Table of mathematical symbols - IES Jovellanos

Table of mathematical symbols - Wikipedia, the free encyclopedia

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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)



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? ? / ?

|...|

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),



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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



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? ~

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.



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