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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Table of mathematical symbols - Wikipedia, the free encyclopedia
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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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