Question 15852: Keep Enumeration Direction and Original List Order Explicit

Original question and givens

Complete nonempty duplicate-free finite integer enumeration elements=[1, 51, -2], zero-based index=1. Give (index,element,enumeration_pairs,finite_enumeration_complete). Enumeration pairs are [position,element], not the reversed injection pairs.

• G001 — Complete nonempty duplicate-free finite integer enumeration elements=[1, 51, -2], zero-based index=1. Give (index,element,enumeration_pairs,finite_enumeration_complete). Enumeration pairs are [position,element], not the reversed injection pairs.

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.

• mko-at-most-countable-set

Step-by-step derivation

DECLARED complete finite integer set in original list order=[1, 51, -2];length=3

nonempty duplicate-free registered family;original order retained;empty-set countability not denied

complete original ordered enumeration=[1, 51, -2];selected zero-based index=1

selected element=51;position_to_element pairs=[[0, 1], [1, 51], [2, -2]]

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

(1, 51, [[0, 1], [1, 51], [2, -2]], finite_enumeration_complete)

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.