Question 7751: Every Declared Codomain Fiber and Missing Target

Original question and givens

Finite types start at 0: Fin(0)=∅→Fin(0), complete images=[]. Check the whole original total table before any candidate evaluation; empty-function properties depend on the declared codomain. Give (original images, all fibers in codomain order 0,…,m−1, missing targets, surjectivity eligibility). An empty codomain has an empty fiber list.

• G001 — Finite types start at 0: Fin(0)=∅→Fin(0), complete images=[]. Check the whole original total table before any candidate evaluation; empty-function properties depend on the declared codomain. Give (original images, all fibers in codomain order 0,…,m−1, missing targets, surjectivity eligibility). An empty codomain has an empty fiber list.

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-surjective

Step-by-step derivation

n=0;m=0;images=[]

all original inputs and outputs form a typed total table;labels start at0

phase=original;targets=[];fibers=[]

missing=[];surjective=Yes

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

([], [], [], Yes)

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.