Table of mathematical symbols - Ies Jovellanos

[Pages:13]Table of mathematical symbols - Wikipedia, the free encyclopedia

P?gina 1 de 13

Table of mathematical symbols

From Wikipedia, the free encyclopedia For the HTML codes of mathematical symbols see mathematical HTML. Note: This article contains special characters.

The following table lists many specialized symbols commonly used in mathematics.

Basic mathematical symbols

Symbol

=

Name

Read as

Explanation

Category

equality

is equal to; equals

x = y means x and y represent the same thing or value.

everywhere

1 + 1 = 2

Examples

!=

inequation

x y means that x and y

do not represent the same thing or value.

is not equal to; does not equal

(The symbols != and 1 2

are primarily from

computer science. They

are avoided in

everywhere mathematical texts.)

<

strict inequality

x < y means x is less

than y.

>

is less than, is greater than, is much less than,

x > y means x is greater than y.

3 < 4 5 > 4.

is much greater than

x y means x is much less than y.

0.003 1000000

x y means x is much

greater than y. order theory

= +

-

?

equal to, is y.

greater than or

equal to

(The symbols = are primarily from computer science. They

3 4 and 5 5 5 4 and 5 5

order theory are avoided in

mathematical texts.)

proportionality

is proportional to; varies as

y x means that y = kx for some constant k.

if y = 2x, then y x

everywhere

addition

plus

4 + 6 means the sum of 4 and 6.

2 + 7 = 9

arithmetic

disjoint union

the disjoint A1 + A2 means the

A1 = {1, 2, 3, 4} A2 = {2, 4, 5, 7}

union of ... and ...

disjoint union of sets A1 A1 + A2 = {(1,1), (2,1), (3,1), (4,1), (2,2),

and A2.

(4,2), (5,2), (7,2)}

set theory

subtraction

minus

9 - 4 means the subtraction of 4 from 9.

8 - 3 = 5

arithmetic

negative sign

negative ; minus

-3 means the negative of the number 3.

arithmetic

-(-5) = 5

set-theoretic complement

A - B means the set that contains all the

minus; without elements of A that are

set theory not in B.

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

multiplication 3 ? 4 means the

times

multiplication of 3 by

arithmetic 4.

7 ? 8 = 56

Cartesian

product

X?Y means the set of

the Cartesian all ordered pairs with

product of ... and ...; the direct

the first element of each pair selected from X

{1,2} ? {3,4} = {(1,3),(1,4),(2,3),(2,4)}

product of ... and the second element

and ...

selected from Y.

set theory

cross product u ? v means the cross

cross

product of vectors u

vector algebra and v

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



16/05/2007

Table of mathematical symbols - Wikipedia, the free encyclopedia

P?gina 3 de 13

? ? / ?

|...|

multiplication 3 ? 4 means the

times

multiplication of 3 by

arithmetic 4.

dot product

u ? v means the dot

dot

product of vectors u

vector algebra and v

7 ? 8 = 56 (1,2,5) ? (3,4,-1) = 6

division

divided by

6 ? 3 or 6 / 3 means the 2 ? 4 = .5

division of 6 by 3.

12 / 4 = 3

arithmetic

plus-minus

plus or minus

6 ? 3 means both 6 + 3 The equation x = 5 ? 4, has two

and 6 - 3.

solutions, x = 7 and x = 3.

arithmetic

plus-minus plus or minus measurement

10 ? 2 or eqivalently 10 ? 20% means the range from 10 - 2 to 10 + 2.

If a = 100 ? 1 mm, then a is 99 mm and 101 mm.

minus-plus

6 ? (3 5) means both

minus or plus 6 + (3 - 5) and 6 - (3 + cos(x ? y) = cos(x) cos(y)

arithmetic 5).

sin(x) sin(y).

square root

the principal x means the positive square root of; number whose square is 4 = 2

square root x.

real numbers

complex square root

if z = r exp(i) is the complex represented in polar square root of ... coordinates with - < (-1) = i square root , then z = r exp

(i /2). complex numbers

absolute value or

modulus

|x| means the distance

along the real line (or

absolute value across the complex

(modulus) of plane) between x and

zero. numbers

|3| = 3 |?5| = |5| | i | = 1 | 3 + 4i | = 5

Euclidean distance

Euclidean distance |x ? y| means the

For x = (1,1), and y = (4,5),



16/05/2007

Table of mathematical symbols - Wikipedia, the free encyclopedia

P?gina 4 de 13

between; Euclidean distance Euclidean norm between x and y.

of

|x ? y| = ([1?4]2 + [1?5]2) = 5

Geometry

Determinant

|A| means the

determinant of determinant of the

Matrix theory matrix A

divides

A single vertical bar is

|

divides

used to denote divisibility.

Since 15 = 3?5, it is true that 3|15 and 5|15.

Number Theory a|b means a divides b.

factorial

!

factorial

n ! is the product 1 ? 2? ... ? n.

4! = 1 ? 2 ? 3 ? 4 = 24

combinatorics

transpose

T

transpose Swap rows for columns Aij = (AT)ji

matrix

operations

probability distribution

X ~ D, means the random variable X has X ~ N(0,1), the standard normal

has distribution the probability

distribution

~

statistics distribution D. Row equivalence A~B means that B can

is row equivalent be generated by using a

to

series of elementary

Matrix theory row operations on A

material

implication

A B means if A is

true then B is also true; if A is false then nothing is said about B.

implies; if ... may mean the same

then

as , or it may have the x = 2 x2 = 4 is true, but x2 = 4 x =

meaning for functions 2 is in general false (since x could be -2).

given below.

propositional may mean the same

logic, Heyting algebra

as , or it may have the

meaning for superset

given below.

material

equivalence

A B means A is true

if and only if; iff

if B is true and A is false if B is false.

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



16/05/2007

Table of mathematical symbols - Wikipedia, the free encyclopedia

P?gina 5 de 13

? ~

propositional logic

The statement ?A is logical negation true if and only if A is

false.

A slash placed through

not

another operator is the ?(?A) A

same as "?" placed in front.

x y ?(x = y)

propositional (The symbol ~ has logic many other uses, so ? or the slash notation is

preferred.)

logical

The statement A B is

conjunction or true if A and B are both meet in a lattice true; else it is false.

and; min

n < 4 n >2 n = 3 when n is a For functions A(x) and natural number.

propositional B(x), A(x) B(x) is

logic, lattice used to mean min(A(x), theory B(x)).

logical disjunction or join in a lattice

or; max

The statement A B is

true if A or B (or both) are true; if both are false, the statement is false.

For functions A(x) and

propositional B(x), A(x) B(x) is

logic, lattice

theory

used to mean max(A (x), B(x)).

n 4 n 2 n 3 when n is a natural number.

exclusive or

The statement A B is

xor

true when either A or

propositional B, but not both, are logic, Boolean true. A B means the

algebra same.

(?A) A is always true, A A is always false.

The direct sum is a

direct sum

special way of

Most commonly, for vector spaces U, V,

combining several one and W, the following consequence is

direct sum of

modules into one

used:

general module (the symbol is used,

is

U = V W (U = V + W) (V W =

Abstract algebra only for logic).

)

universal quantification

for all; for any;

x: P(x) means P(x) is

n

: n2 n.



16/05/2007

Table of mathematical symbols - Wikipedia, the free encyclopedia

P?gina 6 de 13

for each true for all x. predicate logic

existential

quantification x: P(x) means there is there exists at least one x such that n : n is even.

P(x) is true.

predicate logic

uniqueness

!

quantification ! x: P(x) means there there exists is exactly one x such ! n : n + 5 = 2n.

exactly one that P(x) is true.

predicate logic

:= definition

x := y or x y means x

is defined to be another name for y

is defined as (Some writers use to cosh x := (1/2)(exp x + exp (-x))

mean congruence).

A xor B : (A B) ?(A B)

:

{ , } { : } { | }

P : Q means P is everywhere defined to be logically

equivalent to Q.

congruence

ABC DEF means

triangle ABC is is congruent to congruent to (has the

same measurements as) geometry triangle DEF.

congruence relation

... is congruent a b (mod n) means a to ... modulo ... - b is divisible by n

modular arithmetic

5 11 (mod 3)

set brackets

{a,b,c} means the set

the set of ... consisting of a, b, and

set theory c.

= { 1, 2, 3, ...}

set builder

notation

{x : P(x)} means the set

the set of ... such that

of all x for which P(x) is true. {x | P(x)} is the

{n

same as {x : P(x)}.

set theory

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

empty set the empty set

means the set with

no elements. { } means {n the same.

: 1 < n2 < 4} =



16/05/2007

Table of mathematical symbols - Wikipedia, the free encyclopedia

P?gina 7 de 13

{ }

set theory

set membership

is an element of; is not an element

a S means a is an element of the set S; a

(1/2)-1

of

S means a is not an

everywhere, set element of S.

2-1

theory

subset

(subset) A B means

every element of A is also element of B.

(A B) A

(proper subset) A B is a subset of means A B but A B.

(Some writers use the

set theory symbol as if it were

the same as .)

superset

A B means every

element of B is also element of A.

A B means A B but (A B) B is a superset of A B.

(Some writers use the set theory symbol as if it were

the same as .)

(exclusive) A B

set-theoretic union

means the set that contains all the

elements from A, or all

the elements from B,

but not both.

the union of ... "A or B, but not both." and

A B (A B) = B (inclusive)

(inclusive) A B means

union

the set that contains all the elements from A, or

all the elements from B,

or all the elements from

set theory both A and B. "A or B or both".

set-theoretic

intersection

A B means the set that contains all those

{x

: x2 = 1}

= {1}

intersected with; elements that A and B



16/05/2007

Table of mathematical symbols - Wikipedia, the free encyclopedia

P?gina 8 de 13

intersect have in common. set theory

symmetric

difference

AB means the set of

symmetric elements in exactly one {1,5,6,8} {2,5,8} = {1,2,6}

difference of A or B.

set theory

set-theoretic complement

A B means the set that contains all those

minus; without elements of A that are

set theory not in B.

{1,2,3,4}

{3,4,5,6} = {1,2}

function

application

f(x) means the value of

of

the function f at the element x.

If f(x) := x2, then f(3) = 32 = 9.

( )

set theory precedence

grouping

Perform the operations

parentheses

inside the parentheses (8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4. first.

everywhere

function arrow

f:XY

from ... to

f: X Y means the function f maps the set Let f: be defined by f(x) := x2.

set theory,type X into the set Y.

theory

function

o

composition

fog is the function, such if f(x) := 2x, and g(x) := x + 3, then (fog)

composed with that (fog)(x) = f(g(x)). (x) = 2(x + 3).

set theory

natural numbers N means { 1, 2, 3, ...},

N

but see the article on natural numbers for a

= {|a| : a , a 0}

N

different convention. numbers

integers

means {..., -3, -2,

Z

-1, 0, 1, 2, 3, ...} and + means {1, 2, 3,

= {p, -p : p } {0}

Z

numbers ...} = .

rational numbers

means {p/q : p , 3.14000...

Q

q }.

Q

numbers



16/05/2007

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download