Question 5094: Complete Finite Powerset

Original question and givens

Finite integer set A=[-18, 0, 1, 18]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.

• G001 — Finite integer set A=[-18, 0, 1, 18]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.

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-set

Step-by-step derivation

raw integer list=[-18, 0, 1, 18]

extensional set=[-18, 0, 1, 18]

no elements processed

[[]]

processed subset=[];next element=-18

omit=[];include=[-18]

processed subset=[];next element=0

omit=[];include=[0]

processed subset=[-18];next element=0

omit=[-18];include=[-18, 0]

processed subset=[];next element=1

omit=[];include=[1]

processed subset=[-18];next element=1

omit=[-18];include=[-18, 1]

processed subset=[0];next element=1

omit=[0];include=[0, 1]

processed subset=[-18, 0];next element=1

omit=[-18, 0];include=[-18, 0, 1]

processed subset=[];next element=18

omit=[];include=[18]

processed subset=[-18];next element=18

omit=[-18];include=[-18, 18]

processed subset=[0];next element=18

omit=[0];include=[0, 18]

processed subset=[-18, 0];next element=18

omit=[-18, 0];include=[-18, 0, 18]

processed subset=[1];next element=18

omit=[1];include=[1, 18]

processed subset=[-18, 1];next element=18

omit=[-18, 1];include=[-18, 1, 18]

processed subset=[0, 1];next element=18

omit=[0, 1];include=[0, 1, 18]

processed subset=[-18, 0, 1];next element=18

omit=[-18, 0, 1];include=[-18, 0, 1, 18]

(2)^4

power-set cardinality = 16

[[], [-18], [0], [1], [18], [-18, 0], [-18, 1], [-18, 18], [0, 1], [0, 18], [1, 18], [-18, 0, 1], [-18, 0, 18], [-18, 1, 18], [0, 1, 18], [-18, 0, 1, 18]]

all 16 subsets in size-then-numeric-lex order

Reverse checks

• S019 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S018 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S017 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S016 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S015 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S014 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S013 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S012 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S011 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• 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 — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• 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

[[], [-18], [0], [1], [18], [-18, 0], [-18, 1], [-18, 18], [0, 1], [0, 18], [1, 18], [-18, 0, 1], [-18, 0, 18], [-18, 1, 18], [0, 1, 18], [-18, 0, 1, 18]]

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.