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8/17/2019 Mathematical symbols list (+,-,x,_,=,_,_,..
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Mathematical SymbolsList 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
Greek symbols
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
http://www.rapidtables.com/math/symbols/index.htmhttp://www.rapidtables.com/http://www.rapidtables.com/math/symbols/Division_Sign.htmhttp://www.rapidtables.com/math/symbols/Times_Sign.htmhttp://www.rapidtables.com/math/symbols/Times_Sign.htmhttp://www.rapidtables.com/math/symbols/Times_Sign.htmhttp://www.rapidtables.com/math/symbols/Minus_Sign.htmhttp://www.rapidtables.com/math/symbols/Plus_Sign.htmhttp://www.rapidtables.com/math/symbols/Equals_Sign.htmhttp://www.rapidtables.com/http://www.rapidtables.com/math/symbols/index.htmhttp://www.rapidtables.com/math/index.htmhttp://www.rapidtables.com/
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/ division slash division
– horizontal line division / fraction
mod modulo remainder calculation
. period decimal point, decimalseparator
ab power exponent
a^b caret exponent
√a square root √a ∙ √a = a
3√a cube root 3√a ∙ 3√a ∙ 3√a = a
4√a fourth root 4√a ∙ 4√a ∙ 4√a ∙ 4√a = a
n√a n-th root (radical)
% 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 = 90º
º degree 1 turn = 360º
´ arcminute 1º = 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 (90º angle)
|| parallel parallel lines
≅ congruent to equivalence of geometric
shapes and size
~ similarity same shapes, not same size
Δ triangle triangle shape
| x- y| distance distance between points x andy
http://www.rapidtables.com/math/number/PPM.htmhttp://www.rapidtables.com/math/number/PPM.htmhttp://www.rapidtables.com/math/number/Per_mille.htmhttp://www.rapidtables.com/math/number/Percentage.htmhttp://www.rapidtables.com/math/symbols/Division_Sign.htmhttp://www.rapidtables.com/math/symbols/Division_Sign.htm
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π pi constant
π = 3.141592654...
is the ratio between the
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 defin ition equal by definit ion
:= equal by defin ition equal by definit ion
~ 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
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e e constant / Euler's number e = 2.718281828...
γ Euler-Mascheroni constant γ = 0.527721566...
φ golden ratio golden ratio constant
π pi constant
π = 3.141592654...
is the ratio between the
circumference and diameter of a
circle
Linear Algebra Symbols
Symbol Symbol Name Meaning / definition
∙ dot scalar product
× cross vector product
A⊗ B tensor product tensor product of Aand B
inner product
[ ] brackets matrix of numbers
( ) parentheses matrix of numbers
| A | determinant determinant of matrix A
det( A) determinant determinant of matrix A
|| x || double vertical bars norm
A T transpose matrix transpose
A † Hermitian matrix matrix conjugatetranspose
A * Hermitian matrix matrix conjugatetranspose
A -1 inverse matrix A A-1 = I
rank( A) matrix rank rank of matrix A
dim(U ) dimension dimension of matrix A
Probability and statistics symbols
Symbol Symbol Name Meaning / definition
P ( A) probabil ity function probability of event A
P ( A ∩ B) probability of eventsintersectionprobability that of events A andB
P ( A ∪ B) probability of events union probability that of events A or B
P ( A | B) conditional probability function probability of event A givenevent B occured
f ( x) probability density function (pdf) P (a ≤ x ≤ b) = ∫ f ( x) dx
F ( x) cumulative distribution function(cdf) F ( x) = P ( X ≤ x)
μ population mean mean of population values
E ( X ) expectation value expected value of randomvariable X
http://www.rapidtables.com/math/probability/Expectation.htmhttp://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constanthttp://www.rapidtables.com/math/number/e_constant.htm
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E ( X | Y ) conditional expectation expected value of randomvariable X given Y
var ( X ) variance variance of random variable X
σ2 variance variance of population values
std ( X ) standard deviation standard deviation of randomvariable X
σ X standard deviation standard deviation value of
random variable X
median middle value of random
variable x
cov( X ,Y ) covariance covariance of random variablesX and Y
corr ( X ,Y ) correlation correlation of random variablesX and Y
ρ X ,Y correlation correlation of random variables
X and Y
∑ summation summation - sum of all valuesin range of series
∑∑ double summation double summation
Mo mode value that occurs mostfrequently in population
MR mid-range MR = ( xmax+ xmin)/2
Md sample median half the population is below thisvalue
Q1 lower / first quartile 25% of population are below
this value
Q2 median / second quartile 50% of population are below
this value = median of samples
Q3 upper / third quartile 75% of population are below
this value
x sample mean average / arithmetic mean
s 2 sample variance population samples variance
estimator
s sample standard deviation population samples standarddeviation estimator
z x standard score z x = ( x- x) / s x
X ~ distribution of X distribution of random variableX
N ( μ,σ 2) normal distribution gaussian distribution
U (a,b) uniform distribution equal probability in range a,b
exp(λ) exponential distribution f ( x) = λe- λx , x≥0
gamma(c, λ) gamma distribution f ( x) = λ c xc-1e- λx / Γ(c), x≥0
χ 2(k ) chi-square distribution f ( x) = xk /2-1e- x/2 / ( 2k/2
Γ(k /2) )
F (k 1 , k 2) F distribution
Bin(n, p) binomial distribution f (k ) =nC
k pk (1-p)n-k
Poisson(λ) Poisson distribution f (k ) = λk e- λ / k !
Geom( p) geometric distribution f (k ) = p (1-p) k
http://www.rapidtables.com/math/probability/normal_distribution.htmhttp://www.rapidtables.com/math/probability/distribution.htmhttp://www.rapidtables.com/math/probability/standard_deviation.htmhttp://www.rapidtables.com/math/probability/standard_deviation.htmhttp://www.rapidtables.com/math/probability/Variance.htmhttp://www.rapidtables.com/math/probability/Variance.htm
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HG( N , K ,n) hyper-geometric distribution
Bern( p) Bernoulli distribution
Combinatorics Symbols
Symbol Symbol Name Meaning / definition
n! factorial n! = 1·2·3·...·n
n P k permutation
nC k
combination
Set theory symbols
Symbol Symbol Name Meaning / definition
{ } set a collection of elements
A ∩ B intersection objects that belong to set A and set B
A ∪ B union objects that belong to set A or set B
A ⊆ B subset subset has fewer elements or equal tothe set
A ⊂ B proper subset / strict subset subset has fewer elements than the set
A⊄
B not subset left set not a subset of right set
A ⊇ B superset set A has more elements or equal to theset B
A ⊃ B proper superset / strict superset set A has more elements than set B
A ⊅ B 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 membersAc complement all the objects that do not belong to set A
A \ B relative complement objects that belong to A and not to B
A - B relative complement objects that belong to A and not to B
A ∆ B symmetric difference objects that belong to A or B but not totheir intersection
A ⊖ B symmetric difference objects that belong to A or B but not totheir intersection
a∈A element of set membership
x∉A not element of no set membership
(a,b) ordered pair collection of 2 elements
http://www.rapidtables.com/math/algebra/Factorial.htm
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A×B 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
aleph-one cardinality of countable ordinal numbers
set
Ø empty set Ø = { }
universal set set of all possible values
0 natural numbers / whole numbers set
(with zero) 0 = {0,1,2,3,4,...}
1 natural numbers / whole numbers set
(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 | -∞
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∴ therefore
∵ because / since
Calculus & analysis symbols
Symbol Symbol Name Meaning / definition
limit limit value of a function
ε epsilon represents a very smallnumber, near zero
e e constant / Euler's number e = 2.718281828...
y ' derivative derivative - Lagrange's notation
y '' second derivative der ivat ive of der ivat ive
y(n) nth derivative n times derivation
derivative derivative - Leibniz's notation
second derivative der ivat ive of der ivat ive
nth derivative n times derivation
time derivative derivative by time - Newton's
notation
time second derivative derivative of derivative
D x y derivative derivative - Euler's notation
D x2
y second derivative der ivat ive of der ivat ive
partial derivative
∫ integral opposite to derivation
∬ double integral integration of function of 2variables
∭ triple integral integration of function of 3
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
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vector
unit vector
x * y convolution y(t ) = x(t ) * h(t )
Laplace transform F ( s) = { f (t )}
Fourier transform X (ω) = { f (t )}
δ delta function
∞ lemniscate infinity symbol
Numeral symbols
Name European Roman Hebrew
zero 0
one 1 I
two 2 II
three 3 III ג
four 4 IV ד
five 5 V ה
six 6 VI ו
seven 7 VII ז
eight 8 VIII ח
nine 9 IX ט
ten 10 X י
eleven 11 XI יtwelve 12 XII י
thirteen 13 XIII יג
fourteen 14 XIV יד
fifteen 15 XV טו
sixteen 16 XVI טז
seventeen 17 XVII יז
eighteen 18 XVIII יח
nineteen 19 XIX יט
twenty 20 XX כ
thirty 30 XXX ל
fourty 40 XL מ
fifty 50 L נ
sixty 60 LX ס
seventy 70 LXX ע
eighty 80 LXXX פ
ninety 90 XC צ
one hundred 100 C ק
Greek alphabet letters
http://www.rapidtables.com/math/symbols/Infinity_Symbol.htmhttp://www.rapidtables.com/math/symbols/Infinity_Symbol.htmhttp://www.rapidtables.com/math/calculus/laplace_transform.htmhttp://www.rapidtables.com/math/calculus/Convolution.htm
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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 C500000 D
1000000 M
See also
Algebra symbols
Geometry symbols
Statistical symbolsLogic symbols
Set theory symbols
Calculus & analysis symbols
http://www.rapidtables.com/math/symbols/Calculus_Symbols.htmhttp://www.rapidtables.com/math/symbols/Set_Symbols.htmhttp://www.rapidtables.com/math/symbols/Logic_Symbols.htmhttp://www.rapidtables.com/math/symbols/Statistical_Symbols.htmhttp://www.rapidtables.com/math/symbols/Geometry_Symbols.htmhttp://www.rapidtables.com/math/symbols/Algebra_Symbols.htm
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Number symbols
Greek alphabet symbols
Roman numerals
Infinity symbol
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