Cac Ky Hieu Toan Hoc
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Symbols
Symbolin
HTML
Symbolin T E X
NameExplanation ExamplesRead as
Category
=
equality
is equal to;equals
everywhere
x =y meansx andy represent the same thing orvalue.
2 = 21 + 1 = 2
inequality
is not equal to;does not equal
everywhere
x y means thatx andy do not represent the samething or value.
(The forms !=, /= or are generally used inprogramming languages where ease of typing
and use ofASCIItext is preferred.)
2 + 2 5
strict inequality
is less than,is greater than
order theory
x y meansx is greater thany.
3 < 45 > 4
proper subgroup
is a proper subgroup of
group theory
H< G meansHis a proper subgroup ofG.5Z < ZA3 < S3
http://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/Equals_signhttp://en.wikipedia.org/wiki/Equality_(mathematics)http://en.wikipedia.org/wiki/Not_equals_signhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Less-than_signhttp://en.wikipedia.org/wiki/Greater-than_signhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Proper_subgrouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/Equals_signhttp://en.wikipedia.org/wiki/Equality_(mathematics)http://en.wikipedia.org/wiki/Not_equals_signhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Less-than_signhttp://en.wikipedia.org/wiki/Greater-than_signhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Proper_subgrouphttp://en.wikipedia.org/wiki/Group_theory -
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Karp reduction
is Karp reducible to;is polynomial-time many-
one reducible to
computational complexitytheory
L1L2 means that the problemL1 is Karpreducible toL2.[1]
IfL1L2 andL2 P, thenL1 P.
proportionality
is proportional to;varies as
everywhere
yx means thaty = kx for some constant k. ify = 2x, thenyx.
Karp reduction[2]
is Karp reducible to;is polynomial-time many-
one reducible to
computational complexitytheory
AB means theproblemA can be polynomiallyreduced to the problemB.
IfL1L2 andL2 P, thenL1 P.
+ additionplus;add
arithmetic
4 + 6 means the sum of 4 and 6. 2 + 7 = 9
disjoint union A1 +A2 means the disjoint union of setsA1 andA2.A1 = {3, 4, 5, 6} A2 = {7, 8, 9, 10}
http://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-0http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-0http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/Alpha_(letter)http://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-1http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-1http://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/Plus_signhttp://en.wikipedia.org/wiki/Additionhttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Disjoint_unionhttp://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-0http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/Alpha_(letter)http://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-1http://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/Plus_signhttp://en.wikipedia.org/wiki/Additionhttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Disjoint_union -
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the disjoint union of ...
and ...
set theory
A1 +A2 = {(3,1), (4,1), (5,1), (6,1), (7,2), (8,2), (9,2),
(10,2)}
subtraction
minus;take;
subtract
arithmetic
9 4 means the subtraction of 4 from 9. 8 3 = 5
negative sign
negative;minus;
the opposite of
arithmetic
3 means thenegative of the number 3. (5) = 5
set-theoretic complement
minus;without
set theory
A B means the set that contains all the elementsofA that are not inB.
(can also be used for set-theoretic complementas described below.)
{1,2,4} {1,3,4} = {2}
plus-minusplus or minus
6 3 means both 6 + 3 and 6 3. The equationx = 5 4, has two solutions,x = 7 andx = 3.
http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Minus_signhttp://en.wikipedia.org/wiki/Subtractionhttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Negative_numberhttp://en.wikipedia.org/wiki/Negative_numberhttp://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Plus-minus_signhttp://en.wikipedia.org/wiki/Plus-minus_signhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Minus_signhttp://en.wikipedia.org/wiki/Subtractionhttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Negative_numberhttp://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Plus-minus_signhttp://en.wikipedia.org/wiki/Plus-minus_sign -
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arithmeticplus-minus
plus or minus
measurement
10 2 or equivalently 10 20% means the rangefrom 10 2 to 10 + 2.
Ifa = 100 1mm, then a 99 mm and a 101 mm.
minus-plus
minus or plus
arithmetic
6 (3 5) means both 6 + (3 5) and 6 (3 +5).
cos(x y) = cos(x) cos(y) sin(x) sin(y).
multiplication
times;multiplied by
arithmetic
3 4 means the multiplication of 3 by 4.
(The symbol * is generally used in programminglanguages, where ease of typing and use ofASCIItext is preferred.)
7 8 = 56
Cartesian product
the Cartesian product of ...and ...;
the direct product of ...and ...
set theory
XYmeans the set of all ordered pairs with thefirst element of each pair selected from X and the
second element selected from Y.
{1,2} {3,4} = {(1,3),(1,4),(2,3),(2,4)}
cross product
cross
u v means the cross product ofvectorsu and v (1,2,5) (3,4,1) =(22, 16, 2)
http://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Plus-minus_signhttp://en.wikipedia.org/wiki/Measurementhttp://en.wikipedia.org/wiki/Millimetrehttp://en.wikipedia.org/wiki/Millimetrehttp://en.wikipedia.org/wiki/Minus-plus_signhttp://en.wikipedia.org/wiki/Minus-plus_signhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Multiplication_signhttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Cartesian_producthttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Ordered_pairshttp://en.wikipedia.org/wiki/Cross_producthttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Plus-minus_signhttp://en.wikipedia.org/wiki/Measurementhttp://en.wikipedia.org/wiki/Millimetrehttp://en.wikipedia.org/wiki/Minus-plus_signhttp://en.wikipedia.org/wiki/Minus-plus_signhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Multiplication_signhttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Cartesian_producthttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Ordered_pairshttp://en.wikipedia.org/wiki/Cross_producthttp://en.wikipedia.org/wiki/Vector_(geometry) -
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linear algebragroup of units
the group of units of
ring theory
R consists of the set of units of the ring R, along
with the operation of multiplication.
This may also be writtenR* as described below,orU(R).
* multiplicationtimes;
multiplied by
arithmetic
a * b means the product ofa and b.
(Multiplication can also be denoted with or,or even simple juxtaposition. * is generally usedwhere ease of typing and use ofASCIItext is
preferred, such as programming languages.)
4 * 3 means the product of 4 and 3, or 12.
convolution
convolution;convolved with
functional analysis
f*gmeans the convolution offandg..
complex conjugate
conjugate
complex numbers
z* means the complex conjugate ofz.
( can also be used for the conjugate of z, as
described below.)
.
group of units
the group of units of
ring theory
R* consists of the set of units of the ring R, alongwith the operation of multiplication.
This may also be writtenRas described above,orU(R).
hyperreal numbers *Rmeans the set of hyperreal numbers. Other *N is the hypernatural numbers.
http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Asteriskhttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Convolutionhttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Hyperreal_numberhttp://en.wikipedia.org/wiki/Hypernaturalhttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Asteriskhttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Convolutionhttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Hyperreal_numberhttp://en.wikipedia.org/wiki/Hypernatural -
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the (set of) hyperreals
non-standard analysis
sets can be used in place ofR.
Hodge dual
Hodge dual;Hodge star
linear algebra
*v means the Hodge dual of a vectorv. Ifv is a k-vectorwithin an n-dimensional orientedinnerproductspace, then *v is an (nk)-vector.
If are thestandard basis vectors of ,
multiplication
times;multiplied by
arithmetic
3 4 means the multiplication of 3 by 4. 7 8 = 56
dot product
dot
linear algebra
u v means the dot product ofvectorsu and v
(1,2,5) (3,4,1) = 6
placeholder
(silent)
functional analysis
A means a placeholder for an argument of afunction. Indicates the functional nature of anexpression without assigning a specific symbolfor an argument.
tensor product,tensorproduct of modulesmeans the tensor product ofVand U.[3]
means the tensor product of modules Vand Uover the ringR.
{1, 2, 3, 4} {1, 1, 2} ={{1, 2, 3, 4}, {1, 2, 3, 4}, {2, 4, 6, 8}}
http://en.wikipedia.org/wiki/Non-standard_analysishttp://en.wikipedia.org/wiki/Hodge_dualhttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/P-vectorhttp://en.wikipedia.org/wiki/P-vectorhttp://en.wikipedia.org/wiki/P-vectorhttp://en.wikipedia.org/wiki/P-vectorhttp://en.wikipedia.org/wiki/Dimension_(vector_space)http://en.wikipedia.org/wiki/Dimension_(vector_space)http://en.wikipedia.org/wiki/Dimension_(vector_space)http://en.wikipedia.org/wiki/Orientation_(mathematics)http://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Vector_spacehttp://en.wikipedia.org/wiki/Vector_spacehttp://en.wikipedia.org/wiki/Standard_basishttp://en.wikipedia.org/wiki/Standard_basishttp://en.wikipedia.org/wiki/Middle_dothttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Tensor_producthttp://en.wikipedia.org/wiki/Tensor_product_of_moduleshttp://en.wikipedia.org/wiki/Tensor_product_of_moduleshttp://en.wikipedia.org/wiki/Tensor_product_of_moduleshttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-m-nielsen-quantum-71-72-2http://en.wikipedia.org/wiki/Ring_(mathematics)http://en.wikipedia.org/wiki/Non-standard_analysishttp://en.wikipedia.org/wiki/Hodge_dualhttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/P-vectorhttp://en.wikipedia.org/wiki/P-vectorhttp://en.wikipedia.org/wiki/Dimension_(vector_space)http://en.wikipedia.org/wiki/Orientation_(mathematics)http://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Vector_spacehttp://en.wikipedia.org/wiki/Standard_basishttp://en.wikipedia.org/wiki/Middle_dothttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Tensor_producthttp://en.wikipedia.org/wiki/Tensor_product_of_moduleshttp://en.wikipedia.org/wiki/Tensor_product_of_moduleshttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-m-nielsen-quantum-71-72-2http://en.wikipedia.org/wiki/Ring_(mathematics) -
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tensor product of
linear algebra
division (Obelus)
divided by;over
arithmetic
6 3 or 6 3 means the division of 6 by 3.2 4 = 0.5
12 4 = 3
quotient group
mod
group theory
G /Hmeans the quotient of group Gmodulo its
subgroupH.
{0, a, 2a, b, b+a, b+2a} / {0, b} = {{0, b}, {a, b+a}, {2a,
b+2a}}
quotient set
mod
set theory
A/~ means the set of all ~equivalence classesinA.
If we define ~ by x ~ y x y , then/~ = { {x + n : n } : x [0,1) }
square rootthe (principal) square root
of
real numbers
means the nonnegative number whose squareis .
complex square root
the (complex) square rootof
if is represented inpolarcoordinates with , then
.
http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Division_signhttp://en.wikipedia.org/wiki/Fraction_slashhttp://en.wikipedia.org/wiki/Division_(mathematics)http://en.wikipedia.org/wiki/Obelushttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Quotient_grouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Ideal_(ring_theory)http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Equivalence_classhttp://en.wikipedia.org/wiki/Equivalence_classhttp://en.wikipedia.org/wiki/Equivalence_classhttp://en.wikipedia.org/wiki/Radical_symbolhttp://en.wikipedia.org/wiki/Square_roothttp://en.wikipedia.org/wiki/Real_numbershttp://en.wikipedia.org/wiki/Square_root#Square_roots_of_complex_numbershttp://en.wikipedia.org/wiki/Polar_coordinate_systemhttp://en.wikipedia.org/wiki/Polar_coordinate_systemhttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Division_signhttp://en.wikipedia.org/wiki/Fraction_slashhttp://en.wikipedia.org/wiki/Division_(mathematics)http://en.wikipedia.org/wiki/Obelushttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Quotient_grouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Ideal_(ring_theory)http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Equivalence_classhttp://en.wikipedia.org/wiki/Radical_symbolhttp://en.wikipedia.org/wiki/Square_roothttp://en.wikipedia.org/wiki/Real_numbershttp://en.wikipedia.org/wiki/Square_root#Square_roots_of_complex_numbershttp://en.wikipedia.org/wiki/Polar_coordinate_systemhttp://en.wikipedia.org/wiki/Polar_coordinate_system -
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complex numbers
x
mean
overbar; bar
statistics
(often read as x bar) is the mean (averagevalue of ). .
complex conjugate
conjugate
complex numbers
means the complex conjugate ofz.
(z* can also be used for the conjugate of z, asdescribed above.)
.
algebraic closure
algebraic closure of
field theory
is the algebraic closure of the fieldF.The field ofalgebraic numbers is sometimes denoted asbecause it is the algebraic closure of the rational numbers
.
topological closure
(topological) closure of
topology
is the topological closure of the set S.
This may also be denoted as cl(S) orCl(S).
In the space of the real numbers, (the rationalnumbers are dense in the real numbers).
|| absolute value;modulusabsolute value of; modulus
of
numbers
|x| means the distance along the real line (oracross the complex plane) betweenx and zero.
|3| = 3
|5| = |5| = 5
| i | = 1
| 3 + 4i | = 5
http://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Overlinehttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Algebraic_closurehttp://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Algebraic_numberhttp://en.wikipedia.org/wiki/Rational_numbershttp://en.wikipedia.org/wiki/Topological_closurehttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Dense_(topology)http://en.wikipedia.org/wiki/Absolute_valuehttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Real_linehttp://en.wikipedia.org/wiki/Complex_planehttp://en.wikipedia.org/wiki/0_(number)http://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Overlinehttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Algebraic_closurehttp://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Algebraic_numberhttp://en.wikipedia.org/wiki/Rational_numbershttp://en.wikipedia.org/wiki/Topological_closurehttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Dense_(topology)http://en.wikipedia.org/wiki/Absolute_valuehttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Real_linehttp://en.wikipedia.org/wiki/Complex_planehttp://en.wikipedia.org/wiki/0_(number) -
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Euclidean norm orEuclidean length ormagnitude
Euclidean norm of
geometry
|x| means the (Euclidean) length ofvectorx.
Forx = (3,-4)
determinant
determinant of
matrix theory
|A| means the determinant of the matrix A
cardinality
cardinality of;size of;order of
set theory
|X| means the cardinality of the setX.
(# may be used instead as described below.)|{3, 5, 7, 9}| = 4.
||||
norm
norm of;length of
linear algebra
||x || means thenormof the elementx of anormed vector space.[4]
||x +y || ||x || + ||y ||
nearest integer function
nearest integer to
numbers
||x|| means the nearest integer tox.
(This may also be written [x], x, nint(x) orRound(x).)
||1|| = 1, ||1.6|| = 2, ||2.4|| = 2, ||3.49|| = 3
http://en.wikipedia.org/wiki/Euclidean_normhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Determinanthttp://en.wikipedia.org/wiki/Matrix_theoryhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Normed_vector_spacehttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-m-nielsen-quantum-66-3http://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Euclidean_normhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Determinanthttp://en.wikipedia.org/wiki/Matrix_theoryhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Normed_vector_spacehttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-m-nielsen-quantum-66-3http://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Number -
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is incomparable to
order theoryexact divisibility
exactly divides
number theory
pa || n meanspa exactly divides n (i.e.pa divides nbutpa+1 does not).
23 || 360.
#
cardinality
cardinality of;size of;
order of
set theory
#Xmeans the cardinality of the setX.
(|| may be used instead as described above.)
#{4, 6, 8} = 3
connected sum
connected sum of;knot sum of;
knot composition of
topology,knot theory
A#B is the connected sum of the manifoldsA andB. IfA andB are knots, then this denotes the knotsum, which has a slightly stronger condition.
A#Sm is homeomorphic toA, for any manifoldA, and thesphere Sm.
aleph number
aleph
set theory
represents an infinite cardinality (specifically,the -th one, where is an ordinal).
|| =0, which is called aleph-null.
beth number represents an infinite cardinality (similar to
, but does not necessarily index all of the
http://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Divisibilityhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_signhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Connected_sumhttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Knot_theoryhttp://en.wikipedia.org/wiki/Homeomorphichttp://en.wikipedia.org/wiki/Aleph_(letter)http://en.wikipedia.org/wiki/Aleph_numberhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Beth_(letter)http://en.wikipedia.org/wiki/Beth_numberhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Divisibilityhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_signhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Connected_sumhttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Knot_theoryhttp://en.wikipedia.org/wiki/Homeomorphichttp://en.wikipedia.org/wiki/Aleph_(letter)http://en.wikipedia.org/wiki/Aleph_numberhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Beth_(letter)http://en.wikipedia.org/wiki/Beth_number -
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beth
set theory
numbers indexed by . ).
cardinality of the continuum
cardinality of thecontinuum;
c;cardinality of the real
numbers
set theory
The cardinality of is denoted by or by thesymbol (a lowercaseFrakturletter C).
: such thatsuch that;
so that
everywhere
: means such that, and is used in proofs and theset-builder notation (described below).
n : n is even.
field extension
extends;over
field theory
K:Fmeans the fieldKextends the fieldF.
This may also be written asKF.
:
inner product of matrices
inner product of
linear algebra
A :B means the Frobenius inner product of thematricesA andB.
The general inner product is denoted byu, v ,u | v or(u | v), as described below. For
http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Cardinality_of_the_continuumhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Fraktur_(script)http://en.wikipedia.org/wiki/Fraktur_(script)http://en.wikipedia.org/wiki/Colon_(punctuation)http://en.wikipedia.org/wiki/Set-builder_notationhttp://en.wikipedia.org/wiki/Field_extensionhttp://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Cardinality_of_the_continuumhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Fraktur_(script)http://en.wikipedia.org/wiki/Colon_(punctuation)http://en.wikipedia.org/wiki/Set-builder_notationhttp://en.wikipedia.org/wiki/Field_extensionhttp://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Linear_algebra -
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spatial vectors, the dot productnotation,xyiscommon. See also Bra-ket notation.
index of a subgroup
index of subgroup
group theory
The index of a subgroup H in a group G is the"relative size" of H in G: equivalently, thenumber of "copies" (cosets) of H that fill up G
!
factorial
factorial
combinatorics
n! means the product 1 2 ... n. 4! = 1 2 3 4 = 24
logical negation
not
propositional logic
The statement !A is true if and only ifA is false.
A slash placed through another operator is thesame as "!" placed in front.
(The symbol! is primarily from computerscience. It is avoided in mathematical texts,where the notation Ais preferred.)
!(!A) Ax y !(x =y)
~ probability distributionhas distribution
statistics
X ~ D, means the random variableXhas the
probability distributionD.
X~N(0,1), thestandard normal distribution
row equivalence
is row equivalent to
matrix theory
A~B means thatB can be generated by using aseries ofelementary row operations onA
http://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Bra-ket_notationhttp://en.wikipedia.org/wiki/Index_of_a_subgrouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Cosethttp://en.wikipedia.org/wiki/Exclamation_markhttp://en.wikipedia.org/wiki/Factorialhttp://en.wikipedia.org/wiki/Combinatoricshttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Tildehttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Standard_normal_distributionhttp://en.wikipedia.org/wiki/Standard_normal_distributionhttp://en.wikipedia.org/wiki/Elementary_matrix_transformationshttp://en.wikipedia.org/wiki/Matrix_theoryhttp://en.wikipedia.org/wiki/Elementary_row_operationshttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Bra-ket_notationhttp://en.wikipedia.org/wiki/Index_of_a_subgrouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Cosethttp://en.wikipedia.org/wiki/Exclamation_markhttp://en.wikipedia.org/wiki/Factorialhttp://en.wikipedia.org/wiki/Combinatoricshttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Tildehttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Standard_normal_distributionhttp://en.wikipedia.org/wiki/Elementary_matrix_transformationshttp://en.wikipedia.org/wiki/Matrix_theoryhttp://en.wikipedia.org/wiki/Elementary_row_operations -
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same order of magnitude
roughly similar;
poorly approximates
approximation theory
m ~ n means the quantities m and n have the sameorder of magnitude, or general size.
(Note that~ is used for an approximation that ispoor, otherwise use .)
2 ~ 5
8 9 ~ 100
but 2 10
asymptotically equivalent
is asymptotically equivalentto
asymptotic analysis
f~gmeans .x ~ x+1
equivalence relation
are in the same equivalenceclass
everywhere
a ~ b means (and equivalently ). 1 ~ 5 mod 4
approximately equal
is approximately equal to
everywhere
x y meansx is approximately equal toy.
This may also be written, , ~ or . 3.14159
isomorphism
is isomorphic to
group theory
G Hmeans that group G is isomorphic(structurally identical) to groupH.
(can also be used for isomorphic, as describedbelow.)
Q / {1, 1} V,where Q is the quaternion group and Vis theKlein four-group.
wreath product AHmeans the wreath product of the groupA bythe groupH.is isomorphic to the automorphism group of the
complete bipartite graph on (n,n) vertices.
http://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Approximationhttp://en.wikipedia.org/wiki/Approximation_theoryhttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Equivalence_relationhttp://en.wikipedia.org/wiki/Equals_sign#Approximately_equalhttp://en.wikipedia.org/wiki/Isomorphismhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Quaternion_grouphttp://en.wikipedia.org/wiki/Klein_four-grouphttp://en.wikipedia.org/wiki/Klein_four-grouphttp://en.wikipedia.org/wiki/Klein_four-grouphttp://en.wikipedia.org/wiki/Wreath_producthttp://en.wikipedia.org/wiki/Graph_automorphismhttp://en.wikipedia.org/wiki/Complete_bipartite_graphhttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Approximationhttp://en.wikipedia.org/wiki/Approximation_theoryhttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Equivalence_relationhttp://en.wikipedia.org/wiki/Equals_sign#Approximately_equalhttp://en.wikipedia.org/wiki/Isomorphismhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Quaternion_grouphttp://en.wikipedia.org/wiki/Klein_four-grouphttp://en.wikipedia.org/wiki/Klein_four-grouphttp://en.wikipedia.org/wiki/Wreath_producthttp://en.wikipedia.org/wiki/Graph_automorphismhttp://en.wikipedia.org/wiki/Complete_bipartite_graph -
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wreath product of by
group theory
This may also be writtenA wrH.
normal subgroup
is a normal subgroup of
group theory
NG means thatNis a normal subgroup ofgroup G.
Z(G) G
ideal
is an ideal of
ring theory
IR means thatIis an ideal of ringR. (2) Z
antijoin
the antijoin of
relational algebra
RSmeans the antijoin of the relationsR and S,the tuples inR for which there is not a tuple in Sthat is equal on their common attribute names.
R S=R -R S
semidirect product
the semidirect product of
group theory
NHis the semidirect product ofN(a normalsubgroup) andH(a subgroup), with respect to .Also, ifG =NH, then G is said to split overN.
(may also be written the other way round, as, or as .)
semijoin
the semijoin of
RSis the semijoin of the relationsR and S, theset of all tuples inR for which there is a tuple in Sthat is equal on their common attribute names.
R S= a1,..,an(R S)
http://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Normal_subgrouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Ideal_of_a_ringhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Antijoinhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Semidirect_producthttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Semijoinhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Normal_subgrouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Ideal_of_a_ringhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Antijoinhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Semidirect_producthttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Semijoin -
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relational algebra
natural join
the natural join of
relational algebra
RSis the natural join of the relationsR and S,the set of all combinations of tuples inR and Sthat are equal on their common attribute names.
therefore
therefore;so;
hence
everywhere
Sometimes used in proofs beforelogicalconsequences.
All humans are mortal. Socrates is a human. Socrates is mortal.
because
because;since
everywhere
Sometimes used in proofs before reasoning.3331 isprime it has no positive integer factors other than itself and one.
end of proof
QED;
tombstone;Halmos symbol
everywhere
Used to mark the end of a proof.
(May also be written Q.E.D.)
D'Alembertian It is the generalisation of the Laplace operatorinthe sense that it is the differential operator whichis invariant under the isometry group of the
http://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Natural_joinhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Therefore_signhttp://en.wikipedia.org/wiki/Thereforehttp://en.wikipedia.org/wiki/Logical_consequencehttp://en.wikipedia.org/wiki/Logical_consequencehttp://en.wikipedia.org/wiki/Logical_consequencehttp://en.wikipedia.org/wiki/Logical_consequencehttp://en.wikipedia.org/wiki/Because_signhttp://en.wiktionary.org/wiki/becausehttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Tombstone_(typography)http://en.wikipedia.org/wiki/End_of_proofhttp://en.wikipedia.org/wiki/Quod_erat_demonstrandumhttp://en.wikipedia.org/wiki/Tombstone_(typography)http://en.wikipedia.org/wiki/D'Alembertianhttp://en.wikipedia.org/wiki/Laplace_operatorhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Natural_joinhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Therefore_signhttp://en.wikipedia.org/wiki/Thereforehttp://en.wikipedia.org/wiki/Logical_consequencehttp://en.wikipedia.org/wiki/Logical_consequencehttp://en.wikipedia.org/wiki/Because_signhttp://en.wiktionary.org/wiki/becausehttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Tombstone_(typography)http://en.wikipedia.org/wiki/End_of_proofhttp://en.wikipedia.org/wiki/Quod_erat_demonstrandumhttp://en.wikipedia.org/wiki/Tombstone_(typography)http://en.wikipedia.org/wiki/D'Alembertianhttp://en.wikipedia.org/wiki/Laplace_operator -
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non-Euclidean Laplacian
vector calculus
underlying space and it reduces to the Laplaceoperator if restricted to time independentfunctions.
material implication
implies;if then
propositional logic,Heytingalgebra
AB means ifA is true thenB is also true; ifAis false then nothing is said aboutB.
( may mean the same as, or it may have the
meaning forfunctions given below.)
( may mean the same as,[5]or it may havethe meaning forsupersetgiven below.)
x = 2 x2 = 4 is true, butx2 = 4 x = 2 is in general
false (sincex could be 2).
material equivalence
if and only if;iff
propositional logic
AB meansA is true ifB is true andA is false ifB is false.
x + 5 =y + 2 x + 3 =y
logical negation
not
propositional logic
The statement A is true if and only ifA is false.
A slash placed through another operator is thesame as "" placed in front.
(The symbol~ has many other uses, so or the
(A) Ax y (x = y)
http://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Material_implicationhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Heyting_algebrahttp://en.wikipedia.org/wiki/Heyting_algebrahttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-Copi-4http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-Copi-4http://en.wikipedia.org/wiki/Supersethttp://en.wikipedia.org/wiki/Supersethttp://en.wikipedia.org/wiki/Material_equivalencehttp://en.wikipedia.org/wiki/Iffhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Not_signhttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Material_implicationhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Heyting_algebrahttp://en.wikipedia.org/wiki/Heyting_algebrahttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-Copi-4http://en.wikipedia.org/wiki/Supersethttp://en.wikipedia.org/wiki/Material_equivalencehttp://en.wikipedia.org/wiki/Iffhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Not_signhttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Propositional_logic -
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slash notation is preferred. Computer scientistswill often use ! but this is avoided inmathematical texts.)
logical conjunction ormeetin alattice
and;min;meet
propositional logic, latticetheory
The statementAB is true ifA andB are bothtrue; else it is false.
For functionsA(x) andB(x),A(x) B(x) is usedto mean min(A(x), B(x)).
n < 4 n >2 n = 3 when n is a natural number.
wedge product
wedge product;exterior product
linear algebra
u v means the wedge product ofvectorsu andv. This generalizes the cross product to higherdimensions.
(For vectors inR3, can also be used.)
exponentiation
(raised) to the power of
everywhere
a ^ b means a raised to the power ofb
(a ^ bis more commonly writtenab. The symbol^is generally used in programming languages
where ease of typing and use of plain ASCII text
is preferred.)
2^3 = 23 = 8
logical disjunctionorjoinin alattice
or;max;
The statementAB is true ifA orB (or both)are true; if both are false, the statement is false.
For functionsA(x) andB(x),A(x) B(x) is usedto mean max(A(x), B(x)).
n 4 n 2 n 3 when n is a natural number.
http://en.wikipedia.org/wiki/Logical_conjunctionhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Wedge_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Exponentiationhttp://en.wikipedia.org/wiki/Logical_disjunctionhttp://en.wikipedia.org/wiki/Logical_disjunctionhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Logical_conjunctionhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Wedge_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Exponentiationhttp://en.wikipedia.org/wiki/Logical_disjunctionhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Natural_number -
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join
propositional logic, latticetheory
exclusive or
xor
propositional logic, Booleanalgebra
The statementAB is true when either A or B,but not both, are true.AB means the same. (A) A is always true,AA is always false.
direct sum
direct sum of
abstract algebra
The direct sum is a special way of combiningseveral objects into one general object.
(The bun symbol , or thecoproductsymbol,is used; is only for logic.)
Most commonly, for vector spaces U, V, and W, the
following consequence is used:U= V W ( U= V+ W) ( V W= {0})
universal quantification
for all;for any;for each
predicate logic
x:P(x) meansP(x) is true for allx. n: n2 n.
existential quantification
there exists;there is;there are
predicate logic
x:P(x) means there is at least onex such thatP(x) is true.
n: n is even.
http://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Exclusive_orhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Boolean_algebra_(logic)http://en.wikipedia.org/wiki/Boolean_algebra_(logic)http://en.wikipedia.org/wiki/Direct_sumhttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Coproducthttp://en.wikipedia.org/wiki/Coproducthttp://en.wikipedia.org/wiki/Turned_ahttp://en.wikipedia.org/wiki/Universal_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Existential_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Exclusive_orhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Boolean_algebra_(logic)http://en.wikipedia.org/wiki/Boolean_algebra_(logic)http://en.wikipedia.org/wiki/Direct_sumhttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Coproducthttp://en.wikipedia.org/wiki/Turned_ahttp://en.wikipedia.org/wiki/Universal_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Existential_quantificationhttp://en.wikipedia.org/wiki/Predicate_logic -
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!uniqueness quantification
there exists exactly one
predicate logic
! x:P(x) means there is exactly onex such thatP(x) is true.
! n: n + 5 = 2n.
=:
:=
:
definition
is defined as;is equal by definition to
everywhere
x :=y,y =:x orx y meansx is defined to beanother name fory, under certain assumptionstaken in context.
(Some writers use to mean congruence).
P: Q meansPis defined to be logicallyequivalent to Q.
http://en.wikipedia.org/wiki/Uniqueness_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Triple_barhttp://en.wikipedia.org/wiki/Definitionhttp://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Uniqueness_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Triple_barhttp://en.wikipedia.org/wiki/Definitionhttp://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Logical_equivalence -
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congruence
is congruent to
geometry
ABC DEF means triangle ABC is congruent to (has the same measurements as)triangle DEF.
isomorphic
is isomorphic to
abstract algebra
GHmeans that group G is isomorphic(structurally identical) to groupH.
( can also be used for isomorphic, as describedabove.)
.
congruence relation
... is congruent to ... modulo...
modular arithmetic
a b (mod n) means a b is divisible by n 5 2 (mod 3)
{ , }set brackets
the set of
set theory
{a,b,c} means the set consisting ofa, b, and c.[6] = { 1, 2, 3, }
{ : }
{ | }
set builder notation
the set of such that
set theory
{x :P(x)} means the set of allx for whichP(x) istrue.[6] {x |P(x)} is the same as {x :P(x)}.
{n : n2 < 20} = { 1, 2, 3, 4}
http://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Isomorphichttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Triple_barhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/Set_builder_notationhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Isomorphichttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Triple_barhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/Set_builder_notationhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5 -
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{ }
empty set
the empty set
set theory
means the set with no elements.[6] { } means
the same.
{n : 1 < n2 < 4} =
set membership
is an element of;is not an element of
everywhere, set theory
a Smeans a is an element of the set S;[6]aSmeans a is not an element ofS.[6]
(1/2)1
21
subset
is a subset of
set theory
(subset)AB means every element ofA is also
an element ofB.[7]
(proper subset)AB meansAB butA B.
(Some writers use the symbol as if it were thesame as .)
(A B) A
superset
is a superset of
set theory
AB means every element ofB is also anelement ofA.
AB meansAB butA B.
(Some writers use the symbol as if it were thesame as.)
(AB) B
set-theoretic union
the union of or ;
AB means the set of those elements which areeither inA, or inB, or in both.[7]
AB (AB) =B
http://en.wikipedia.org/wiki/%C3%98_(disambiguation)http://en.wikipedia.org/wiki/Empty_sethttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/Element_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/Subsethttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6http://en.wikipedia.org/wiki/Supersethttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Union_(set_theory)http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6http://en.wikipedia.org/wiki/%C3%98_(disambiguation)http://en.wikipedia.org/wiki/Empty_sethttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/Element_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-3-5http://en.wikipedia.org/wiki/Subsethttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6http://en.wikipedia.org/wiki/Supersethttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Union_(set_theory)http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6 -
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union
set theory
set-theoretic intersection
intersected with;intersect
set theory
A B means the set that contains all thoseelements thatA andB have in common.[7]
{x :x2 = 1} = {1}
symmetric difference
symmetric difference
set theory
A B means the set of elements in exactly one ofA orB.
(Not to be confused with delta, , describedbelow.)
{1,5,6,8} {2,5,8} = {1,2,6}
set-theoretic complement
minus;without
set theory
AB means the set that contains all thoseelements ofA that are not inB.[7]
( can also be used for set-theoretic complementas described above.)
{1,2,3,4} {3,4,5,6} = {1,2}
functionarrow
from to
set theory, type theory
f:X Ymeans the functionfmaps the setXintothe set Y. Letf: {0} be defined by f(x) :=x2.
functionarrow
maps to
f: ab means the functionfmaps the element ato the element b.
Letf:xx+1 (the successor function).
http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Intersection_(set_theory)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6http://en.wikipedia.org/wiki/Symmetric_differencehttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6http://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6http://en.wikipedia.org/wiki/Arrow_(symbol)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Intuitionistic_type_theoryhttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Intersection_(set_theory)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6http://en.wikipedia.org/wiki/Symmetric_differencehttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-4-6http://en.wikipedia.org/wiki/Arrow_(symbol)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Intuitionistic_type_theoryhttp://en.wikipedia.org/wiki/Function_(mathematics) -
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set theory
function composition
composed with
set theory
fgis the function, such that (fg)(x) =f(g(x)).[8] iff(x) := 2x, andg(x) :=x + 3, then (fg)(x) = 2(x + 3).
N
natural numbers
N;
the (set of) natural numbers
numbers
N means either { 0, 1, 2, 3, ...} or { 1, 2, 3, ...}.
The choice depends on the area of mathematicsbeing studied; e.g.number theorists prefer the
latter; analysts,set theorists andcomputerscientists prefer the former. To avoid confusion,
always check an author's definition ofN.
Set theorists often use the notation (forleastinfinite ordinal) to denote the set of naturalnumbers (including zero), along with the
standard ordering relation .
= {|a| : a } or = {|a| > 0: a }
Z
integers
Z;the (set of) integers
numbers
means {..., 3, 2, 1, 0, 1, 2, 3, ...}.
+ or> means {1, 2, 3, ...} . * or means {0,
1, 2, 3, ...} .
= {p, p :p {0}}
nintegers mod n
Zn;the (set of) integers modulo
n
n means {[0], [1], [2], ...[n1]} with additionand multiplication modulo n.
Note that any letter may be used instead ofn,such asp. To avoid confusion with p-adic
3 = {[0], [1], [2]}
http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Function_compositionhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-5-7http://en.wikipedia.org/wiki/Nhttp://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Analysis_(mathematics)http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Least_infinite_ordinalhttp://en.wikipedia.org/wiki/Least_infinite_ordinalhttp://en.wikipedia.org/wiki/Least_infinite_ordinalhttp://en.wikipedia.org/wiki/Zhttp://en.wikipedia.org/wiki/Integerhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Function_compositionhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-d-goldrei-set-5-7http://en.wikipedia.org/wiki/Nhttp://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Analysis_(mathematics)http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Least_infinite_ordinalhttp://en.wikipedia.org/wiki/Least_infinite_ordinalhttp://en.wikipedia.org/wiki/Zhttp://en.wikipedia.org/wiki/Integerhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Modular_arithmetic -
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p
Zn
Zp
numbersnumbers, use/por/(p) instead.
p-adic integers
the (set of)p-adic integers
numbers
Note that any letter may be used instead ofp,such asnorl.
P
projective space
P;
the projective space;the projective line;the projective plane
topology
means a space with a point at infinity. ,
probability
the probability of
probability theory
(X) means the probability of the eventXoccurring.
This may also be written as P(X), Pr(X), P[X] orPr[X].
If a fair coin is flipped, (Heads) = (Tails) = 0.5.
Q
rational numbers
Q;the (set of) rational
numbers;the rationals
means {p/q :p, q}. 3.14000...
http://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/P-adic_integershttp://en.wikipedia.org/wiki/P-adic_integershttp://en.wikipedia.org/wiki/P-adic_integershttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Phttp://en.wikipedia.org/wiki/Projective_planehttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Qhttp://en.wikipedia.org/wiki/Rational_numberhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/P-adic_integershttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Phttp://en.wikipedia.org/wiki/Projective_planehttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Qhttp://en.wikipedia.org/wiki/Rational_number -
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numbers
R
real numbers
R;the (set of) real numbers;
the reals
numbers
means the set of real numbers.
(1)
C
complex numbers
C;the (set of) complex
numbers
numbers
means {a + bi : a,b}. i = (1)
H
quaternions or Hamiltonianquaternions
H;the (set of) quaternions
numbers
means {a + bi + cj + dk: a,b,c,d}.
OBig O notation
big-oh of
Computational complexitytheory
The Big O notation describes the limitingbehaviorof a function, when the argument tendstowards a particular value orinfinity.
If f(x) = 6x4 2x3 + 5 and g(x) = x4 , then
http://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Rhttp://en.wikipedia.org/wiki/Real_numberhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Chttp://en.wikipedia.org/wiki/Complex_numberhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Hhttp://en.wikipedia.org/wiki/Quaternionhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Ohttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Infinityhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Rhttp://en.wikipedia.org/wiki/Real_numberhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Chttp://en.wikipedia.org/wiki/Complex_numberhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Hhttp://en.wikipedia.org/wiki/Quaternionhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Ohttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Infinity -
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infinity
infinity
numbers
is an element of the extended number line thatis greater than all real numbers; it often occurs in
limits.
floor
floor;greatest integer;
entier
numbers
x means the floor ofx, i.e. the largest integerless than or equal tox.
(This may also be written [x], floor(x) orint(x).)
4 = 4, 2.1 = 2, 2.9 = 2, 2.6 = 3
ceiling
ceiling
numbers
x means the ceiling ofx, i.e. the smallest integergreater than or equal tox.
(This may also be written ceil(x) orceiling(x).)
4 = 4, 2.1 = 3, 2.9 = 3, 2.6 = 2
nearest integer function
nearest integer to
numbers
x means the nearest integer tox.
(This may also be written [x], ||x||, nint(x) orRound(x).)
2 = 2, 2.6 = 3, -3.4 = -3, 4.49 = 4
[ : ]degree of a field extension
the degree of
field theory
[K:F] means the degree of the extensionK:F.
[(2) : ] = 2
[ : ] = 2
[ : ] =
[ ] equivalence class [a] means the equivalence class ofa, i.e. {x :x ~a}, where ~ is an equivalence relation.Let a ~ b be trueiffa b (mod 5).
Then [2] = {, 8, 3, 2, 7, }.
http://en.wikipedia.org/wiki/Infinityhttp://en.wikipedia.org/wiki/Infinityhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Extended_real_number_linehttp://en.wikipedia.org/wiki/Limit_(mathematics)http://en.wikipedia.org/wiki/Floor_and_ceiling_functionshttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Floor_and_ceiling_functionshttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Degree_of_a_field_extensionhttp://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Brackethttp://en.wikipedia.org/wiki/Equivalence_classhttp://en.wikipedia.org/wiki/Equivalence_relationhttp://en.wikipedia.org/wiki/Iffhttp://en.wikipedia.org/wiki/Iffhttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Infinityhttp://en.wikipedia.org/wiki/Infinityhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Extended_real_number_linehttp://en.wikipedia.org/wiki/Limit_(mathematics)http://en.wikipedia.org/wiki/Floor_and_ceiling_functionshttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Floor_and_ceiling_functionshttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Degree_of_a_field_extensionhttp://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Brackethttp://en.wikipedia.org/wiki/Equivalence_classhttp://en.wikipedia.org/wiki/Equivalence_relationhttp://en.wikipedia.org/wiki/Iffhttp://en.wikipedia.org/wiki/Modular_arithmetic -
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[ , ][ , , ]
the equivalence class of
abstract algebra
[a]R means the same, but withR as theequivalence relation.
floor
floor;greatest integer;
entier
numbers
[x] means the floor ofx, i.e. the largest integerless than or equal tox.
(This may also be writtenx, floor(x) orint(x).Not to be confused with the nearest integer
function, as described below.)
[3] = 3, [3.5] = 3, [3.99] = 3, [3.7] = 4
nearest integer function
nearest integer to
numbers
[x] means the nearest integer tox.
(This may also be writtenx, ||x||, nint(x) orRound(x).Not to be confused with the floorfunction, as described above.)
[2] = 2, [2.6] = 3, [-3.4] = -3, [4.49] = 4
Iverson bracket
1 if true, 0 otherwise
propositional logic
[S] maps a true statement Sto 1 and a falsestatement Sto 0.
[0=5]=0, [7>0]=1, [2 {2,3,4}]=1, [5 {2,3,4}]=0
image
image of under
everywhere
f[X] means {f(x) :xX}, the image of thefunctionfunder the setX dom(f).
(This may also be written asf(X) if there is norisk of confusing the image offunderXwith thefunction applicationfofX.Another notation isImf, the image offunder its domain.)
closed interval . 0 and 1/2 are in the interval [0,1].
http://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Floor_and_ceiling_functionshttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Iverson_brackethttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Image_(mathematics)http://en.wikipedia.org/wiki/Domain_of_a_functionhttp://en.wikipedia.org/wiki/Closed_intervalhttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Floor_and_ceiling_functionshttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Iverson_brackethttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Image_(mathematics)http://en.wikipedia.org/wiki/Domain_of_a_functionhttp://en.wikipedia.org/wiki/Closed_interval -
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closed interval
order theorycommutator
the commutator of
group theory, ring theory
[g, h] =g1h1gh (orghg1h1), ifg, h G (agroup).
[a, b] = ab ba, ifa, bR (a ring orcommutative algebra).
xy =x[x,y] (group theory).
[AB, C] =A[B, C] + [A, C]B (ring theory).
triple scalar product
the triple scalar product of
vector calculus
[a, b, c] = a b c, the scalar product ofabwith c.
[a, b, c] = [b, c, a] = [c, a, b].
( )
( , )
functionapplication
of
set theory
f(x) means the value of the functionfat theelementx.
Iff(x) :=x2, thenf(3) = 32 = 9.
image
image of under
everywhere
f(X) means {f(x) :xX}, the image of thefunctionfunder the setX dom(f).
(This may also be written asf[X] if there is a risk
of confusing the image offunderXwith thefunction applicationfofX.Another notation isImf, the image offunder its domain.)
combinations
(from) n choose r means the number of combinations ofrelements drawn from a set ofn elements.
http://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Commutatorhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Group_(mathematics)http://en.wikipedia.org/wiki/Ring_(algebra)http://en.wikipedia.org/wiki/Commutative_algebrahttp://en.wikipedia.org/wiki/Triple_scalar_producthttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Scalar_producthttp://en.wikipedia.org/wiki/Cross_producthttp://en.wikipedia.org/wiki/Cross_producthttp://en.wikipedia.org/wiki/Brackethttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Image_(mathematics)http://en.wikipedia.org/wiki/Domain_of_a_functionhttp://en.wikipedia.org/wiki/Combinationhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Commutatorhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Group_(mathematics)http://en.wikipedia.org/wiki/Ring_(algebra)http://en.wikipedia.org/wiki/Commutative_algebrahttp://en.wikipedia.org/wiki/Triple_scalar_producthttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Scalar_producthttp://en.wikipedia.org/wiki/Cross_producthttp://en.wikipedia.org/wiki/Brackethttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Image_(mathematics)http://en.wikipedia.org/wiki/Domain_of_a_functionhttp://en.wikipedia.org/wiki/Combination -
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combinatorics(This may also be written asnCr.)precedence grouping
parentheses
everywhere
Perform the operations inside the parenthesesfirst.
(8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.
tuple
tuple; n-tuple;ordered pair/triple/etc;row vector; sequence
everywhere
An ordered list (or sequence, or horizontal vector,or row vector) of values.
(Note that the notation (a,b) is ambiguous: itcould be an ordered pair or an open interval. Set
theorists and computer scientists often use angle
bracketsinstead of parentheses.)
(a, b) is an ordered pair (or 2-tuple).
(a, b, c) is an ordered triple (or 3-tuple).
( ) is the empty tuple (or 0-tuple).
highest common factor
highest common factor;greatest common divisor;
hcf; gcd
number theory
(a, b) means the highest common factor ofa andb.
(This may also be written hcf(a, b) orgcd(a, b).)
(3, 7) = 1 (they are coprime); (15, 25) = 5.
( , )
] , [
open interval
open interval
order theory
.
(Note that the notation (a,b) is ambiguous: itcould be an ordered pair or an open interval. The
notation ]a,b[ can be used instead.)
4 is not in the interval (4, 18).(0, +) equals the set of positive real numbers.
(( )) multichoose means n multichoosex.
http://en.wikipedia.org/wiki/Combinatoricshttp://en.wikipedia.org/wiki/Tuplehttp://en.wikipedia.org/wiki/Empty_tuplehttp://en.wikipedia.org/wiki/Highest_common_factorhttp://en.wikipedia.org/wiki/Open_intervalhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Multichoosehttp://en.wikipedia.org/wiki/Combinatoricshttp://en.wikipedia.org/wiki/Tuplehttp://en.wikipedia.org/wiki/Empty_tuplehttp://en.wikipedia.org/wiki/Highest_common_factorhttp://en.wikipedia.org/wiki/Open_intervalhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Multichoose -
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multichoose
combinatorics( , ]
] , ]
left-open interval
half-open interval;left-open interval
order theory
. (1, 7] and (, 1]
[ , )
[ , [
right-open interval
half-open interval;
right-open interval
order theory
.[4, 18) and [1, +)
,
inner product
inner product of
linear algebra
u,v means the inner product of u and v, whereu and v are members of an inner product space.
Note that the notationu, v may beambiguous: it could mean the inner product or
the linear span.
There are many variants of the notation, such asu | v and(u | v), which are described below.For spatial vectors, thedot productnotation,xyis common. For matrices, the colon notation
A :Bmay be used. As andcan be hard totype, the more keyboard friendly forms < and>are sometimes seen. These are avoided in
The standard inner product between two vectorsx = (2, 3)andy = (1, 5) is:
x, y= 2 1 + 3 5 = 13
http://en.wikipedia.org/wiki/Combinatoricshttp://en.wikipedia.org/wiki/Half-open_intervalhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Half-open_intervalhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Inner_product_spacehttp://en.wikipedia.org/wiki/Linear_spanhttp://en.wikipedia.org/wiki/Linear_spanhttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Combinatoricshttp://en.wikipedia.org/wiki/Half-open_intervalhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Half-open_intervalhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Inner_product_spacehttp://en.wikipedia.org/wiki/Linear_spanhttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_product -
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mathematical texts.
average
average of
statistics
let S be a subset of N for example, representsthe average of all the element in S.
for a time series :g(t) (t= 1, 2,...)
we can define the structurefunctions Sq( ):
linear span
(linear) span of;linear hull of
linear algebra
S means the span of S V. That is, it is theintersection of all subspaces ofVwhich contain S.u1, u2, is shorthand for { u1, u2, } .
Note that the notationu, v may beambiguous: it could mean theinner productor
the linear span.
The span ofSmay also be written as Sp(S).
.
subgroup generated by a set
the subgroup generated by
group theory
means the smallest subgroup ofG (where S G, a group) containing every element ofS.
is shorthand for .
In S3, and
.
tuple
tuple; n-tuple;ordered pair/triple/etc;row vector; sequence
everywhere
An ordered list (or sequence, or horizontal vector,or row vector) of values.
(The notation (a,b) is often used as well.)
is an ordered pair (or 2-tuple).
is an ordered triple (or 3-tuple).
is theempty tuple (or 0-tuple).
| inner product u | v means the inner product of u and v,where u and v are members of aninner product
http://en.wikipedia.org/wiki/Averagehttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Algebraic_structurehttp://en.wikipedia.org/wiki/Algebraic_structurehttp://en.wikipedia.org/wiki/Linear_spanhttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Generating_set_of_a_grouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Dihedral_group_of_order_6http://en.wikipedia.org/wiki/Dihedral_group_of_order_6http://en.wikipedia.org/wiki/Dihedral_group_of_order_6http://en.wikipedia.org/wiki/Tuplehttp://en.wikipedia.org/wiki/Empty_tuplehttp://en.wikipedia.org/wiki/Empty_tuplehttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Inner_product_spacehttp://en.wikipedia.org/wiki/Inner_product_spacehttp://en.wikipedia.org/wiki/Averagehttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Algebraic_structurehttp://en.wikipedia.org/wiki/Linear_spanhttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Generating_set_of_a_grouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Dihedral_group_of_order_6http://en.wikipedia.org/wiki/Tuplehttp://en.wikipedia.org/wiki/Empty_tuplehttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Inner_product_space -
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(|)inner product of
linear algebra
space.[9] (u | v) means the same.
Another variant of the notation isu, v which
is described above. For spatial vectors, the dotproductnotation,xyis common. For matrices,the colon notationA :Bmay be used. Asandcan be hard to type, the more keyboardfriendly forms < and> are sometimes seen.These are avoided in mathematical texts.
|
ket vector
the ket ;the vector
Dirac notation
| means the vector with label , which is in aHilbert space.
A qubit's state can be represented as |0 + |1 , where andare complex numbers s.t. ||2 + ||2 = 1.
|
bra vector
the bra ;the dual of
Dirac notation
| means the dual of the vector | , a linearfunctional which maps a ket | onto the inner product | .
summation
sum over from to of
arithmetic
means a1 + a2 + + an.= 12 + 22 + 32 + 42
= 1 + 4 + 9 + 16 = 30
productproduct over from to means a1a2an. = (1+2)(2+2)(3+2)(4+2)
http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Inner_product_spacehttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-m-nielsen-quantum-62-8http://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Ket_vectorhttp://en.wikipedia.org/wiki/Dirac_notationhttp://en.wikipedia.org/wiki/Hilbert_spacehttp://en.wikipedia.org/wiki/Qubithttp://en.wikipedia.org/wiki/Bra_vectorhttp://en.wikipedia.org/wiki/Dirac_notationhttp://en.wikipedia.org/wiki/Linear_functionalhttp://en.wikipedia.org/wiki/Linear_functionalhttp://en.wikipedia.org/wiki/Linear_functionalhttp://en.wikipedia.org/wiki/Sigma_(letter)http://en.wikipedia.org/wiki/Summationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Pi_(letter)http://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Inner_product_spacehttp://en.wikipedia.org/wiki/List_of_mathematical_symbols#cite_note-m-nielsen-quantum-62-8http://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Ket_vectorhttp://en.wikipedia.org/wiki/Dirac_notationhttp://en.wikipedia.org/wiki/Hilbert_spacehttp://en.wikipedia.org/wiki/Qubithttp://en.wikipedia.org/wiki/Bra_vectorhttp://en.wikipedia.org/wiki/Dirac_notationhttp://en.wikipedia.org/wiki/Linear_functionalhttp://en.wikipedia.org/wiki/Linear_functionalhttp://en.wikipedia.org/wiki/Sigma_(letter)http://en.wikipedia.org/wiki/Summationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Pi_(letter)http://en.wikipedia.org/wiki/Multiplication -
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of
arithmetic
= 3 4 5 6 = 360
Cartesian product
the Cartesian product of;the direct product of
set theory
means the set of all (n+1)-tuples
(y0, ,yn).
coproduct
coproduct over from to of
category theory
A general construction which subsumes thedisjoint union of sets and of topological spaces,the free product of groups, and the direct sumof
modules and vector spaces. The coproduct of afamily of objects is essentially the "least specific"object to which each object in the family admits amorphism.
delta
delta;change in
calculus
x means a (non-infinitesimal) change inx.
(If the change becomes infinitesimal, and even dare used instead. Not to be confused with the
symmetric difference, written , above.)
is the gradient of a straight line
Laplacian
Laplace operator
vector calculus
The Laplace operator is a second orderdifferential operator in n-dimensional Euclideanspace
If is a twice-differentiablereal-valued function, then the
Laplacian of is defined by
http://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Cartesian_producthttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/N-tuplehttp://en.wikipedia.org/wiki/Coproducthttp://en.wikipedia.org/wiki/Category_theoryhttp://en.wikipedia.org/wiki/Disjoint_unionhttp://en.wikipedia.org/wiki/Disjoint_union_(topology)http://en.wikipedia.org/wiki/Disjoint_union_(topology)http://en.wikipedia.org/wiki/Free_producthttp://en.wikipedia.org/wiki/Direct_sumhttp://en.wikipedia.org/wiki/Direct_sumhttp://en.wikipedia.org/wiki/Morphismhttp://en.wikipedia.org/wiki/Delta_(letter)http://en.wikipedia.org/wiki/Delta_(letter)http://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Laplacianhttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Real-valuedhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Cartesian_producthttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/N-tuplehttp://en.wikipedia.org/wiki/Coproducthttp://en.wikipedia.org/wiki/Category_theoryhttp://en.wikipedia.org/wiki/Disjoint_unionhttp://en.wikipedia.org/wiki/Disjoint_union_(topology)http://en.wikipedia.org/wiki/Free_producthttp://en.wikipedia.org/wiki/Direct_sumhttp://en.wikipedia.org/wiki/Morphismhttp://en.wikipedia.org/wiki/Delta_(letter)http://en.wikipedia.org/wiki/Delta_(letter)http://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Laplacianhttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Real-valued -
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Dirac delta function
Dirac delta of
hyperfunction
(x)
Kronecker delta
Kronecker delta of
hyperfunction
ij
partial derivative
partial;
d
calculus
f/xi means the partial derivative offwith
respect toxi, wherefis a function on (x1, ,xn).Iff(x,y) :=x2y, then f/x = 2xy
boundary
boundary of
topology
Mmeans the boundary ofM {x : ||x|| 2} = {x : ||x|| = 2}
degree of a polynomial
degree of
algebra
fmeans the degree of the polynomialf.
(This may also be written degf.)(x2 1) = 2
gradient
del;nabla;
f(x1, , xn) is the vector of partial derivatives(f/ x1, , f/ xn).
Iff(x,y,z) := 3xy +z, then f= (3y, 3x, 2z)
http://en.wikipedia.org/wiki/Delta_(letter)http://en.wikipedia.org/wiki/Dirac_delta_functionhttp://en.wikipedia.org/wiki/Hyperfunctionhttp://en.wikipedia.org/wiki/Kronecker_deltahttp://en.wikipedia.org/wiki/Hyperfunctionhttp://en.wikipedia.org/wiki/Rounded_dhttp://en.wikipedia.org/wiki/Partial_derivativehttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Boundary_(topology)http://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Degree_of_a_polynomialhttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Nabla_symbolhttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Delhttp://en.wikipedia.org/wiki/Nabla_symbolhttp://en.wikipedia.org/wiki/Delta_(letter)http://en.wikipedia.org/wiki/Dirac_delta_functionhttp://en.wikipedia.org/wiki/Hyperfunctionhttp://en.wikipedia.org/wiki/Kronecker_deltahttp://en.wikipedia.org/wiki/Hyperfunctionhttp://en.wikipedia.org/wiki/Rounded_dhttp://en.wikipedia.org/wiki/Partial_derivativehttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Boundary_(topology)http://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Degree_of_a_polynomialhttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Nabla_symbolhttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Delhttp://en.wikipedia.org/wiki/Nabla_symbol -
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gradient of
vector calculusdivergence
del dot;divergence of
vector calculus
If , then.
curl
curl of
vector calculus
If , then
.
derivative
prime;derivative of
calculus
f(x) means the derivative of the functionfat thepointx, i.e., theslopeof the tangent tofatx.
(The single-quote character' is sometimes usedinstead, especially in ASCII text.)
Iff(x) :=x2, thenf(x) = 2x
derivative
dot;time derivative of
calculus
means the derivative ofx with respect to time.
That is .Ifx(t) := t2, then .
http://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Divergencehttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Curl_(mathematics)http://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Prime_(symbol)http://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Slopehttp://en.wikipedia.org/wiki/Slopehttp://en.wikipedia.org/wiki/Slopehttp://en.wikipedia.org/wiki/Tangenthttp://en.wikipedia.org/wiki/Newton's_notationhttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Divergencehttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Curl_(mathematics)http://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Prime_(symbol)http://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Slopehttp://en.wikipedia.org/wiki/Tangenthttp://en.wikipedia.org/wiki/Newton's_notationhttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Calculus -
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indefinite integral orantiderivative
indefinite integral ofthe antiderivative of
calculus
f(x) dx means a function whose derivative isf. x2
dx =x3
/3 + C
definite integral
integral from to of with respect to
calculus
abf(x) dx means the signed area between thex-axis and the graph of thefunctionfbetweenx = aandx = b.
abx2 dx = b3/3 a3/3;
line integral
line/ path/ curve/ integralof along
calculus
Cfds means the integral offalong the curve C,, where r is a
parametrization ofC.
(If the curve is closed, the symbol may be usedinstead, as described below.)
Contour integral;closed line integral
contour integral of
calculus
Similar to the integral, but used to denote a singleintegration over a closed curve or loop. It issometimes used in physics texts involvingequations regarding Gauss's Law, and while theseformulas involve a closed surface integral, therepresentations describe only the first integrationof the volume over the enclosing surface.Instances where the latter requires simultaneousdouble integration, the symbol would be moreappropriate. A third related symbol is the closed
IfCis a Jordan curve about 0, then .
http://en.wikipedia.org/wiki/Integral_symbolhttp://en.wikipedia.org/wiki/Indefinite_integralhttp://en.wikipedia.org/wiki/Antiderivativehttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Definite_integralhttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Areahttp://en.wikipedia.org/wiki/Graph_(functions)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Line_integralhttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Line_integralhttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Gauss's_Lawhttp://en.wikipedia.org/wiki/Surface_integralhttp://en.wikipedia.org/wiki/Jordan_curvehttp://en.wikipedia.org/wiki/Integral_symbolhttp://en.wikipedia.org/wiki/Indefinite_integralhttp://en.wikipedia.org/wiki/Antiderivativehttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Definite_integralhttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Areahttp://en.wikipedia.org/wiki/Graph_(functions)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Line_integralhttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Line_integralhttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Gauss's_Lawhttp://en.wikipedia.org/wiki/Surface_integralhttp://en.wikipedia.org/wiki/Jordan_curve -
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volume integral, denoted by the symbol .
The contour integral can also frequently be found
with a subscript capital letterC,
C, denotingthat a closed loop integral is, in fact, around acontourC, or sometimes dually appropriately, acircle C. In representations of Gauss's Law, asubscript capital S, S, is used to denote that theintegration is over a closed surface.
projection
Projection of
relational algebra
restricts to theattribute set.
Pi
pi;3.1415926;
227
mathematical constant
Used in various formulasinvolving circles; isequivalent to the amount of area a circle wouldtake up in a square of equal width with an area of4 square units, roughly 3.14/4. It is also the ratioof the circumference to the diameter of a circle.
A=R2=314.16R=10
selection
Selection of
relational algebra
The selection selects all those tuplesinfor which holds between the and the
attribute. The selection selects all thosetuples in for which holds between theattribut