial predecessors and closed intervals.

Step identifiers and dependencies

Rule: natural_zero_convention · Uses: G001

S002 · implies

Before

initial n=15;successor count k=7

After

[15]

Conditions: none

Include the initial point;even k=0 has one item.Do not apply a successor before starting the list.

Step identifiers and dependencies

Rule: successor_window_initial · Uses: G001, S001

S003 · calculation

Before

successor step1 := sum(15, 1)

After

successor step1 = 16

Conditions: none

Add1 to the preceding natural at each step.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S002

S004 · calculation

Before

successor step2 := sum(16, 1)

After

successor step2 = 17

Conditions: none

Add1 to the preceding natural at each step.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S003

S005 · calculation

Before

successor step3 := sum(17, 1)

After

successor step3 = 18

Conditions: none

Add1 to the preceding natural at each step.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S004

S006 · calculation

Before

successor step4 := sum(18, 1)

After

successor step4 = 19

Conditions: none

Add1 to the preceding natural at each step.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S005

S007 · calculation

Before

successor step5 := sum(19, 1)

After

successor step5 = 20

Conditions: none

Add1 to the preceding natural at each step.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S006

S008 · calculation

Before

successor step6 := sum(20, 1)

After

successor step6 = 21

Conditions: none

Add1 to the preceding natural at each step.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S007

S009 · calculation

Before

successor step7 := sum(21, 1)

After

successor step7 = 22

Conditions: none

Add1 to the preceding natural at each step.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S008

S010 · implies

Before

[15, 16, 17, 18, 19, 20, 21, 22]

After

7 successors and 8 total entries

Conditions: none

Applying k successors produces k+1 entries,retaining the full order and initial point.

Step identifiers and dependencies

Rule: successor_window_length · Uses: G001, S009

Reverse checks

  • S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S009 · premise_and_result_audit — Recompute successor step7 with exact rational arithmetic, not rounded decimals.
  • S008 · premise_and_result_audit — Recompute successor step6 with exact rational arithmetic, not rounded decimals.
  • S007 · premise_and_result_audit — Recompute successor step5 with exact rational arithmetic, not rounded decimals.
  • S006 · premise_and_result_audit — Recompute successor step4 with exact rational arithmetic, not rounded decimals.
  • S005 · premise_and_result_audit — Recompute successor step3 with exact rational arithmetic, not rounded decimals.
  • S004 · premise_and_result_audit — Recompute successor step2 with exact rational arithmetic, not rounded decimals.
  • S003 · premise_and_result_audit — Recompute successor step1 with exact rational arithmetic, not rounded decimals.
  • 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

[15, 16, 17, 18, 19, 20, 21, 22]

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: ec05f0f6474d6fa286734ef3c2c61c19041796bab7fa03734204361496d3c4cf
  • candidate record SHA-256: 7838f444bff07abacdc97baa1f3d8b768de17fef156ce09ee2621a6ee2ca9622
  • semantic review receipt SHA-256: b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289
  • question-first witness SHA-256: caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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