This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.
This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20261008-advance-20261011-r04-set-foundations · 2026-10-08 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
The raw integer list is entries=[]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[0, 0]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[0]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [0].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[-2, 1, -2]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-2, 1]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-2, 1].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[3, -3, 0, 3]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-3, 0, 3]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-3, 0, 3].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[4, -4, 0, 4]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-4, 0, 4]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-4, 0, 4].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[5, -5, 0, 5]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-5, 0, 5]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-5, 0, 5].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[6, -6, 0, 6]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-6, 0, 6]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-6, 0, 6].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[7, -7, 0, 7]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-7, 0, 7]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-7, 0, 7].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[8, -8, 0, 8]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-8, 0, 8]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-8, 0, 8].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[9, -9, 0, 9]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-9, 0, 9]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-9, 0, 9].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[10, -10, 0, 10]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-10, 0, 10]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-10, 0, 10].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[11, -11, 0, 11]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-11, 0, 11]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-11, 0, 11].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[12, -12, 0, 12]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-12, 0, 12]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-12, 0, 12].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[13, -13, 0, 13]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-13, 0, 13]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-13, 0, 13].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[14, -14, 0, 14]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-14, 0, 14]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-14, 0, 14].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[15, -15, 0, 15]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-15, 0, 15]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-15, 0, 15].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[16, -16, 0, 16]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-16, 0, 16]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-16, 0, 16].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[17, -17, 0, 17]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-17, 0, 17]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-17, 0, 17].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[18, -18, 0, 18]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-18, 0, 18]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-18, 0, 18].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[19, -19, 0, 19]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-19, 0, 19]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-19, 0, 19].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[20, -20, 0, 20]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-20, 0, 20]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-20, 0, 20].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[21, -21, 0, 21]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-21, 0, 21]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-21, 0, 21].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[22, -22, 0, 22]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-22, 0, 22]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-22, 0, 22].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[23, -23, 0, 23]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-23, 0, 23]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-23, 0, 23].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
The raw integer list is entries=[24, -24, 0, 24]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.
[-24, 0, 24]
Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-24, 0, 24].
Reviewed step-by-step derivation
Set · qf-density11-set-normalized-enumeration · candidate
Finite integer sets A=[0, 1] and B=[1, 0, 1]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(Yes, [], [])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (Yes, [], []).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[] and B=[-1]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [], [-1])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [], [-1]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-2] and B=[]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-2], [])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-2], []).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-3, 0, 3] and B=[0, 3, 4]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-3], [4])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-3], [4]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-4, 0, 4] and B=[0, 4, 5]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-4], [5])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-4], [5]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-5, 0, 5] and B=[0, 5, 6]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-5], [6])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-5], [6]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-6, 0, 6] and B=[0, 6, 7]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-6], [7])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-6], [7]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-7, 0, 7] and B=[0, 7, 8]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-7], [8])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-7], [8]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-8, 0, 8] and B=[0, 8, 9]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-8], [9])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-8], [9]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-9, 0, 9] and B=[0, 9, 10]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-9], [10])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-9], [10]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-10, 0, 10] and B=[0, 10, 11]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-10], [11])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-10], [11]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-11, 0, 11] and B=[0, 11, 12]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-11], [12])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-11], [12]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-12, 0, 12] and B=[0, 12, 13]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-12], [13])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-12], [13]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-13, 0, 13] and B=[0, 13, 14]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-13], [14])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-13], [14]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-14, 0, 14] and B=[0, 14, 15]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-14], [15])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-14], [15]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-15, 0, 15] and B=[0, 15, 16]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-15], [16])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-15], [16]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-16, 0, 16] and B=[0, 16, 17]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-16], [17])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-16], [17]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-17, 0, 17] and B=[0, 17, 18]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-17], [18])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-17], [18]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-18, 0, 18] and B=[0, 18, 19]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-18], [19])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-18], [19]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-19, 0, 19] and B=[0, 19, 20]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-19], [20])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-19], [20]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-20, 0, 20] and B=[0, 20, 21]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-20], [21])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-20], [21]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-21, 0, 21] and B=[0, 21, 22]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-21], [22])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-21], [22]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-22, 0, 22] and B=[0, 22, 23]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-22], [23])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-22], [23]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-23, 0, 23] and B=[0, 23, 24]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-23], [24])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-23], [24]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer sets A=[-24, 0, 24] and B=[0, 24, 25]; repeated elements count once. Give (are A and B equal?, A\B, B\A), with increasing difference lists.
(No, [-24], [25])
Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-24], [25]).
Reviewed step-by-step derivation
Set · qf-density11-set-equality-defect · candidate
Finite integer set A=[]; raw candidates=[] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([], [])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([], []).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[0]; raw candidates=[0, 1, 1] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([0], [1])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([0], [1]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-2, 0]; raw candidates=[-2, 2, 0, 2] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-2, 0], [2])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-2, 0], [2]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-3, 0]; raw candidates=[-3, 3, 0, 3] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-3, 0], [3])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-3, 0], [3]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-4, 0]; raw candidates=[-4, 4, 0, 4] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-4, 0], [4])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-4, 0], [4]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-5, 0]; raw candidates=[-5, 5, 0, 5] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-5, 0], [5])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-5, 0], [5]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-6, 0]; raw candidates=[-6, 6, 0, 6] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-6, 0], [6])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-6, 0], [6]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-7, 0]; raw candidates=[-7, 7, 0, 7] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-7, 0], [7])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-7, 0], [7]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-8, 0]; raw candidates=[-8, 8, 0, 8] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-8, 0], [8])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-8, 0], [8]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-9, 0]; raw candidates=[-9, 9, 0, 9] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-9, 0], [9])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-9, 0], [9]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-10, 0]; raw candidates=[-10, 10, 0, 10] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-10, 0], [10])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-10, 0], [10]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-11, 0]; raw candidates=[-11, 11, 0, 11] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-11, 0], [11])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-11, 0], [11]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-12, 0]; raw candidates=[-12, 12, 0, 12] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-12, 0], [12])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-12, 0], [12]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-13, 0]; raw candidates=[-13, 13, 0, 13] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-13, 0], [13])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-13, 0], [13]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-14, 0]; raw candidates=[-14, 14, 0, 14] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-14, 0], [14])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-14, 0], [14]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-15, 0]; raw candidates=[-15, 15, 0, 15] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-15, 0], [15])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-15, 0], [15]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-16, 0]; raw candidates=[-16, 16, 0, 16] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-16, 0], [16])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-16, 0], [16]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-17, 0]; raw candidates=[-17, 17, 0, 17] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-17, 0], [17])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-17, 0], [17]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-18, 0]; raw candidates=[-18, 18, 0, 18] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-18, 0], [18])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-18, 0], [18]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-19, 0]; raw candidates=[-19, 19, 0, 19] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-19, 0], [19])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-19, 0], [19]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-20, 0]; raw candidates=[-20, 20, 0, 20] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-20, 0], [20])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-20, 0], [20]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-21, 0]; raw candidates=[-21, 21, 0, 21] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-21, 0], [21])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-21, 0], [21]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-22, 0]; raw candidates=[-22, 22, 0, 22] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-22, 0], [22])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-22, 0], [22]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-23, 0]; raw candidates=[-23, 23, 0, 23] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-23, 0], [23])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-23, 0], [23]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[-24, 0]; raw candidates=[-24, 24, 0, 24] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
([-24, 0], [24])
Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-24, 0], [24]).
Reviewed step-by-step derivation
Set · qf-density11-set-candidate-partition · candidate
Finite integer set A=[]. 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.
[[]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[0]. 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.
[[], [0]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [0]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-2, 1]. 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.
[[], [-2], [1], [-2, 1]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-2], [1], [-2, 1]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-3, 0, 1, 3]. 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.
[[], [-3], [0], [1], [3], [-3, 0], [-3, 1], [-3, 3], [0, 1], [0, 3], [1, 3], [-3, 0, 1], [-3, 0, 3], [-3, 1, 3], [0, 1, 3], [-3, 0, 1, 3]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-3], [0], [1], [3], [-3, 0], [-3, 1], [-3, 3], [0, 1], [0, 3], [1, 3], [-3, 0, 1], [-3, 0, 3], [-3, 1, 3], [0, 1, 3], [-3, 0, 1, 3]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-4, 0, 1, 4]. 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.
[[], [-4], [0], [1], [4], [-4, 0], [-4, 1], [-4, 4], [0, 1], [0, 4], [1, 4], [-4, 0, 1], [-4, 0, 4], [-4, 1, 4], [0, 1, 4], [-4, 0, 1, 4]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-4], [0], [1], [4], [-4, 0], [-4, 1], [-4, 4], [0, 1], [0, 4], [1, 4], [-4, 0, 1], [-4, 0, 4], [-4, 1, 4], [0, 1, 4], [-4, 0, 1, 4]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-5, 0, 1, 5]. 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.
[[], [-5], [0], [1], [5], [-5, 0], [-5, 1], [-5, 5], [0, 1], [0, 5], [1, 5], [-5, 0, 1], [-5, 0, 5], [-5, 1, 5], [0, 1, 5], [-5, 0, 1, 5]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-5], [0], [1], [5], [-5, 0], [-5, 1], [-5, 5], [0, 1], [0, 5], [1, 5], [-5, 0, 1], [-5, 0, 5], [-5, 1, 5], [0, 1, 5], [-5, 0, 1, 5]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-6, 0, 1, 6]. 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.
[[], [-6], [0], [1], [6], [-6, 0], [-6, 1], [-6, 6], [0, 1], [0, 6], [1, 6], [-6, 0, 1], [-6, 0, 6], [-6, 1, 6], [0, 1, 6], [-6, 0, 1, 6]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-6], [0], [1], [6], [-6, 0], [-6, 1], [-6, 6], [0, 1], [0, 6], [1, 6], [-6, 0, 1], [-6, 0, 6], [-6, 1, 6], [0, 1, 6], [-6, 0, 1, 6]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-7, 0, 1, 7]. 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.
[[], [-7], [0], [1], [7], [-7, 0], [-7, 1], [-7, 7], [0, 1], [0, 7], [1, 7], [-7, 0, 1], [-7, 0, 7], [-7, 1, 7], [0, 1, 7], [-7, 0, 1, 7]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-7], [0], [1], [7], [-7, 0], [-7, 1], [-7, 7], [0, 1], [0, 7], [1, 7], [-7, 0, 1], [-7, 0, 7], [-7, 1, 7], [0, 1, 7], [-7, 0, 1, 7]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-8, 0, 1, 8]. 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.
[[], [-8], [0], [1], [8], [-8, 0], [-8, 1], [-8, 8], [0, 1], [0, 8], [1, 8], [-8, 0, 1], [-8, 0, 8], [-8, 1, 8], [0, 1, 8], [-8, 0, 1, 8]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-8], [0], [1], [8], [-8, 0], [-8, 1], [-8, 8], [0, 1], [0, 8], [1, 8], [-8, 0, 1], [-8, 0, 8], [-8, 1, 8], [0, 1, 8], [-8, 0, 1, 8]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-9, 0, 1, 9]. 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.
[[], [-9], [0], [1], [9], [-9, 0], [-9, 1], [-9, 9], [0, 1], [0, 9], [1, 9], [-9, 0, 1], [-9, 0, 9], [-9, 1, 9], [0, 1, 9], [-9, 0, 1, 9]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-9], [0], [1], [9], [-9, 0], [-9, 1], [-9, 9], [0, 1], [0, 9], [1, 9], [-9, 0, 1], [-9, 0, 9], [-9, 1, 9], [0, 1, 9], [-9, 0, 1, 9]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-10, 0, 1, 10]. 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.
[[], [-10], [0], [1], [10], [-10, 0], [-10, 1], [-10, 10], [0, 1], [0, 10], [1, 10], [-10, 0, 1], [-10, 0, 10], [-10, 1, 10], [0, 1, 10], [-10, 0, 1, 10]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-10], [0], [1], [10], [-10, 0], [-10, 1], [-10, 10], [0, 1], [0, 10], [1, 10], [-10, 0, 1], [-10, 0, 10], [-10, 1, 10], [0, 1, 10], [-10, 0, 1, 10]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-11, 0, 1, 11]. 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.
[[], [-11], [0], [1], [11], [-11, 0], [-11, 1], [-11, 11], [0, 1], [0, 11], [1, 11], [-11, 0, 1], [-11, 0, 11], [-11, 1, 11], [0, 1, 11], [-11, 0, 1, 11]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-11], [0], [1], [11], [-11, 0], [-11, 1], [-11, 11], [0, 1], [0, 11], [1, 11], [-11, 0, 1], [-11, 0, 11], [-11, 1, 11], [0, 1, 11], [-11, 0, 1, 11]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-12, 0, 1, 12]. 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.
[[], [-12], [0], [1], [12], [-12, 0], [-12, 1], [-12, 12], [0, 1], [0, 12], [1, 12], [-12, 0, 1], [-12, 0, 12], [-12, 1, 12], [0, 1, 12], [-12, 0, 1, 12]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-12], [0], [1], [12], [-12, 0], [-12, 1], [-12, 12], [0, 1], [0, 12], [1, 12], [-12, 0, 1], [-12, 0, 12], [-12, 1, 12], [0, 1, 12], [-12, 0, 1, 12]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-13, 0, 1, 13]. 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.
[[], [-13], [0], [1], [13], [-13, 0], [-13, 1], [-13, 13], [0, 1], [0, 13], [1, 13], [-13, 0, 1], [-13, 0, 13], [-13, 1, 13], [0, 1, 13], [-13, 0, 1, 13]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-13], [0], [1], [13], [-13, 0], [-13, 1], [-13, 13], [0, 1], [0, 13], [1, 13], [-13, 0, 1], [-13, 0, 13], [-13, 1, 13], [0, 1, 13], [-13, 0, 1, 13]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-14, 0, 1, 14]. 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.
[[], [-14], [0], [1], [14], [-14, 0], [-14, 1], [-14, 14], [0, 1], [0, 14], [1, 14], [-14, 0, 1], [-14, 0, 14], [-14, 1, 14], [0, 1, 14], [-14, 0, 1, 14]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-14], [0], [1], [14], [-14, 0], [-14, 1], [-14, 14], [0, 1], [0, 14], [1, 14], [-14, 0, 1], [-14, 0, 14], [-14, 1, 14], [0, 1, 14], [-14, 0, 1, 14]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-15, 0, 1, 15]. 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.
[[], [-15], [0], [1], [15], [-15, 0], [-15, 1], [-15, 15], [0, 1], [0, 15], [1, 15], [-15, 0, 1], [-15, 0, 15], [-15, 1, 15], [0, 1, 15], [-15, 0, 1, 15]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-15], [0], [1], [15], [-15, 0], [-15, 1], [-15, 15], [0, 1], [0, 15], [1, 15], [-15, 0, 1], [-15, 0, 15], [-15, 1, 15], [0, 1, 15], [-15, 0, 1, 15]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-16, 0, 1, 16]. 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.
[[], [-16], [0], [1], [16], [-16, 0], [-16, 1], [-16, 16], [0, 1], [0, 16], [1, 16], [-16, 0, 1], [-16, 0, 16], [-16, 1, 16], [0, 1, 16], [-16, 0, 1, 16]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-16], [0], [1], [16], [-16, 0], [-16, 1], [-16, 16], [0, 1], [0, 16], [1, 16], [-16, 0, 1], [-16, 0, 16], [-16, 1, 16], [0, 1, 16], [-16, 0, 1, 16]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-17, 0, 1, 17]. 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.
[[], [-17], [0], [1], [17], [-17, 0], [-17, 1], [-17, 17], [0, 1], [0, 17], [1, 17], [-17, 0, 1], [-17, 0, 17], [-17, 1, 17], [0, 1, 17], [-17, 0, 1, 17]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-17], [0], [1], [17], [-17, 0], [-17, 1], [-17, 17], [0, 1], [0, 17], [1, 17], [-17, 0, 1], [-17, 0, 17], [-17, 1, 17], [0, 1, 17], [-17, 0, 1, 17]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
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.
[[], [-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]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-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]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-19, 0, 1, 19]. 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.
[[], [-19], [0], [1], [19], [-19, 0], [-19, 1], [-19, 19], [0, 1], [0, 19], [1, 19], [-19, 0, 1], [-19, 0, 19], [-19, 1, 19], [0, 1, 19], [-19, 0, 1, 19]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-19], [0], [1], [19], [-19, 0], [-19, 1], [-19, 19], [0, 1], [0, 19], [1, 19], [-19, 0, 1], [-19, 0, 19], [-19, 1, 19], [0, 1, 19], [-19, 0, 1, 19]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-20, 0, 1, 20]. 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.
[[], [-20], [0], [1], [20], [-20, 0], [-20, 1], [-20, 20], [0, 1], [0, 20], [1, 20], [-20, 0, 1], [-20, 0, 20], [-20, 1, 20], [0, 1, 20], [-20, 0, 1, 20]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-20], [0], [1], [20], [-20, 0], [-20, 1], [-20, 20], [0, 1], [0, 20], [1, 20], [-20, 0, 1], [-20, 0, 20], [-20, 1, 20], [0, 1, 20], [-20, 0, 1, 20]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-21, 0, 1, 21]. 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.
[[], [-21], [0], [1], [21], [-21, 0], [-21, 1], [-21, 21], [0, 1], [0, 21], [1, 21], [-21, 0, 1], [-21, 0, 21], [-21, 1, 21], [0, 1, 21], [-21, 0, 1, 21]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-21], [0], [1], [21], [-21, 0], [-21, 1], [-21, 21], [0, 1], [0, 21], [1, 21], [-21, 0, 1], [-21, 0, 21], [-21, 1, 21], [0, 1, 21], [-21, 0, 1, 21]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-22, 0, 1, 22]. 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.
[[], [-22], [0], [1], [22], [-22, 0], [-22, 1], [-22, 22], [0, 1], [0, 22], [1, 22], [-22, 0, 1], [-22, 0, 22], [-22, 1, 22], [0, 1, 22], [-22, 0, 1, 22]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-22], [0], [1], [22], [-22, 0], [-22, 1], [-22, 22], [0, 1], [0, 22], [1, 22], [-22, 0, 1], [-22, 0, 22], [-22, 1, 22], [0, 1, 22], [-22, 0, 1, 22]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-23, 0, 1, 23]. 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.
[[], [-23], [0], [1], [23], [-23, 0], [-23, 1], [-23, 23], [0, 1], [0, 23], [1, 23], [-23, 0, 1], [-23, 0, 23], [-23, 1, 23], [0, 1, 23], [-23, 0, 1, 23]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-23], [0], [1], [23], [-23, 0], [-23, 1], [-23, 23], [0, 1], [0, 23], [1, 23], [-23, 0, 1], [-23, 0, 23], [-23, 1, 23], [0, 1, 23], [-23, 0, 1, 23]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Finite integer set A=[-24, 0, 1, 24]. 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.
[[], [-24], [0], [1], [24], [-24, 0], [-24, 1], [-24, 24], [0, 1], [0, 24], [1, 24], [-24, 0, 1], [-24, 0, 24], [-24, 1, 24], [0, 1, 24], [-24, 0, 1, 24]]
Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-24], [0], [1], [24], [-24, 0], [-24, 1], [-24, 24], [0, 1], [0, 24], [1, 24], [-24, 0, 1], [-24, 0, 24], [-24, 1, 24], [0, 1, 24], [-24, 0, 1, 24]].
Reviewed step-by-step derivation
Set · qf-density11-set-powerset-enumeration · candidate
Canonical question JSONL · English JSONL · Validation report