list of mathematical symbols

5/21/2018 List of Mathematical Symbols

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List of mathematical symbolsFrom Wikipedia, the free encyclopedia

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This is a list of symbols found within all branches ofmathematicsto express a formula or to replace aconstant.

When reading the list, it is important to recognize that a mathematical concept is independent of the symbol chosen to represent it. Formany of the symbols below, the symbol is usually synonymous with the corresponding concept (ultimately an arbitrary choice made

as a result of the cumulative history of mathematics), but in some situations a different convention may be used. For example,

depending on context, "" may represent congruence or a definition. Further, in mathematical logic, numerical equality is sometimesrepresented by "" instead of "=", with the latter representing equality ofwell-formed formulas.In short, convention dictates themeaning.

Each symbol is shown both inHTML,whose display depends on the browser's access to an appropriate font installed on the particular

device, and inTEX,as an image.

Contents

[hide]

1 Symbols

2 Variations

3 See also

4 References

5 External links
http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#mw-headhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#mw-headhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#mw-headhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#p-searchhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#p-searchhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#p-searchhttp://en.wikipedia.org/wiki/Wikipedia:WikiProject_Lists#Incomplete_listshttp://en.wikipedia.org/wiki/Wikipedia:WikiProject_Lists#Incomplete_listshttp://en.wikipedia.org/wiki/Wikipedia:WikiProject_Lists#Incomplete_listshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&action=edithttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&action=edithttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&action=edithttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&action=edithttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&action=edithttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&action=edithttp://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/wiki/Template:Citation_neededhttp://en.wikipedia.org/wiki/Template:Citation_neededhttp://en.wikipedia.org/wiki/Template:Citation_neededhttp://en.wikipedia.org/wiki/Wikipedia:Verifiability#Burden_of_evidencehttp://en.wikipedia.org/wiki/Wikipedia:Verifiability#Burden_of_evidencehttp://en.wikipedia.org/wiki/Wikipedia:Verifiability#Burden_of_evidencehttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Constanthttp://en.wikipedia.org/wiki/Constanthttp://en.wikipedia.org/wiki/Constanthttp://en.wikipedia.org/wiki/Well-formed_formulahttp://en.wikipedia.org/wiki/Well-formed_formulahttp://en.wikipedia.org/wiki/Well-formed_formulahttp://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yeshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yeshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yeshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#Symbolshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#Symbolshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#Variationshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#Variationshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#See_alsohttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#See_alsohttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#Referenceshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#Referenceshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#External_linkshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#External_linkshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#External_linkshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#Referenceshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#See_alsohttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#Variationshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#Symbolshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yeshttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/Well-formed_formulahttp://en.wikipedia.org/wiki/Constanthttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Wikipedia:Verifiability#Burden_of_evidencehttp://en.wikipedia.org/wiki/Template:Citation_neededhttp://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&action=edithttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&action=edithttp://en.wikipedia.org/wiki/Wikipedia:WikiProject_Lists#Incomplete_listshttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#p-searchhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#mw-head


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Symbols

Sym

bolin

HTM

L

Sym

bolin

TE

X

Name

Explanation ExamplesRead as

Category

=

equality

is equal to;equals

everywhere

means and represent the samething or value.

inequality

is not equal to;

does not equal

everywhere

means that and do not representthe same thing or value.

(The forms!=, /= or are generally used

in programming languages where ease oftyping and use ofASCIItext is preferred.)

strict inequality

is less than,is greater than

order theory

means is less than .

means is greater than .

proper subgroup

is a propersubgroup of

means is a proper subgroup of.
http://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/Equals_signhttp://en.wikipedia.org/wiki/Equals_signhttp://en.wikipedia.org/wiki/Equality_(mathematics)http://en.wikipedia.org/wiki/Equality_(mathematics)http://en.wikipedia.org/wiki/Not_equals_signhttp://en.wikipedia.org/wiki/Not_equals_signhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Less-than_signhttp://en.wikipedia.org/wiki/Less-than_signhttp://en.wikipedia.org/wiki/Greater-than_signhttp://en.wikipedia.org/wiki/Greater-than_signhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Proper_subgrouphttp://en.wikipedia.org/wiki/Proper_subgrouphttp://en.wikipedia.org/wiki/Proper_subgrouphttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Greater-than_signhttp://en.wikipedia.org/wiki/Less-than_signhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Not_equals_signhttp://en.wikipedia.org/wiki/Equality_(mathematics)http://en.wikipedia.org/wiki/Equals_signhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/TeXhttp://en.wikipedia.org/wiki/HTMLhttp://en.wikipedia.org/wiki/HTML


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group theory

(very)strict

inequality

is much less than,is much greater

than

order theory

xymeansxis much less thany.

xymeansxis much greater thany.0.0031000000

asymptotic

comparison

is of smallerorder than,

is of greater orderthan

analytic number

theory

gmeans the growth offisasymptotically bounded byg.

(This isI. M. Vinogradov's notation.

nother notation is theBig O notation,which looks likef= O(g).)

xex

inequality

is less than or

equal to,

is greater than orequal to

order theory

xymeansxis less than or equal toy.

xymeansxis greater than or equal toy.

(The forms = are generally used inprogramming languages where ease of

typing and use ofASCIItext is preferred.)

3 4 and 5 5

5 4 and 5 5

subgroup

is a subgroup of

group theory

H GmeansHis a subgroup of G.Z ZA3 S3
http://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Much-less-than_signhttp://en.wikipedia.org/wiki/Much-less-than_signhttp://en.wikipedia.org/wiki/Much-greater-than_signhttp://en.wikipedia.org/wiki/Much-greater-than_signhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Analytic_number_theoryhttp://en.wikipedia.org/wiki/Analytic_number_theoryhttp://en.wikipedia.org/wiki/Analytic_number_theoryhttp://en.wikipedia.org/wiki/I._M._Vinogradovhttp://en.wikipedia.org/wiki/I._M._Vinogradovhttp://en.wikipedia.org/wiki/I._M._Vinogradovhttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/Less_than_or_equal_tohttp://en.wikipedia.org/wiki/Less_than_or_equal_tohttp://en.wikipedia.org/wiki/Greater_than_or_equal_tohttp://en.wikipedia.org/wiki/Greater_than_or_equal_tohttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Subgrouphttp://en.wikipedia.org/wiki/Subgrouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Subgrouphttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Greater_than_or_equal_tohttp://en.wikipedia.org/wiki/Less_than_or_equal_tohttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/I._M._Vinogradovhttp://en.wikipedia.org/wiki/Analytic_number_theoryhttp://en.wikipedia.org/wiki/Analytic_number_theoryhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Inequality_(mathematics)http://en.wikipedia.org/wiki/Much-greater-than_signhttp://en.wikipedia.org/wiki/Much-less-than_signhttp://en.wikipedia.org/wiki/Group_theory


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reduction

is reducible to

computationalcomplexity

theory

Bmeans theproblemAcan be reducedto the problemB. Subscripts can be added

to the to indicate what kind of reduction.

If

then

congruence

relation

...is less than ... isgreater than...

modular

arithmetic

7k 28 (mod 2) is only true if kis an eveninteger. Assume that the problem requires kto be non-negative; the domain is defined as

0 k.

10a 5 (mod 5) for 1 a10

vector inequality

... is less than orequal... is greater

than or equal...

order theory

xymeans that each component of vectorxis less than or equal to each corresponding

component of vectory.

xymeans that each component of vectorxis greater than or equal to each

corresponding component of vectory.

It is important to note thatxy remainstrue if every element is equal. However, ifthe operator is changed,xy is true if and

only ifxy is also true.

Karp reduction

is Karp reducibleto;

is polynomial-

L1L2means that the problemL1is Karpreducible toL2.

[1]

IfL1L2andL2P,thenL1P.
http://en.wikipedia.org/wiki/Reduction_(complexity)http://en.wikipedia.org/wiki/Reduction_(complexity)http://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Inequality_(mathematics)#Vector_inequalitieshttp://en.wikipedia.org/wiki/Inequality_(mathematics)#Vector_inequalitieshttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-1http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-1http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-1http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-1http://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Inequality_(mathematics)#Vector_inequalitieshttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Reduction_(complexity)


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time many-one

reducible to

computational

complexitytheory

proportionality

is proportional to;

varies as

everywhere

xmeans thaty= kxfor some constant k. ify= 2x, thenyx.

Karp reduction

is Karp reducible

to;is polynomial-

time many-one

reducible to

computational

complexitytheory

Bmeans theproblemAcan bepolynomially reduced to the problemB.

IfL1L2andL2P,thenL1P.

+

addition

plus;

add

arithmetic

4 + 6 means the sum of 4 and 6. 2 + 7 = 9

disjoint union

the disjoint union

1+A2means the disjoint union of setsA1

andA2.

A1= {3, 4, 5, 6} A2= {7, 8, 9, 10}A1+A2= {(3,1), (4,1), (5,1), (6,1), (7,2), (8,2), (9,2),

(10,2)}
http://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/Plus_signhttp://en.wikipedia.org/wiki/Plus_signhttp://en.wikipedia.org/wiki/Additionhttp://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/Arithmetichttp://en.wikipedia.org/wiki/Disjoint_unionhttp://en.wikipedia.org/wiki/Disjoint_unionhttp://en.wikipedia.org/wiki/Disjoint_unionhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Additionhttp://en.wikipedia.org/wiki/Plus_signhttp://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/Computational_problemhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/Karp_reductionhttp://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theory


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of ... and ...

set theory

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 thenegativeof the number 3. (5) = 5

set-theoretic

complement

minus;

without

set theory

Bmeans the set that contains all theelements ofAthat are not inB.

(can also be used for set-theoreticcomplement as described below.)

{1,2,4} {1,3,4} = {2}

plus-minus

plus or minus

arithmetic

6 3 means both 6 + 3 and 6 3. The equationx= 5 4, has two solutions,x= 7 andx= 3.

plus-minus 10 2 or equivalently 10 20% means therange from 10 2 to 10 + 2.

If a= 100 1mm,then a 99 mm and a 101 mm.
http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Minus_signhttp://en.wikipedia.org/wiki/Minus_signhttp://en.wikipedia.org/wiki/Subtractionhttp://en.wikipedia.org/wiki/Subtractionhttp://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/Arithmetichttp://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/Arithmetichttp://en.wikipedia.org/wiki/Negative_numberhttp://en.wikipedia.org/wiki/Negative_numberhttp://en.wikipedia.org/wiki/Negative_numberhttp://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://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/Plus-minus_signhttp://en.wikipedia.org/wiki/Plus-minus_signhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Plus-minus_signhttp://en.wikipedia.org/wiki/Plus-minus_signhttp://en.wikipedia.org/wiki/Millimetrehttp://en.wikipedia.org/wiki/Millimetrehttp://en.wikipedia.org/wiki/Millimetrehttp://en.wikipedia.org/wiki/Millimetrehttp://en.wikipedia.org/wiki/Plus-minus_signhttp://en.wikipedia.org/wiki/Arithmetichttp://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/Complement_(set_theory)http://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Negative_numberhttp://en.wikipedia.org/wiki/Arithmetichttp://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/Subtractionhttp://en.wikipedia.org/wiki/Minus_signhttp://en.wikipedia.org/wiki/Naive_set_theory


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plus or minus

measurement

minus-plus

minus or plus

arithmetic

6 (3 5) means both 6 + (3 5) and 6 (3 + 5).

cos(xy) = 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 inprogramming languages, where ease of

typing and use ofASCIItext is preferred.)

7 8 = 56

Cartesian product

the Cartesianproduct of ... and

...;

the direct productof ... and ...

set theory

Ymeans the set of allordered pairswith

the first 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

linear algebra

u vmeans the cross product ofvectorsuand v

(1,2,5) (3,4,1) =(22, 16, 2)

group of units

the group of units

Rconsists of the set of units of the ringR,

along with the operation of multiplication.
http://en.wikipedia.org/wiki/Measurementhttp://en.wikipedia.org/wiki/Measurementhttp://en.wikipedia.org/wiki/Minus-plus_signhttp://en.wikipedia.org/wiki/Minus-plus_signhttp://en.wikipedia.org/wiki/Minus-plus_signhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Multiplication_signhttp://en.wikipedia.org/wiki/Multiplication_signhttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Cartesian_producthttp://en.wikipedia.org/wiki/Cartesian_producthttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Ordered_pairshttp://en.wikipedia.org/wiki/Ordered_pairshttp://en.wikipedia.org/wiki/Ordered_pairshttp://en.wikipedia.org/wiki/Cross_producthttp://en.wikipedia.org/wiki/Cross_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Cross_producthttp://en.wikipedia.org/wiki/Ordered_pairshttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Cartesian_producthttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Multiplication_signhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Minus-plus_signhttp://en.wikipedia.org/wiki/Minus-plus_signhttp://en.wikipedia.org/wiki/Measurement


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of

ring theory

This may also be writtenR* as described

below, orU(R).

*

multiplication

times;

multiplied by

arithmetic

a* bmeans the product of aand b.

(Multiplication can also be denoted with

or, or even simple juxtaposition.* isgenerally used where ease of typing and use

ofASCIItext is preferred, such as

rogramming languages.)

4 * 3 means the product of 4 and 3, or 12.

convolution

convolution;

convolved with

functional

analysis

*gmeans the convolution offandg.

.

complex

conjugate

conjugate

complex numbers

* 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 ringR,

along with the operation of multiplication.

This may also be writtenRas described

above, orU(R).

hyperreal*Rmeans the set of hyperreal numbers.

Other sets can be used in place of R.*Nis thehypernaturalnumbers.
http://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Asteriskhttp://en.wikipedia.org/wiki/Asteriskhttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Convolutionhttp://en.wikipedia.org/wiki/Convolutionhttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Hyperreal_numberhttp://en.wikipedia.org/wiki/Hypernaturalhttp://en.wikipedia.org/wiki/Hypernaturalhttp://en.wikipedia.org/wiki/Hypernaturalhttp://en.wikipedia.org/wiki/Hypernaturalhttp://en.wikipedia.org/wiki/Hyperreal_numberhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Group_of_unitshttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Convolutionhttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Asteriskhttp://en.wikipedia.org/wiki/Ring_theory


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numbers

the (set of)hyperreals

non-standard

analysis

Hodge dual

Hodge dual;

Hodge star

linear algebra

*vmeans the Hodge dual of a vector v. If vis ak-vectorwithin ann-dimensional

orientedinner productspace,then *vis an

(nk)-vector.

If are thestandard basisvectors of ,

multiplication

times;

multiplied by

arithmetic

3 4 means the multiplication of 3 by 4. 7 8 = 56

dot product

dot

linear algebra

u vmeans the dot product ofvectorsuand (1,2,5) (3,4,1) = 6

placeholder

(silent)

functional

analysis

A means a placeholder for an argument of

a function. Indicates the functional nature ofan expression without assigning a specific

symbol for an argument.
http://en.wikipedia.org/wiki/Hyperreal_numberhttp://en.wikipedia.org/wiki/Hyperreal_numberhttp://en.wikipedia.org/wiki/Non-standard_analysishttp://en.wikipedia.org/wiki/Non-standard_analysishttp://en.wikipedia.org/wiki/Non-standard_analysishttp://en.wikipedia.org/wiki/Hodge_dualhttp://en.wikipedia.org/wiki/Hodge_dualhttp://en.wikipedia.org/wiki/Linear_algebrahttp://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/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/Vector_spacehttp://en.wikipedia.org/wiki/Standard_basishttp://en.wikipedia.org/wiki/Standard_basishttp://en.wikipedia.org/wiki/Standard_basishttp://en.wikipedia.org/wiki/Middle_dothttp://en.wikipedia.org/wiki/Middle_dothttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Functional_analysishttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Multiplicationhttp://en.wikipedia.org/wiki/Middle_dothttp://en.wikipedia.org/wiki/Standard_basishttp://en.wikipedia.org/wiki/Vector_spacehttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Orientation_(mathematics)http://en.wikipedia.org/wiki/Dimension_(vector_space)http://en.wikipedia.org/wiki/P-vectorhttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Hodge_dualhttp://en.wikipedia.org/wiki/Non-standard_analysishttp://en.wikipedia.org/wiki/Non-standard_analysishttp://en.wikipedia.org/wiki/Hyperreal_number


10/54

tensor product,

tensor product ofmodules

tensor product of

linear algebra

means the tensor product of Vand

U.[3] means the tensor product of

modules Vand Uover theringR.

{1, 2, 3, 4}{1, 1, 2} ={{1, 2, 3, 4}, {1, 2, 3, 4}, {2, 4, 6, 8}}

KulkarniNomizu product

KulkarniNomizu product

tensor algebra

Derived from thetensor productof two

symmetric type (0,2)tensors;it has the

algebraic symmetries of theRiemann

tensor. has components

.

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 G

moduloits subgroupH.

{0, a, 2a, b, b+a, b+2a} / {0, b} = {{0, b}, {a, b+a},

{2a, b+2a}}

quotient set

mod

set theory

/~ means the set of all ~equivalenceclassesinA.

If we define ~ by x ~ yx y , then/~ = { {x+ n: n} : x [0,1) }
http://en.wikipedia.org/wiki/Tensor_producthttp://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/Linear_algebrahttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-m-nielsen-quantum-71-72-3http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-m-nielsen-quantum-71-72-3http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-m-nielsen-quantum-71-72-3http://en.wikipedia.org/wiki/Ring_(mathematics)http://en.wikipedia.org/wiki/Ring_(mathematics)http://en.wikipedia.org/wiki/Ring_(mathematics)http://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_producthttp://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_producthttp://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_producthttp://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_producthttp://en.wikipedia.org/wiki/Tensor_algebrahttp://en.wikipedia.org/wiki/Tensor_algebrahttp://en.wikipedia.org/wiki/Tensor_producthttp://en.wikipedia.org/wiki/Tensor_producthttp://en.wikipedia.org/wiki/Tensor_producthttp://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Riemann_tensorhttp://en.wikipedia.org/wiki/Riemann_tensorhttp://en.wikipedia.org/wiki/Riemann_tensorhttp://en.wikipedia.org/wiki/Riemann_tensorhttp://en.wikipedia.org/wiki/Division_signhttp://en.wikipedia.org/wiki/Division_signhttp://en.wikipedia.org/wiki/Fraction_slashhttp://en.wikipedia.org/wiki/Division_(mathematics)http://en.wikipedia.org/wiki/Division_(mathematics)http://en.wikipedia.org/wiki/Obelushttp://en.wikipedia.org/wiki/Obelushttp://en.wikipedia.org/wiki/Obelushttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Quotient_grouphttp://en.wikipedia.org/wiki/Quotient_grouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Ideal_(ring_theory)http://en.wikipedia.org/wiki/Ideal_(ring_theory)http://en.wikipedia.org/wiki/Set_theoryhttp://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/Equivalence_classhttp://en.wikipedia.org/wiki/Equivalence_classhttp://en.wikipedia.org/wiki/Equivalence_classhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Ideal_(ring_theory)http://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Quotient_grouphttp://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Obelushttp://en.wikipedia.org/wiki/Division_(mathematics)http://en.wikipedia.org/wiki/Fraction_slashhttp://en.wikipedia.org/wiki/Division_signhttp://en.wikipedia.org/wiki/Riemann_tensorhttp://en.wikipedia.org/wiki/Riemann_tensorhttp://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Tensor_producthttp://en.wikipedia.org/wiki/Tensor_algebrahttp://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_producthttp://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_producthttp://en.wikipedia.org/wiki/Ring_(mathematics)http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-m-nielsen-quantum-71-72-3http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Tensor_product_of_moduleshttp://en.wikipedia.org/wiki/Tensor_product_of_moduleshttp://en.wikipedia.org/wiki/Tensor_product


11/54

square root

the (principal)square root of

real numbers

means the nonnegative number whosesquare is .

complex square

root

the (complex)

square root of

complex numbers

if is represented inpolar

coordinateswith , then

.

x

mean

overbar;

bar

statistics

(often read as x bar) is themean(average value of ). .

complexconjugate

conjugate

complex numbers

means the complex conjugate ofz.

(z* can also be used for the conjugate of z,

as described above.)

.

finite sequence,tuple

finite sequence,tuple

model theory

means the finite sequence/tuple

..
http://en.wikipedia.org/wiki/Radical_symbolhttp://en.wikipedia.org/wiki/Radical_symbolhttp://en.wikipedia.org/wiki/Square_roothttp://en.wikipedia.org/wiki/Square_roothttp://en.wikipedia.org/wiki/Real_numbershttp://en.wikipedia.org/wiki/Real_numbershttp://en.wikipedia.org/wiki/Square_root#Square_roots_of_complex_numbershttp://en.wikipedia.org/wiki/Square_root#Square_roots_of_complex_numbershttp://en.wikipedia.org/wiki/Square_root#Square_roots_of_complex_numbershttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Polar_coordinate_systemhttp://en.wikipedia.org/wiki/Polar_coordinate_systemhttp://en.wikipedia.org/wiki/Polar_coordinate_systemhttp://en.wikipedia.org/wiki/Polar_coordinate_systemhttp://en.wikipedia.org/wiki/Overlinehttp://en.wikipedia.org/wiki/Overlinehttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Sequencehttp://en.wikipedia.org/wiki/Sequencehttp://en.wikipedia.org/wiki/Tuplehttp://en.wikipedia.org/wiki/Tuplehttp://en.wikipedia.org/wiki/Model_theoryhttp://en.wikipedia.org/wiki/Model_theoryhttp://en.wikipedia.org/wiki/Model_theoryhttp://en.wikipedia.org/wiki/Tuplehttp://en.wikipedia.org/wiki/Sequencehttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Overlinehttp://en.wikipedia.org/wiki/Polar_coordinate_systemhttp://en.wikipedia.org/wiki/Polar_coordinate_systemhttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Square_root#Square_roots_of_complex_numbershttp://en.wikipedia.org/wiki/Square_root#Square_roots_of_complex_numbershttp://en.wikipedia.org/wiki/Real_numbershttp://en.wikipedia.org/wiki/Square_roothttp://en.wikipedia.org/wiki/Radical_symbol


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algebraic closure

algebraic closureof

field theory

is the algebraic closure of the fieldF.

The field ofalgebraic numbersis sometimes denoted as

because it is the algebraic closure of therational

numbers .

topological

closure

(topological)

closure of

topology

is the topological closure of the set S.

This may also be denoted ascl(S) orCl(S).

In the space of the real numbers, (the rationalnumbers aredensein the real numbers).

unit vector

hat

geometry

(pronounced "a hat") is thenormalizedversionof vector , having length 1.

||

absolute value;

modulus

absolute value of;

modulus of

numbers

|x| means the distance along thereal line(oracross thecomplex plane)betweenxand

zero.

|3| = 3

|5| = |5| = 5

| i| = 1

| 3 + 4i| = 5

Euclidean normor Euclidean

length or

magnitude

Euclidean norm

|x| means the (Euclidean) length ofvectorx.For x= (3,-4)
http://en.wikipedia.org/wiki/Algebraic_closurehttp://en.wikipedia.org/wiki/Algebraic_closurehttp://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Algebraic_numberhttp://en.wikipedia.org/wiki/Algebraic_numberhttp://en.wikipedia.org/wiki/Algebraic_numberhttp://en.wikipedia.org/wiki/Rational_numbershttp://en.wikipedia.org/wiki/Rational_numbershttp://en.wikipedia.org/wiki/Rational_numbershttp://en.wikipedia.org/wiki/Rational_numbershttp://en.wikipedia.org/wiki/Topological_closurehttp://en.wikipedia.org/wiki/Topological_closurehttp://en.wikipedia.org/wiki/Topological_closurehttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Dense_(topology)http://en.wikipedia.org/wiki/Dense_(topology)http://en.wikipedia.org/wiki/Dense_(topology)http://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Absolute_valuehttp://en.wikipedia.org/wiki/Absolute_valuehttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Real_linehttp://en.wikipedia.org/wiki/Real_linehttp://en.wikipedia.org/wiki/Real_linehttp://en.wikipedia.org/wiki/Complex_planehttp://en.wikipedia.org/wiki/Complex_planehttp://en.wikipedia.org/wiki/Complex_planehttp://en.wikipedia.org/wiki/0_(number)http://en.wikipedia.org/wiki/0_(number)http://en.wikipedia.org/wiki/Euclidean_normhttp://en.wikipedia.org/wiki/Euclidean_normhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Euclidean_normhttp://en.wikipedia.org/wiki/0_(number)http://en.wikipedia.org/wiki/Complex_planehttp://en.wikipedia.org/wiki/Real_linehttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Absolute_valuehttp://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Dense_(topology)http://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Topological_closurehttp://en.wikipedia.org/wiki/Topological_closurehttp://en.wikipedia.org/wiki/Rational_numbershttp://en.wikipedia.org/wiki/Rational_numbershttp://en.wikipedia.org/wiki/Algebraic_numberhttp://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Algebraic_closure


13/54

of

geometry

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 elementxof a

normed vector space.[4]

||x+y|| ||x|| + ||y||

nearest integerfunction

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

divisor,divides

divides

a|bmeans adivides b.

abmeans adoes not divide b.

(This symbol can be difficult to type, and its

Since 15 = 35, it is true that 3|15 and 5|15.
http://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Determinanthttp://en.wikipedia.org/wiki/Determinanthttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Linear_algebrahttp://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/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-m-nielsen-quantum-66-4http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-m-nielsen-quantum-66-4http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-m-nielsen-quantum-66-4http://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Vertical_barhttp://en.wikipedia.org/wiki/Divisorhttp://en.wikipedia.org/wiki/Divisorhttp://en.wikipedia.org/wiki/Division_(mathematics)http://en.wikipedia.org/wiki/Division_(mathematics)http://en.wikipedia.org/wiki/Division_(mathematics)http://en.wikipedia.org/wiki/Division_(mathematics)http://en.wikipedia.org/wiki/Divisorhttp://en.wikipedia.org/wiki/Vertical_barhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/wiki/Nearest_integer_functionhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-m-nielsen-quantum-66-4http://en.wikipedia.org/wiki/Normed_vector_spacehttp://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Norm_(mathematics)http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Determinanthttp://en.wikipedia.org/wiki/Geometry


14/54

number theorynegation is rare, so a regular but slightly

shorter vertical bar| character can beused.)

conditional

probability

given

probability

P(A|B) means the probability of the event aoccurring given that boccurs.

if X is a uniformly random day of the yearP(X is May25 | X is in May) = 1/31

restriction

restriction of to ;

restricted to

set theory

|Ameans the functionfrestricted to the set

, that is, it is the function withdomainAdom(f) that agrees withf.

The functionf: R Rdefined byf(x) =x2is notinjective, butf|R

+is injective.

such that

such that;so that

everywhere

| means such that, see ":" (describedbelow).

S = {(x,y) | 0 < y < f(x)}The set of (x,y) such that y is greater than 0 and less

than f(x).

||

parallel

is parallel to

geometry

x||ymeansxis parallel toy. If l|| mand mnthen ln.

incomparability

is incomparable

x||ymeansxis incomparable toy. {1,2} || {2,3} under set containment.
http://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Conditional_probabilityhttp://en.wikipedia.org/wiki/Conditional_probabilityhttp://en.wikipedia.org/wiki/Conditional_probabilityhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Restriction_(mathematics)http://en.wikipedia.org/wiki/Restriction_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Domain_(function)http://en.wikipedia.org/wiki/Domain_(function)http://en.wikipedia.org/wiki/Domain_(function)http://en.wikipedia.org/wiki/Parallel_(geometry)http://en.wikipedia.org/wiki/Parallel_(geometry)http://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Comparabilityhttp://en.wikipedia.org/wiki/Comparabilityhttp://en.wikipedia.org/wiki/Comparabilityhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Parallel_(geometry)http://en.wikipedia.org/wiki/Domain_(function)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Restriction_(mathematics)http://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Conditional_probabilityhttp://en.wikipedia.org/wiki/Conditional_probabilityhttp://en.wikipedia.org/wiki/Number_theory


15/54

to

order theory

exactdivisibility

exactly divides

number theory

a|| nmeanspaexactly divides n(i.e.padivides nbutp

a+1does not).

23|| 360.

#

cardinality

cardinality of;size of;

order of

set theory

#Xmeans the cardinality of the setX.

(|| may be used instead as describedabove.)

#{4, 6, 8} = 3

connected sum

connected sum

of;

knot sum of;knot composition

of

topology,knottheory

#Bis the connected sum of the manifolds

andB. IfAandBare knots, then thisdenotes the knot sum, which has a slightly

stronger condition.

A#SmishomeomorphictoA, for any manifoldA, and

the sphere Sm.

primorial

primorial

number theory

n# is product of all prime numbers less than

or equal to n.12# = 2 3 5 7 11 = 2310
http://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Order_theoryhttp://en.wikipedia.org/wiki/Divisibilityhttp://en.wikipedia.org/wiki/Divisibilityhttp://en.wikipedia.org/wiki/Divisibilityhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_signhttp://en.wikipedia.org/wiki/Number_signhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Connected_sumhttp://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/Knot_theoryhttp://en.wikipedia.org/wiki/Knot_theoryhttp://en.wikipedia.org/wiki/Knot_theoryhttp://en.wikipedia.org/wiki/Homeomorphichttp://en.wikipedia.org/wiki/Homeomorphichttp://en.wikipedia.org/wiki/Homeomorphichttp://en.wikipedia.org/wiki/Primorialhttp://en.wikipedia.org/wiki/Primorialhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Primorialhttp://en.wikipedia.org/wiki/Homeomorphichttp://en.wikipedia.org/wiki/Knot_theoryhttp://en.wikipedia.org/wiki/Knot_theoryhttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Connected_sumhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Number_signhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Divisibilityhttp://en.wikipedia.org/wiki/Order_theory


16/54

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

beth

set theory

represents an infinite cardinality (similarto , but does not necessarily index all ofthe numbers indexed by . ).

cardinality of thecontinuum

cardinality of the

continuum;c;

cardinality of thereal numbers

set theory

The cardinality of is denoted by or bythe symbol (a lowercaseFrakturletter C).

:

such that

such that;

so that

everywhere

: means such that, and is used in proofsand theset-builder notation(described

below).

n: nis even.

field extension

extends;over

field theory

K:Fmeans the fieldKextends the fieldF.

This may also be written asKF.:
http://en.wikipedia.org/wiki/Aleph_(letter)http://en.wikipedia.org/wiki/Aleph_numberhttp://en.wikipedia.org/wiki/Aleph_numberhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Beth_(letter)http://en.wikipedia.org/wiki/Beth_(letter)http://en.wikipedia.org/wiki/Beth_numberhttp://en.wikipedia.org/wiki/Beth_numberhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Cardinality_of_the_continuumhttp://en.wikipedia.org/wiki/Cardinality_of_the_continuumhttp://en.wikipedia.org/wiki/Cardinality_of_the_continuumhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Fraktur_(script)http://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/Colon_(punctuation)http://en.wikipedia.org/wiki/Set-builder_notationhttp://en.wikipedia.org/wiki/Set-builder_notationhttp://en.wikipedia.org/wiki/Set-builder_notationhttp://en.wikipedia.org/wiki/Field_extensionhttp://en.wikipedia.org/wiki/Field_extensionhttp://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Field_theory_(mathematics)http://en.wikipedia.org/wiki/Field_extensionhttp://en.wikipedia.org/wiki/Set-builder_notationhttp://en.wikipedia.org/wiki/Colon_(punctuation)http://en.wikipedia.org/wiki/Fraktur_(script)http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Cardinality_of_the_continuumhttp://en.wikipedia.org/wiki/Cardinality_of_the_continuumhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Beth_numberhttp://en.wikipedia.org/wiki/Beth_(letter)http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Aleph_numberhttp://en.wikipedia.org/wiki/Aleph_(letter)


17/54

inner productofmatrices

inner product of

linear algebra

:Bmeans the Frobenius inner product of

the matricesAandB.

The general inner product is denoted byu,

v, u| vor(u| v), as described below. Forspatial vectors, thedot productnotation,xyis common.See alsoBra-ket notation.

index of a

subgroup

index ofsubgroup

group theory

The index of a subgroup H in a group G is

the "relative size" of H in G: equivalently,the number 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 !Ais true if and only ifAis

false.

A slash placed through another operator is

the same as "!" placed in front.

(The symbol! is primarily from computerscience. It is avoided in mathematical texts,

where the notationAis preferred.)

!(!A)A

xy!(x=y)

~ probability

distribution~ D, means therandom variableXhas the

probability distributionD.X~N(0,1), thestandard normal distribution
http://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Inner_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Bra-ket_notationhttp://en.wikipedia.org/wiki/Bra-ket_notationhttp://en.wikipedia.org/wiki/Bra-ket_notationhttp://en.wikipedia.org/wiki/Index_of_a_subgrouphttp://en.wikipedia.org/wiki/Index_of_a_subgrouphttp://en.wikipedia.org/wiki/Index_of_a_subgrouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Cosethttp://en.wikipedia.org/wiki/Cosethttp://en.wikipedia.org/wiki/Cosethttp://en.wikipedia.org/wiki/Exclamation_markhttp://en.wikipedia.org/wiki/Exclamation_markhttp://en.wikipedia.org/wiki/Factorialhttp://en.wikipedia.org/wiki/Factorialhttp://en.wikipedia.org/wiki/Combinatoricshttp://en.wikipedia.org/wiki/Combinatoricshttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Tildehttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Standard_normal_distributionhttp://en.wikipedia.org/wiki/Standard_normal_distributionhttp://en.wikipedia.org/wiki/Standard_normal_distributionhttp://en.wikipedia.org/wiki/Standard_normal_distributionhttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Tildehttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Combinatoricshttp://en.wikipedia.org/wiki/Factorialhttp://en.wikipedia.org/wiki/Exclamation_markhttp://en.wikipedia.org/wiki/Cosethttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Index_of_a_subgrouphttp://en.wikipedia.org/wiki/Index_of_a_subgrouphttp://en.wikipedia.org/wiki/Bra-ket_notationhttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Inner_product


18/54

has distribution

statistics

row equivalence

is row equivalentto

matrix theory

~Bmeans thatBcan be generated by usinga series ofelementary row operationsonA

sameorder of

magnitude

roughly similar;

poorly

approximates

approximationtheory

m~ nmeans the quantities mand nhave the

sameorder of magnitude,or general size.

(Note that~ is used for an approximationthat is poor, otherwise use .)

2 ~ 5

8 9 ~ 100

but 2 10

asymptoticallyequivalent

is asymptoticallyequivalent to

asymptotic

analysis

~gmeans .x ~ x+1

equivalencerelation

are in the same

equivalence class

a~ bmeans (and equivalently

).1 ~ 5 mod 4
http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Elementary_matrix_transformationshttp://en.wikipedia.org/wiki/Elementary_matrix_transformationshttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Elementary_row_operationshttp://en.wikipedia.org/wiki/Elementary_row_operationshttp://en.wikipedia.org/wiki/Elementary_row_operationshttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Approximationhttp://en.wikipedia.org/wiki/Approximationhttp://en.wikipedia.org/wiki/Approximationhttp://en.wikipedia.org/wiki/Approximation_theoryhttp://en.wikipedia.org/wiki/Approximation_theoryhttp://en.wikipedia.org/wiki/Approximation_theoryhttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Equivalence_relationhttp://en.wikipedia.org/wiki/Equivalence_relationhttp://en.wikipedia.org/wiki/Equivalence_relationhttp://en.wikipedia.org/wiki/Equivalence_relationhttp://en.wikipedia.org/wiki/Equivalence_relationhttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Approximation_theoryhttp://en.wikipedia.org/wiki/Approximation_theoryhttp://en.wikipedia.org/wiki/Approximationhttp://en.wikipedia.org/wiki/Approximationhttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Elementary_row_operationshttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Elementary_matrix_transformationshttp://en.wikipedia.org/wiki/Statistics


19/54

everywhere

approximately

equal

is approximatelyequal to

everywhere

xymeansxis approximately equal toy.

This may also be written, , ~,(LibraSymbol), or.

3.14159

isomorphism

is isomorphic to

group theory

GHmeans that group Gis isomorphic(structurally identical) to groupH.

(can also be used for isomorphic, asdescribed below.)

Q/ {1, 1} V,where Qis thequaternion groupand Vis theKleinfour-group.

wreath product

wreath product of by

group theory

Hmeans the wreath product of thegroupAby the groupH.

This may also be writtenAwrH.

is isomorphic to theautomorphismgroup ofthecomplete bipartite graphon (n,n) vertices.

normal subgroup

is a normalsubgroup of

group theory

Gmeans thatNis a normal subgroup of

group G.Z(G) G

ideal

is an ideal of

ring theory

IRmeans thatIis an ideal of ringR. (2) Z
http://en.wikipedia.org/wiki/Equals_sign#Approximately_equalhttp://en.wikipedia.org/wiki/Equals_sign#Approximately_equalhttp://en.wikipedia.org/wiki/Isomorphismhttp://en.wikipedia.org/wiki/Isomorphismhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Quaternion_grouphttp://en.wikipedia.org/wiki/Quaternion_grouphttp://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/Klein_four-grouphttp://en.wikipedia.org/wiki/Wreath_producthttp://en.wikipedia.org/wiki/Wreath_producthttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Graph_automorphismhttp://en.wikipedia.org/wiki/Graph_automorphismhttp://en.wikipedia.org/wiki/Graph_automorphismhttp://en.wikipedia.org/wiki/Complete_bipartite_graphhttp://en.wikipedia.org/wiki/Complete_bipartite_graphhttp://en.wikipedia.org/wiki/Complete_bipartite_graphhttp://en.wikipedia.org/wiki/Normal_subgrouphttp://en.wikipedia.org/wiki/Normal_subgrouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Ideal_of_a_ringhttp://en.wikipedia.org/wiki/Ideal_of_a_ringhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Ring_theoryhttp://en.wikipedia.org/wiki/Ideal_of_a_ringhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Normal_subgrouphttp://en.wikipedia.org/wiki/Complete_bipartite_graphhttp://en.wikipedia.org/wiki/Graph_automorphismhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Wreath_producthttp://en.wikipedia.org/wiki/Klein_four-grouphttp://en.wikipedia.org/wiki/Klein_four-grouphttp://en.wikipedia.org/wiki/Quaternion_grouphttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Isomorphismhttp://en.wikipedia.org/wiki/Equals_sign#Approximately_equal


20/54

antijoin

the antijoin of

relational algebra

RSmeans the antijoin of the relationsR

and S, the tuples inRfor which there is nota tuple in Sthat is equal on their common

attribute names.

R S=R-R S

semidirectproduct

the semidirectproduct of

group theory

His the semidirect product ofN(anormal subgroup) andH(a subgroup), with

respect to . Also, if G=NH, then Gissaid to split overN.

(may also be written the other way round,as, or as.)

semijoin

the semijoin of

relational algebra

RSis the semijoin of the relationsRand

S, the set of all tuples inRfor which there isa tuple in Sthat is equal on their common

attribute names.

R S= a1,..,an(R S)

natural join

the natural join of

relational algebra

RSis the natural join of the relationsRand S, the set of all combinations of tuples

inRand Sthat are equal on their commonattribute names.

therefore

therefore;so;

hence

everywhere

Sometimes used in proofs beforelogical

consequences.All humans are mortal. Socrates is a human. Socratesis mortal.

because Sometimes used in proofs before reasoning. 11 isprimeit has no positive integer factors otherthan itself and one.
http://en.wikipedia.org/wiki/Antijoinhttp://en.wikipedia.org/wiki/Antijoinhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Semidirect_producthttp://en.wikipedia.org/wiki/Semidirect_producthttp://en.wikipedia.org/wiki/Semidirect_producthttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Semijoinhttp://en.wikipedia.org/wiki/Semijoinhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Natural_joinhttp://en.wikipedia.org/wiki/Natural_joinhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Therefore_signhttp://en.wikipedia.org/wiki/Therefore_signhttp://en.wikipedia.org/wiki/Thereforehttp://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.wikipedia.org/wiki/Because_signhttp://en.wiktionary.org/wiki/becausehttp://en.wiktionary.org/wiki/becausehttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wiktionary.org/wiki/becausehttp://en.wikipedia.org/wiki/Because_signhttp://en.wikipedia.org/wiki/Logical_consequencehttp://en.wikipedia.org/wiki/Logical_consequencehttp://en.wikipedia.org/wiki/Thereforehttp://en.wikipedia.org/wiki/Therefore_signhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Natural_joinhttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Semijoinhttp://en.wikipedia.org/wiki/Group_theoryhttp://en.wikipedia.org/wiki/Semidirect_producthttp://en.wikipedia.org/wiki/Semidirect_producthttp://en.wikipedia.org/wiki/Relational_algebrahttp://en.wikipedia.org/wiki/Antijoin


21/54

because;

since

everywhere

end of proof

QED;

tombstone;Halmos symbol

everywhere

Used to mark the end of a proof.

(May also be writtenQ.E.D.)

D'Alembertian

non-Euclidean

Laplacian

vector calculus

It is the generalisation of theLaplaceoperatorin the sense that it is the

differential operator which is invariant

under the isometry group of the underlyingspace and it reduces to the Laplace operator

if restricted to time independent functions.

material

implication

implies;

if then

propositional

logic,Heytingalgebra

Bmeans ifAis true thenBis also true;

ifAis false then nothing is said aboutB.

( may mean the same as, or it mayhave the meaning forfunctionsgiven

below.)

(may mean the same as,[5]or it mayhave the meaning forsupersetgiven below.)

x= 2x2= 4 is true, butx2= 4x= 2 is in generalfalse (sincexcould be 2).
http://en.wikipedia.org/wiki/Tombstone_(typography)http://en.wikipedia.org/wiki/End_of_proofhttp://en.wikipedia.org/wiki/End_of_proofhttp://en.wikipedia.org/wiki/Quod_erat_demonstrandumhttp://en.wikipedia.org/wiki/Quod_erat_demonstrandumhttp://en.wikipedia.org/wiki/Tombstone_(typography)http://en.wikipedia.org/wiki/Tombstone_(typography)http://en.wikipedia.org/wiki/D%27Alembertianhttp://en.wikipedia.org/wiki/D%27Alembertianhttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/Laplace_operatorhttp://en.wikipedia.org/wiki/Laplace_operatorhttp://en.wikipedia.org/wiki/Laplace_operatorhttp://en.wikipedia.org/wiki/Laplace_operatorhttp://en.wikipedia.org/wiki/Material_implicationhttp://en.wikipedia.org/wiki/Material_implicationhttp://en.wikipedia.org/wiki/Material_implicationhttp://en.wikipedia.org/wiki/Propositional_logichttp://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/Heyting_algebrahttp://en.wikipedia.org/wiki/Heyting_algebrahttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Heyting_algebrahttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-Copi-5http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-Copi-5http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-Copi-5http://en.wikipedia.org/wiki/Supersethttp://en.wikipedia.org/wiki/Supersethttp://en.wikipedia.org/wiki/Supersethttp://en.wikipedia.org/wiki/Supersethttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-Copi-5http://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Heyting_algebrahttp://en.wikipedia.org/wiki/Heyting_algebrahttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Material_implicationhttp://en.wikipedia.org/wiki/Material_implicationhttp://en.wikipedia.org/wiki/Laplace_operatorhttp://en.wikipedia.org/wiki/Laplace_operatorhttp://en.wikipedia.org/wiki/Vector_calculushttp://en.wikipedia.org/wiki/D%27Alembertianhttp://en.wikipedia.org/wiki/Tombstone_(typography)http://en.wikipedia.org/wiki/Quod_erat_demonstrandumhttp://en.wikipedia.org/wiki/End_of_proofhttp://en.wikipedia.org/wiki/Tombstone_(typography)


22/54

material

equivalence

if and only if;

iff

propositionallogic

BmeansAis true ifBis true andAis

false ifBis false.

x+ 5 =y+ 2x+ 3 =y

logical negation

not

propositionallogic

The statement Ais true if and only ifAis

false.

A slash placed through another operator is

the same as "" placed in front.

(The symbol~ has many other uses, so orthe slash notation is preferred. Computerscientists will often use! but this is avoided

in mathematical texts.)

(A)Axy(x=y)

logicalconjunctionor

meetin alattice

and;min;

meet

propositional

logic,lattice

theory

The statementABis true ifAandBareboth true; else it is false.

For functionsA(x) andB(x),A(x) B(x) isused to mean min(A(x), B(x)).

n< 4 n>2n= 3 when nis anatural number.

wedge product

wedge product;

uvmeans the wedge product of anymultivectorsuand v. In three dimensionalEuclidean spacethe wedge product and the
http://en.wikipedia.org/wiki/Material_equivalencehttp://en.wikipedia.org/wiki/Material_equivalencehttp://en.wikipedia.org/wiki/Material_equivalencehttp://en.wikipedia.org/wiki/Iffhttp://en.wikipedia.org/wiki/Iffhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Not_signhttp://en.wikipedia.org/wiki/Not_signhttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Logical_conjunctionhttp://en.wikipedia.org/wiki/Logical_conjunctionhttp://en.wikipedia.org/wiki/Logical_conjunctionhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Maxima_and_minimahttp://en.wikipedia.org/wiki/Maxima_and_minimahttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_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/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Wedge_producthttp://en.wikipedia.org/wiki/Wedge_producthttp://en.wikipedia.org/wiki/Multivectorhttp://en.wikipedia.org/wiki/Multivectorhttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Multivectorhttp://en.wikipedia.org/wiki/Wedge_producthttp://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Maxima_and_minimahttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Logical_conjunctionhttp://en.wikipedia.org/wiki/Logical_conjunctionhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Logical_negationhttp://en.wikipedia.org/wiki/Not_signhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Iffhttp://en.wikipedia.org/wiki/Material_equivalencehttp://en.wikipedia.org/wiki/Material_equivalence


23/54

exterior product

exterior algebra

cross product of twovectorsare each other's

Hodge dual.

exponentiation

(raised) to thepower of

everywhere

a^ bmeans araised to the power of b

(a^ bis more commonly writtenab. The

symbol^ is generally used in programming

languages where ease of typing and use oflain ASCII text is preferred.)

2^3 = 23= 8

logical

disjunctionoroinin alattice

or;

max;join

propositional

logic,lattice

theory

The statementABis true ifAorB(orboth) are true; if both are false, the

statement is false.

For functionsA(x) andB(x),A(x) B(x) isused to mean max(A(x), B(x)).

n 4 n 2n 3 when nis anatural number.

exclusive or

xor

propositional

logic,Booleanalgebra

The statementABis true when either Aor B, but not both, are true.ABmeans thesame.

(A)Ais always true,AAis always false.

direct sum

direct sum of

abstract algebra

The direct sum is a special way of

combining several objects into one generalobject.

(The bun symbol, or thecoproduct

Most commonly, for vector spaces U, V, and W, thefollowing consequence is used:

U= VW(U= V+ W) (V W= {0})
http://en.wikipedia.org/wiki/Exterior_algebrahttp://en.wikipedia.org/wiki/Exterior_algebrahttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Hodge_dualhttp://en.wikipedia.org/wiki/Hodge_dualhttp://en.wikipedia.org/wiki/Exponentiationhttp://en.wikipedia.org/wiki/Exponentiationhttp://en.wikipedia.org/wiki/Logical_disjunctionhttp://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/Lattice_(order)http://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_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/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Exclusive_orhttp://en.wikipedia.org/wiki/Exclusive_orhttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://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/Boolean_algebra_(logic)http://en.wikipedia.org/wiki/Boolean_algebra_(logic)http://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Direct_sumhttp://en.wikipedia.org/wiki/Direct_sumhttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Coproducthttp://en.wikipedia.org/wiki/Coproducthttp://en.wikipedia.org/wiki/Coproducthttp://en.wikipedia.org/wiki/Coproducthttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Direct_sumhttp://en.wikipedia.org/wiki/Boolean_algebra_(logic)http://en.wikipedia.org/wiki/Boolean_algebra_(logic)http://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Exclusive_orhttp://en.wikipedia.org/wiki/Natural_numberhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Propositional_logichttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Logical_disjunctionhttp://en.wikipedia.org/wiki/Logical_disjunctionhttp://en.wikipedia.org/wiki/Exponentiationhttp://en.wikipedia.org/wiki/Hodge_dualhttp://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Exterior_algebra


24/54

symbol,is used; is only for logic.)

universal

quantification

for all;for any;

for each

predicate logic

x:P(x) meansP(x) is true for allx. n: n2 n.

existentialquantification

there exists;there is;

there are

predicate logic

x:P(x) means there is at least onexsuchthatP(x) is true.

n: nis even.

!

uniquenessquantification

there exists

exactly one

predicate logic

!x:P(x) means there is exactly onexsuchthatP(x) is true.

! n: n+ 5 = 2n.

=:

:=

definition

is defined as;

is equal bydefinition to

everywhere

x:=y,y=:xorxymeansxis defined tobe another name fory, under certain

assumptions taken in context.

(Some writers use to meancongruence).

P:QmeansPis defined to belogicallyequivalentto Q.
http://en.wikipedia.org/wiki/Turned_ahttp://en.wikipedia.org/wiki/Turned_ahttp://en.wikipedia.org/wiki/Universal_quantificationhttp://en.wikipedia.org/wiki/Universal_quantificationhttp://en.wikipedia.org/wiki/Universal_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Existential_quantificationhttp://en.wikipedia.org/wiki/Existential_quantificationhttp://en.wikipedia.org/wiki/Existential_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Uniqueness_quantificationhttp://en.wikipedia.org/wiki/Uniqueness_quantificationhttp://en.wikipedia.org/wiki/Uniqueness_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Definitionhttp://en.wikipedia.org/wiki/Definitionhttp://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Logical_equivalencehttp://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Definitionhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Uniqueness_quantificationhttp://en.wikipedia.org/wiki/Uniqueness_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Existential_quantificationhttp://en.wikipedia.org/wiki/Existential_quantificationhttp://en.wikipedia.org/wiki/Predicate_logichttp://en.wikipedia.org/wiki/Universal_quantificationhttp://en.wikipedia.org/wiki/Universal_quantificationhttp://en.wikipedia.org/wiki/Turned_a


25/54

:

congruence

is congruent to

geometry

ABC DEF means triangle ABC iscongruent to (has the same measurementsas) triangle DEF.

isomorphic

is isomorphic to

abstract algebra

GHmeans that group Gis isomorphic(structurally identical) to groupH.

( can also be used for isomorphic, asdescribed above.)

.

congruencerelation

... is congruent to

a b(mod n) means a bis divisible by n 5 2 (mod 3)
http://en.wikipedia.org/wiki/Triple_barhttp://en.wikipedia.org/wiki/Triple_barhttp://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Isomorphichttp://en.wikipedia.org/wiki/Isomorphichttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Triple_barhttp://en.wikipedia.org/wiki/Triple_barhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Congruence_relationhttp://en.wikipedia.org/wiki/Triple_barhttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Isomorphichttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Triple_bar


26/54

... modulo ...

modulararithmetic

{,

}

setbrackets

the set of

set theory

{a,b,c} means the set consisting of a, b, and

c.[6]

= { 1, 2, 3, }

{ :

}

{ |

}

{ ;

}

set buildernotation

the set of suchthat

set theory

{x:P(x)} means the set of allxfor which

P(x) is true.[6]

{x|P(x)} is the same as {x:P(x)}.

{n: n2< 20} = { 1, 2, 3, 4}

{ }

empty set

the empty set

set theory

means the set with no elements.[6]{ }means the same.

{n: 1 < n2< 4} =
http://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/wiki/Set_builder_notationhttp://en.wikipedia.org/wiki/Set_builder_notationhttp://en.wikipedia.org/wiki/Set_builder_notationhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/wiki/%C3%98_(disambiguation)http://en.wikipedia.org/wiki/%C3%98_(disambiguation)http://en.wikipedia.org/wiki/Empty_sethttp://en.wikipedia.org/wiki/Empty_sethttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Empty_sethttp://en.wikipedia.org/wiki/%C3%98_(disambiguation)http://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Set_builder_notationhttp://en.wikipedia.org/wiki/Set_builder_notationhttp://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&printable=yes#cite_note-d-goldrei-set-3-6http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Curly_bracketshttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Modular_arithmetic


27/54

set membership

is an element of;is not an element

of

everywhere,settheory

aSmeans ais an element of the set S;[6]a

Smeans ais not an element of S.[6]

(1/2)1

21

subset

is a subset of

set theory

(subset)ABmeans every element ofAisalso an element ofB.

[7]

(proper subset)ABmeansABbutAB.

(Some writers use the symbolas if it werethe same as.)

(AB) A

superset

is a superset of

set theory

Bmeans every element ofBis also anelement ofA.

BmeansABbutAB.

(Some writers use the symbolas if it werethe same as.)

(AB) B

set-theoretic

union

the union of or;

union

set theory

Bmeans the set of those elementswhich are either inA, or inB, or in both.

[7]

AB(AB) =B
http://en.wikipedia.org/wiki/Element_(mathematics)http://en.wikipedia.org/wiki/Element_(mathematics)http://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/wiki/Naive_set_theoryhttp://en.wikipedia.org/w/index.php?title=List_of_ma