Returned 93 matches (100 formulae, 79 docs)
    Lookup 5.000 ms, Re-ranking 0.141 ms
    Found 36561 tuple postings, 24343 formulae, 7367 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Strong_antichain.html
x , y A [ x y ¬ z X [ z x z y ] ] .

Doc 2
0.1417
0.5501
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Zermelo–Fraenkel_set_theory.html
x y z [ z x z y ] .
x y z ( x z y z ) .
z [ z x z y ] w [ x w y w ] .
x y [ z ( z x z y ) x = y ] .
x [ a ( a x ) y ( y x ¬ z ( z y z x ) ) ] .
z w 1 w 2 w n y x [ x y ( x z ϕ ) ] .
x y [ z ( z x z y ) w ( x w y w ) ] ,

Doc 3
0.1239
0.4010
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Implementation_of_mathematics_in_set_theory.html
x , y , z ( x F y x F z y = z )
x , y , z ( x R y y R z x R z )
x , y ( x R y y R x )
{ ( x , y ) x y x y }
x y = def . { z : z x z y }

Doc 4
0.1160
0.1160
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Normed_algebra.html
x , y A x y x y

Doc 5
0.1007
0.2098
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Glossary_of_Lie_algebras.html
x , y A
κ ( x , y ) := Tr ( ad x ad y ) x , y 𝔤
ϕ ( [ x , y ] ) = [ ϕ ( x ) , ϕ ( y ) ] x , y 𝔤 1 .
Doc 6
0.0987
0.0987
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Syntactic_monoid.html
u S v x , y M ( x u y S x v y S ) .

Doc 7
0.0984
0.0984
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Lambda_calculus_definition.html
x z M [ x := y ] [ z ] = M [ z ]

Doc 8
0.0963
0.2374
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Pseudo-order.html
x , y : ¬ ( x < y y < x )
x , y : ¬ ( x < y y < x ) x = y
x , y , z : x < y ( x < z z < y )
Doc 9
0.0893
0.1620
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Bijection,_injection_and_surjection.html
x , y A , x y f ( x ) f ( y ) .
x , y A , f ( x ) = f ( y ) x = y .

Doc 10
0.0835
0.2114
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/General_set_theory.html
x y [ z [ z x z y ] x = y ] .
z y x [ x y ( x z ϕ ( x ) ) ] .
x y \exist w z [ z w ( z x z = y ) ] .
Doc 11
0.0826
0.0826
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Axiom_schema_of_predicative_separation.html
x y z ( z y z x ϕ ( z ) )

Doc 12
0.0811
0.0811
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/ST_type_theory.html
x , y [ x y [ x R y y R x ] ]

Doc 13
0.0798
0.0798
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Banach_algebra.html
x , y A : x y x y

Doc 14
0.0793
0.2515
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Whitehead's_point-free_geometry.html
z [ z < x z < y ] x y .
z [ x z and y z ] .
x < y z [ x < z < y ] .
( x z and z y ) x y .

Doc 15
0.0793
0.2909
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Universal_hashing.html
x , y U , x y
x , y U , x y
x , y U , x y
x , y U , x y : Pr h H [ h ( x ) = h ( y ) ] 1 m

Doc 16
0.0749
0.5849
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Peano_axioms.html
x , y N x < y z N x + z = y
x , y N
x , y N
x , y N
x , y , z N
x , y , z N
x , y , z N
x , y , z N
x , y , z N
x , y , z N

Doc 17
0.0696
0.0696
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Subadditivity.html
x , y A , f ( x + y ) f ( x ) + f ( y ) .

Doc 18
0.0688
0.1680
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Well-quasi-ordering.html
x , y X , x y x S y S
i , x , y X , x y x S i y S i
x y x y y x
Doc 19
0.0686
0.1981
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Arithmetic_combinatorics.html
A + A := { x + y : x , y A } ,
A - A := { x - y : x , y A } ,
A A := { x y : x , y A }
Doc 20
0.0683
0.1275
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Skew_lattice.html
x , y A
x z = y z

Doc 21
0.0683
0.1160
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Near_sets.html
x , y A
x , y X

Doc 22
0.0683
0.0683
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Quasinorm.html
x , y A

Doc 23
0.0683
0.0683
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Differential_algebra.html
x , y A

Doc 24
0.0682
0.0682
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/C-minimal_theory.html
x y [ x y z y C ( x ; y z ) ] .

Doc 25
0.0681
0.1661
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Mereology.html
P P x y z [ P z y and ¬ O z x ] .
¬ P x y z [ P z x and ¬ O z y and ¬ v [ P P v z ] ] .
P x y z [ O z x O z y ] .
Doc 26
0.0671
0.1975
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Total_order.html
x , y A 1
x , y A 2
x , y A 1 A 2
Doc 27
0.0671
0.1150
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Symmetry_of_diatomic_molecules.html
x , y G
( x * y ) * z = x * ( y * z ) x , y , z G

Doc 28
0.0671
0.0671
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Clebsch–Gordan_coefficients_for_SU(3).html
x , y G

Doc 29
0.0671
0.0671
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/ACE_Encrypt.html
x , y A

Doc 30
0.0658
0.1316
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Alternatization.html
x , y S ,
x , y V ,

Doc 31
0.0630
0.0630
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Ideal_(ring_theory).html
x , y I : x - y I

Doc 32
0.0625
0.0625
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Triangle_inequality.html
x + y x + y x , y V

Doc 33
0.0610
0.1175
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/First-order_logic.html
x y [ z ( z x z y ) x = y ]
x y [ z ( z x z y ) z ( x z y z ) ]

Doc 34
0.0592
0.0592
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Partially_ordered_ring.html
x + z y + z

Doc 35
0.0592
0.0592
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/T-norm_fuzzy_logics.html
x * z y * z

Doc 36
0.0587
0.1068
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Let_expression.html
x = y and ( L z ) [ x := y ]
let x : x = y in z = z [ x := y ]

Doc 37
0.0581
0.0581
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Axiom_of_adjunction.html
x y w z [ z w ( z x z = y ) ] .

Doc 38
0.0575
0.0575
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Valuation_ring.html
x A [ x ] = A [ x ] .

Doc 39
0.0573
0.0573
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Banach_space.html
x , y H : y , x

Doc 40
0.0571
0.1053
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Ancestral_relation.html
𝟏𝟏𝟓 : I ( R ) x y z [ ( x R y x R z ) y = z ]
x y ( F x x R y F y )

Doc 41
0.0568
0.0568
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Skew-symmetric_matrix.html
x + y , A ( x + y ) = 0

Doc 42
0.0564
0.0564
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Tarski's_theorem_about_choice.html
x , y B , x y

Doc 43
0.0557
0.1055
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Ackermann_set_theory.html
x y ( z ( z x z y ) x = y ) .
x V y ( y x ) y ( y x ¬ z ( z y z x ) ) .

Doc 44
0.0554
0.1580
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Heyting_algebra.html
x , y H : ¬ ( x y ) = ¬ x ¬ y .
¬ ( ¬ x ¬ y ) = x y for all regular x , y H ,
x , y H : ¬ ( x y ) = ¬ ¬ ( ¬ x ¬ y ) .
Doc 45
0.0550
0.0550
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/General_frame.html
A = { x F ; y F ( x R y y A ) }

Doc 46
0.0541
0.0541
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Demonic_composition.html
{ ( x , z ) | x ( S R ) z y Y ( x R y y S z ) } .

Doc 47
0.0526
0.1579
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Program_synthesis.html
x x y x
x x y x
x y y y
Doc 48
0.0521
0.0521
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Method_of_analytic_tableaux.html
x , y . P ( x , y ) Q ( f ( x ) )

Doc 49
0.0519
0.1474
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Reproducing_kernel_Hilbert_space.html
K ( x , y ) 2 K ( x , x ) K ( y , y ) x , y X .
x , y X
x , y X
Doc 50
0.0502
0.0502
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Fermat's_Last_Theorem.html
x / z , y / z

Doc 51
0.0502
0.0502
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Boolean_algebra.html
x y = ¬ ( x y )

Doc 52
0.0494
0.0494
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Dense_order.html
x y x R y ( z x R z z R y ) .

Doc 53
0.0493
0.0980
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Alexandrov_topology.html
{ S X : x , y X x S y x y S , }
τ = { G X : x , y X x G x y y G , }

Doc 54
0.0490
0.0490
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Apartness_relation.html
x , y : A . f ( x ) # B f ( y ) \Rarr x # A y

Doc 55
0.0488
0.0488
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Quasi-set_theory.html
z ( z x z y )

Doc 56
0.0486
0.0486
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Single_crossing_condition.html
x , x y F ( x ) G ( y )

Doc 57
0.0483
0.0483
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Johnson_bound.html
d = min x , y C , x y d ( x , y )

Doc 58
0.0483
0.0483
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Plotkin_bound.html
d = min x , y C , x y d ( x , y )

Doc 59
0.0480
0.0480
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Max-flow_min-cut_theorem.html
( x , y ) , x A , y A c

Doc 60
0.0478
0.0956
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/CAT(k)_space.html
x , y X
x , y X

Doc 61
0.0478
0.0956
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Partially_ordered_space.html
x , y X
x , y X

Doc 62
0.0478
0.0951
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Prewellordering.html
x , y X
x y x y y x

Doc 63
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Bose–Mesner_algebra.html
x , y X

Doc 64
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Bitopological_space.html
x , y X

Doc 65
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Quotient_space_(topology).html
x , y X

Doc 66
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Equivalence_of_metrics.html
x , y X

Doc 67
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Utility.html
x , y X

Doc 68
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Heap_(mathematics).html
x , y X

Doc 69
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Maximal_element.html
x , y X

Doc 70
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Metric_map.html
x , y X

Doc 71
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Nakamura_number.html
x , y X

Doc 72
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Boehmians.html
x , y X

Doc 73
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Uniformly_smooth_space.html
x , y X

Doc 74
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Infrastructure_(number_theory).html
x , y X

Doc 75
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Discrete_space.html
x , y X

Doc 76
0.0478
0.0478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Locally_connected_space.html
x , y X

Doc 77
0.0469
0.0469
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Sahlqvist_formula.html
x y z [ ( R x y R y z ) R x z ]

Doc 78
0.0468
0.0468
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Graph_algebra.html
x , y V , ( x , y ) E

Doc 79
0.0468
0.0468
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Singleton_bound.html
d = min { x , y C : x y } d ( x , y )