Complete nonempty duplicate-free finite integer list elements=[14, -15, 66] in original list order. Give (elements,injection_pairs,injective?,finite_implies_at_most_countable). Each injection pair is [element,zero_based_position].
G001 — Complete nonempty duplicate-free finite integer list elements=[14, -15, 66] in original list order. Give (elements,injection_pairs,injective?,finite_implies_at_most_countable). Each injection pair is [element,zero_based_position].
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.
DECLARED complete finite integer set in original list order=[14, -15, 66];length=3
After
nonempty duplicate-free registered family;original order retained;empty-set countability not denied
Conditions: none
Completeness is the declared set premise,not inferred for an unknown universe from samples.Keep order and reject duplicates rather than sorting or deduplicating.The family's empty-list rejection is an interface limit,not denial of empty-set countability.
Send each element to its unique zero-based position.Equal positions mean the same list entry,so this is injective into the naturals.The direction is element to position,opposite to enumeration.
Send each element to its unique zero-based position.Equal positions mean the same list entry,so this is injective into the naturals.The direction is element to position,opposite to enumeration.
Send each element to its unique zero-based position.Equal positions mean the same list entry,so this is injective into the naturals.The direction is element to position,opposite to enumeration.
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.