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Mathematical Symbols
List of all mathematical symbols and signs - meaning and examples.
Basic math symbols
Geometry symbols
Algebra symbols
Probability & statistics symbols
Set theory symbols
Logic symbols
Calculus & analysis symbols
Number symbols
Greeksymbols
Roman numerals
Basic math symbols
Symbol Symbol Name Meaning / definition
= equals sign equality
not equal sign inequality
> strict inequality greater than
< strict inequality less than
inequality greater than or equal to
inequality less than or equal to
() parentheses calculate expression inside first
[] brackets calculate expression inside first
+ plus sign addition
minus sign subtraction
plus - minus both plus and minus operations
minus - plus both minus and plus operations
* asterisk multiplication
times sign multiplication
multiplication dot multiplication
division sign / obelus division
/ division slash division
horizontal line division / fraction
mod modulo remainder calculation
decimal point, decimal
. period
separator
ab power exponent
a^b caret exponent
a square root a a = a
3
a cube root 3
a 3a 3a = a
4
a fourth root a 4a 4a 4a = a
4
n n-th root (radical)
a
% percent 1% = 1/100
per-mille 1 = 1/1000 = 0.1%
ppm per-million 1ppm = 1/1000000
ppb per-billion 1ppb = 1/1000000000
ppt per-trillion 1ppt = 10-12
Geometry symbols
Symbol Symbol Name Meaning / definition
angle formed by two rays
measured angle
spherical angle
right angle = 90
degree 1 turn = 360
arcminute 1 = 60
arcsecond 1 = 60
line infinite line
AB line segment line from point A to point B
ray line that start from point A
arc arc from point A to point B
| perpendicular perpendicular lines (90 angle)
|| parallel parallel lines
equivalence of geometric
congruent to
shapes and size
similarity same shapes, not same size
~
triangle triangle shape
|x-y| distance distance between points x and y
= 3.141592654...
is the ratio between the
pi constant
circumference and diameter of
a circle
rad radians radians angle unit
grad grads grads angle unit
Algebra symbols
Symbol Symbol Name Meaning / definition
x x variable unknown value to find
equivalence identical to
equal by definition equal by definition
:= equal by definition equal by definition
~ approximately equal weak approximation
approximately equal approximation
proportional to proportional to
lemniscate infinity symbol
much less than much less than
much greater than much greater than
() parentheses calculate expression inside first
[] brackets calculate expression inside first
{} braces set
x floor brackets rounds number to lower integer
x ceiling brackets rounds number to upper integer
x! exclamation mark factorial
|x| single vertical bar absolute value
f (x) function of x maps values of x to f(x)
(f g) function composition (f g) (x) = f (g(x))
(a,b) open interval (a,b) = {x | a < x < b}
[a,b] closed interval [a,b] = {x | a x b}
delta change / difference
discriminant = b2 - 4ac
summation - sum of all values in
sigma
range of series
sigma double summation
product - product of all values in
capital pi
range of series
e e constant / Euler's number e = 2.718281828...
Euler-Mascheroni constant = 0.527721566...
golden ratio golden ratio constant
= 3.141592654...
is the ratio between the
pi constant
circumference and diameter of
a circle
Linear Algebra Symbols
Symbol Symbol Name Meaning / definition
dot scalar product
cross vector product
tensor product of A
AB tensor product
and B
inner product
[] brackets matrix of numbers
() parentheses matrix of numbers
determinant of matrix
|A| determinant
A
determinant of matrix
det(A) determinant
A
|| x double vertical bars norm
||
AT transpose matrix transpose
matrix conjugate
A Hermitian matrix
transpose
matrix conjugate
A* Hermitian matrix
transpose
A -1 inverse matrix A A-1 = I
rank(A) matrix rank rank of matrix A
dimension of matrix
dim(U) dimension A
Probability and statistics symbols
Symbol Symbol Name Meaning / definition
P(A) probability function probability of event A
probability of events probability that of events A and
P(A B) intersection B
P(A B) probability of events union probability that of events A or B
probability of event A given
P(A | B) conditional probability function
event B occured
probability density function
f (x) (pdf) P(a x b) = f (x) dx
cumulative distribution function
F(x) (cdf) F(x) = P(X x)
population mean mean of population values
expected value of random
E(X) expectation value
variable X
expected value of random
E(X | Y) conditional expectation
variable X given Y
var(X) variance variance of random variable X
2 variance variance of population values
standard deviation of random
std(X) standard deviation
variable X
standard deviation value of
X standard deviation
random variable X
middle value of random variable
median
x
covariance of random variables
cov(X,Y) covariance
X and Y
correlation of random variables
corr(X,Y) correlation
X and Y
correlation of random variables
X,Y correlation
X and Y
summation - sum of all values in
summation
range of series
double summation double summation
value that occurs most
Mo mode
frequently in population
MR mid-range MR = (xmax+xmin)/2
half the population is below this
Md sample median
value
25% of population are below
Q1 lower / first quartile
this value
50% of population are below
Q2 median / second quartile this value = median of samples
75% of population are below
Q3 upper / third quartile
this value
x sample mean average / arithmetic mean
population samples variance
s2 sample variance
estimator
population samples standard
s sample standard deviation
deviation estimator
zx standard score zx = (x-x) / sx
distribution of random variable
X~ distribution of X
X
N(,2) normal distribution gaussian distribution
U(a,b) uniform distribution equal probability in range a,b
exp() exponential distribution f (x) = e-x , x0
f (x) = c xc-1e-x / (c),
gamma(c, ) gamma distribution
x0
f (x) = xk/2-1e-x/2 / ( 2k/2
2
(k) chi-square distribution
(k/2) )
F (k1, k2) F distribution
Bin(n,p) binomial distribution f (k) = nCk pk(1-p)n-k
Poisson() Poisson distribution f (k) = ke- / k!
Geom(p) geometric distribution f (k) = p (1-p) k
HG(N,K,n) hyper-geometric distribution
Bern(p) Bernoulli distribution
Combinatorics Symbols
Symbol Symbol Name Meaning / definition
n! factorial n! = 123...n
nPk permutation
nCk
combination
Set theory symbols
Symbol Symbol Name Meaning / definition
{} set a collection of elements
AB intersection objects that belong to set A and set B
AB union objects that belong to set A or set B
subset has fewer elements or equal to
AB subset
the set
AB proper subset / strict subset subset has fewer elements than the set
AB not subset left set not a subset of right set
set A has more elements or equal to the
AB superset
set B
AB proper superset / strict superset set A has more elements than set B
AB not superset set A is not a superset of set B
2A power set all subsets of A
power set all subsets of A
A=B equality both sets have the same members
Ac complement all the objects that do not belong to set A
A\B relative complement objects that belong to A and not to B
relative complement objects that belong to A and not to B
A-B
objects that belong to A or B but not to
AB symmetric difference
their intersection
objects that belong to A or B but not to
A B symmetric difference
their intersection
aA element of set membership
xA not element of no set membership
(a,b) ordered pair collection of 2 elements
AB cartesian product set of all ordered pairs from A and B
|A| cardinality the number of elements of set A
#A cardinality the number of elements of set A
aleph-null infinite cardinality of natural numbers set
cardinality of countable ordinal numbers
aleph-one
set
empty set ={}
universal set set of all possible values
natural numbers / whole numbers set
0 (with zero) 0 = {0,1,2,3,4,...}
natural numbers / whole numbers set
1 (without zero) 1 = {1,2,3,4,5,...}
integer numbers set = {...-3,-2,-1,0,1,2,3,...}
rational numbers set = {x | x=a/b, a,b }
real numbers set = {x | - < x <}
= {z | z=a+bi, -<a<, -
complex numbers set
<b<}
Logic symbols
Symbol Symbol Name Meaning / definition
and and
^ caret / circumflex and
& ampersand and
+ plus or
reversed caret or
| vertical line or
x' single quote not - negation
x bar not - negation
not not - negation
! exclamation mark not - negation
circled plus / oplus exclusive or - xor
~ tilde negation
implies
equivalent if and only if (iff)
equivalent if and only if (iff)
for all
there exists
there does not exists
therefore
because / since
Calculus & analysis symbols
Symbol Symbol Name Meaning / definition
limit limit value of a function
represents a very small number,
epsilon
near zero
e e constant / Euler's number e = 2.718281828...
y' derivative derivative - Lagrange's notation
y '' second derivative derivative of derivative
y(n) nth derivative n times derivation
derivative derivative - Leibniz's notation
second derivative derivative of derivative
nth derivative n times derivation
derivative by time - Newton's
time derivative
notation
time second derivative derivative of derivative
Dx y derivative derivative - Euler's notation
Dx2 y second derivative derivative of derivative
partial derivative
integral opposite to derivation
integration of function of 2
double integral
variables
integration of function of 3
triple integral
variables
closed contour / line integral
closed surface integral
closed volume integral
[a,b] closed interval [a,b] = {x | a x b}
(a,b) open interval (a,b) = {x | a < x < b}
i imaginary unit i -1
z* complex conjugate z = a+bi z*=a-bi
z complex conjugate z = a+bi z = a-bi
nabla / del gradient / divergence operator
vector
unit vector
x*y convolution y(t) = x(t) * h(t)
Laplace transform F(s) = {f (t)}
Fourier transform X() = {f (t)}
delta function
lemniscate infinity symbol
Numeral symbols
Name European Roman Hebrew
zero 0
one 1 I
two 2 II
three 3 III
four 4 IV
five 5 V
six 6 VI
seven 7 VII
eight 8 VIII
nine 9 IX
ten 10 X
eleven 11 XI
twelve 12 XII
thirteen 13 XIII
fourteen 14 XIV
fifteen 15 XV
sixteen 16 XVI
seventeen 17 XVII
eighteen 18 XVIII
nineteen 19 XIX
twenty 20 XX
thirty 30 XXX
fourty 40 XL
fifty 50 L
sixty 60 LX
seventy 70 LXX
eighty 80 LXXX
ninety 90 XC
one hundred 100 C
Greek alphabet letters
Greek Symbol
Greek Letter Name English Equivalent
Upper Case Lower Case
Alpha al-fa
Beta be-ta
Gamma ga-ma
Delta del-ta
Epsilon ep-si-lon
Zeta ze-ta
Eta eh-ta
Theta te-ta
Iota io-ta
Kappa ka-pa
Lambda lam-da
Mu m-yoo
Nu noo
Xi x-ee
Omicron o-mee-c-ron
Pi pa-yee
Rho row
Sigma sig-ma
Tau ta-oo
Upsilon oo-psi-lon
Phi f-ee
Chi kh-ee
Psi p-see
Omega o-me-ga
Roman numerals
Number Roman numeral
0 not defined
1 I
2 II
3 III
4 IV
5 V
6 VI
7 VII
8 VIII
9 IX
10 X
11 XI
12 XII
13 XIII
14 XIV
15 XV
16 XVI
17 XVII
18 XVIII
19 XIX
20 XX
30 XXX
40 XL
50 L
60 LX
70 LXX
80 LXXX
90 XC
100 C
200 CC
300 CCC
400 CD
500 D
600 DC
700 DCC
800 DCCC
900 CM
1000 M
5000 V
10000 X
50000 L
100000 C
500000 D
1000000 M
See also
