Use complete finite domain size=22≥0 and codomain size=20≥1, with a total map understood but no particular map table supplied. Give (domain_count, codomain_count, domain_larger, collision_forced_by_size, general_reverse_implication_claim, boundary).
G001 — Use complete finite domain size=22≥0 and codomain size=20≥1, with a total map understood but no particular map table supplied. Give (domain_count, codomain_count, domain_larger, collision_forced_by_size, general_reverse_implication_claim, boundary).
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.
Retain the historical interface marker in the original snapshot while listing ordered source fields here,without JavaScript or external lookup.Field labels are not additional mathematical evidence,and No retains the source claim scope.
domain larger=Yes;size-forced collision=Yes;if a total map were injective,each fibre<=1 implies domain<=codomain
Conditions: none
If the source is larger but every fibre contains at most1 source,there can be at most codomain-many sources,a contradiction.So every total map collides.When the strict size premise fails,this premise does not force a collision;it is not an audit of an unspecified map.
ACTUAL size comparison=Yes;no given total-map array
After
general reverse implication CLAIM=No;domain<=codomain does not in GENERAL force a given map injective;special empty/singleton cases are not denied
Conditions: none
A constant map from2 points to2 points refutes the general reverse implication.This does not say every map failing the strict size premise collides.Empty/singleton cases may be injective by definition;the final No does not deny them.
S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
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
(22, 20, Yes, Yes, No, premise_guarantees_collision_but_converse_does_not_guarantee_injectivity)
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.