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Math Symbols: We are unable to visualize mathematics without math symbols, whether it’s a simple addition problem or a difficult calculus problem. These mathematical symbols are necessary for various mathematical processes. These math symbols are employed in a variety of mathematical domains. from the representation of the equation to the explanation of what’s going on between the two integers. In mathematical operations, all math symbols are utilized to represent diverse concepts. Mathematical dimensions include algebra, trigonometry, geometry, and number theory, and the concept of maths is entirely based on numbers and math symbols. So in this article we dive into different sorts of math symbols of various math chapters such as Algebra, Sets, probability, calculus, math symbols greek, numerical symbols and more.
Math Symbols
It’s worth noting that Mathematics is entirely dependent on numbers and math symbols. In various conceptions, the primary use of all math symbols is to carry out mathematical operations.There are numerous other uses for math symbols besides referring to distinct quantities.
 Math symbols in many topics and It aids in the representation of quantities.
 Establishes quantitative relationships.
 It aids in determining the type of operation we must carry out.
Mathematical Symbols with Names
Math symbols are ubiquitous and help to bridge the language gap. It all revolves around numbers, symbols, and formulas in mathematics. To express mathematical ideas, basic mathematical symbols are utilised. The symbolvalue relationship relates to the fundamental mathematical condition. We’re here talking about the fundamental mathematical symbols with Names that we are learning from our childhood.
Basic Math symbols  
Math Symbol  Symbol Name in Maths  Meaning  Example 
≠  not equal sign  inequality  9 ≠ 5 
=  equal sign  equality  10 = 8 + 2 
<  strict inequality  less than  9 < 18 
>  strict inequality  greater than  8 > 1 
≤  inequality  less than or equal to 
x ≤ y, means, y = x or y > x

≥  inequality  greater than or equal to 
a ≥ b, means, a = b or a > b, but not viceversa

−  minus sign  subtraction  8 − 2 = 6 
+  plus sign  addition  9 + 2 = 11 
∓  minus – plus  both minus and plus operations 
1 ∓ 4 = 3 and 5

±  plus – minus  both plus and minus operations 
5 ± 3 = 8 and 2

×  times sign  multiplication  4 × 3 = 12 
[ ]  brackets  calculate expression inside first 
[ 3×6] + 2 = 20 + 3 = 23

( )  parentheses  calculate expression inside first 
3 × (3 + 7) = 3 × 10 = 30

n√a  nth root (radical)  n√a · n√a · · · n times = a 
for n=3, n√8 = 2

ppm  permillion  1 ppm = 1/1000000 
10ppm × 30 = 0.0003

‰  permille  1‰ = 1/1000 = 0.1% 
10‰ × 30 = 0.3

ppt  pertrillion  1ppt = 1012 
10ppt × 30 = 3×1010

ppb  perbillion  1 ppb = 1/1000000000 
10 ppb × 30 = 3×107

*  asterisk  multiplication  2 * 3 = 6 
÷  division sign / obelus  division  15 ÷ 5 = 3 
∙  multiplication dot  multiplication  2 ∙ 3 = 6 
–  horizontal line  division / fraction  8/2 = 4 
/  division slash  division  6 ⁄ 2 = 3 
mod  modulo  remainder calculation  7 mod 3 = 1 
ab  power  exponent  24 = 16 
.  period  decimal point, decimal separator 
4.36 = 4 +(36/100)

√a  square root  √a · √a = a  √9 = ±3 
a^b  caret  exponent  2 ^ 3 = 8 
4√a  fourth root  4√a ·4√a · 4√a · 4√a = a  4√16= ± 2 
3√a  cube root  3√a ·3√a · 3√a = a  3√343 = 7 
%  percent  1% = 1/100  10% × 30 = 3 
Math Symbols List Logical
To execute various processes, a logical math symbols list is employed. The logical math symbols make referring to mathematical quantities easier. The logical math symbols not only relate to distinct quantities, but they also express the connections between two quantities and help to concise the interpretation.
Logical Math Symbols  
Math Symbols  Symbol Name in Math  Meaning  Example 
⋅  and  and  x ⋅ y 
&  ampersand  and  x & y 
+  plus  or  x + y 
^  caret / circumflex  and  x ^ y 
⇔  equivalent 
if and only if (iff)

– 
↔  equivalent 
if and only if (iff)

– 
∨  reversed caret  or  x ∨ y 
  vertical line  or  x  y 
x’  single quote  not – negation  x’ 
x  bar  not – negation  x 
¬  not  not – negation  ¬ x 
!  exclamation mark  not – negation  ! x 
⊕  circled plus / oplus  exclusive or – xor  x ⊕ y 
~  tilde  negation  ~ x 
⇒  implies  –  – 
∴  therefore  –  – 
∵ 
because / since

–  – 
∀  for all  –  – 
∃  there exists  –  – 
∄ 
there does not exists

–  – 
Math Symbols Greek
We frequently employ Greek symbols in other subjects as well. In their work, mathematicians utilize Greek alphabets and math symbols Greek to denote variables, constants, functions, and so on. The names of some of the most regularly used Greek symbols in mathematics are mentioned below.
Math Symbols Greek  
Upper Case Letter  Lower Case Letter  Greek Letter Name  How to Pronounce 
English Equivalent/ Meaning

Α  α  Alpha  alfa  a 
Β  β  Beta  beta  b 
Γ  γ  Gamma  gama  g 
Δ  δ  Delta  delta  d 
Ε  ε  Epsilon  epsilon  e 
Ζ  ζ  Zeta  Zeta  z 
Η  η  Eta  ehta  h 
Θ  θ  Theta  teta  th 
Ι  ι  Iota  iota  i 
Κ  κ  Kappa  kapa  k 
Λ  λ  Lambda  lamda  l 
Μ  μ  Mu  myoo  m 
Μ  μ  Mu  myoo  m 
Ν  ν  Nu  noo  n 
Ν  ν  Nu  noo  n 
Ξ  ξ  Xi  xee  x 
Ο  ο  Omicron  omeecron  o 
Π  π  Pi  payee  p 
Ρ  ρ  Rho  row  r 
Σ  σ  Sigma  sigma  s 
Τ  τ  Tau  taoo  t 
Υ  υ  Upsilon  oopsilon  u 
Φ  φ  Phi  fee  ph 
Χ  χ  Chi  khee  ch 
Ψ  ψ  Psi  psee  ps 
Ω  ω  Omega  omega  o 
Geometry Symbols
Geometry is an important subject of mathematics that is concerned with the features of geometric object configurations such as lines that are parallel, angles, circles, points, and so on. Here we include all of the geometry symbols that students should be familiar with.
Geometry Symbols in Mathematics  
Math Symbol  Symbol Name  Meaning  Example 
deg  degree  1 turn = 360deg  α = 60deg 
∠  angle  formed by two rays  ∠ABC = 30° 
°  degree  1 turn = 360°  α = 60° 
measured angle

the angle we are talking about  ABC = 30°  
spherical angle

AOB = 30°  
∟  right angle  α = 90°  
grad  gradians/gons  grads angle unit  360° = 400 grad 
g  gradians/gons  grads angle unit  360° = 400 g 
′  prime  arcminute, 1° = 60′  α = 60°59′ 
″  double prime  arcsecond, 1′ = 60″  α = 60°59′59″ 
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)  AC ⊥ BC 
∥  parallel  parallel lines  AB ∥ CD 
≅  congruent to  equivalence of geometric shapes and size  ∆ABC≅ ∆XYZ 
~  similarity  same shapes, not same size  ∆ABC~ ∆XYZ 
Δ  triangle  triangle shape  ΔABC≅ ΔBCD 
xy  distance  distance between points x and y   xy  = 5 
π  pi constant  π = 3.141592654…is the ratio between the circumference and diameter of a circle  c = π⋅d = 2⋅π⋅r 
rad  radians  radians angle unit  360° = 2π rad 
c  radians  radians angle unit  360° = 2π c 
Algebra Symbols
These math symbols in algebra indicate nonfixed quantities known as variables. Algebra is a mathematical aspect that involves symbols and the rules used to deceive those symbols. Mathematics discusses the link between variables in algebra. Look at the table below, where we discussed almost all algebra symbols.
Algebra Symbols  
Math Symbol  Symbol Name  Meaning  Example 
f (x)  function of x  maps values of x to f(x)  f (x) = 3x+5 
 x   single vertical bar  absolute value   5  = 5 
≡  equivalence  identical to  
x  x variable  unknown value to find 
when 2x = 4, then x = 2

:=  equal by definition 
equal by definition


≜  equal by definition 
equal by definition


≈  approximately equal  approximation 
sin(0.01) ≈ 0.01

~  approximately equal  weak approximation  11 ~ 10 
∞  lemniscate 
infinity symbol


∝  proportional to  proportional to 
y ∝ x when y = kx, k constant

≫  much greater than  much greater than  1000000 ≫ 1 
≪  much less than  much less than  1 ≪ 1000000 
[ ]  brackets  calculate expression inside first 
[(1+2)*(1+5)] = 18

( )  parentheses  calculate expression inside first  2 * (3+5) = 16 
⌊x⌋  floor brackets  rounds number to lower integer  ⌊4.3⌋= 4 
{ }  braces  set  
x!  exclamation mark  factorial 
4! = 1*2*3*4 = 24

⌈x⌉  ceiling brackets  rounds number to upper integer  ⌈4.3⌉= 5 
π  pi constant  π = 3.141592654… is the ratio between the circumference and diameter of a circle 
c = π·d = 2·π·r

φ  golden ratio 
golden ratio constant


(a,b)  open interval  (a,b) = {x  a < x < b}  x ∈ (2,6) 
(f ∘g)  function composition  (f ∘g) (x) = f (g(x)) 
f (x)=3x, g(x)=x1 ⇒(f ∘g)(x)=3(x1)

∆  delta  change / difference  ∆t = t1 – t0 
[a,b]  closed interval  [a,b] = {x  a ≤ x ≤ b}  x ∈ [2,6] 
∑  sigma  summation – sum of all values in range of series 
∑ xi= x1+x2+…+xn

∆  discriminant  Δ = b2 – 4ac  
∑∑  sigma 
double summation


e  e constant / Euler’s number  e = 2.718281828… 
e = lim (1+1/x)x , x→∞

∏  capital pi  product – product of all values in range of series  ∏ xi=x1∙x2∙…∙xn 
γ  EulerMascheroni constant 
γ = 0.527721566…

Math Symbols Name in English: Linear Algebra
All math symbols name in English related to the Linear Algebra section are discussed below.
Linear Algebra Symbols  
Math Symbol  Symbol Name  Meaning  Example 
 A   determinant 
determinant of matrix A


·  dot  scalar product  a · b 
×  cross  vector product  a × b 
A⊗B  tensor product  tensor product of A and B  A ⊗ B 
inner product  
[ ]  brackets 
matrix of numbers


( )  parentheses 
matrix of numbers


 x   double vertical bars  norm  
det(A)  determinant 
determinant of matrix A


dim(U)  dimension  dimension of matrix A  dim(U) = 3 
AT  transpose  matrix transpose  (AT)ij = (A)ji 
A†  Hermitian matrix  matrix conjugate transpose  (A†)ij = (A)ji 
A*  Hermitian matrix  matrix conjugate transpose  (A*)ij = (A)ji 
A 1  inverse matrix  A A1 = I  
rank(A)  matrix rank  the rank of matrix A  rank(A) = 3 
Probability and Statistics Symbols
Statistics and probability are two distinct but connected academic areas. Probability is the likelihood that something will occur – the probability that it is that an event will occur. Probability distributions are frequently used in statistical analysis, and the two disciplines are frequently studied together. Students investigate Probability and Statistics Symbols, Naming Meanings, and Examples in the table below
Probability and Statistics Symbols  
Math Symbols  Symbol Name  Meaning  Example 
∑  summation 
summation – sum of all values in the range of series


∑∑  double summation 
double summation


P(A)  probability function  probability of event A  P(A)= 0.5 
P(A ∩ B)  probability of events intersection  the probability that events A and B 
P(A ∩ B)= 0.5

P(A ∪ B)  probability of events union  probability that events A or B 
P(A ∪ B)= 0.5

P(A  B)  conditional probability function  probability of event A given event B occurred  P(A  B)= 0.3 
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  μ= 10 
E( X )  expectation value  the expected value of random variable X  E( X ) = 10 
E( X  Y )  conditional expectation  expected value of random variable X given Y 
E( X  Y = 2 ) = 5

var( X )  variance  variance of random variable X  var( X )= 4 
σ2  variance  variance of population values  σ2= 4 
std( X )  standard deviation  standard deviation of random variable X  std( X ) = 2 
σx  standard deviation  standard deviation value of random variable X  σx = 2 
median 
middle value of random variable x


cov( X,Y )  covariance  covariance of random variables X and Y  cov( X,Y )= 4 
corr( X,Y )  correlation  correlation of random variables X and Y 
corr( X,Y )= 0.6

cov( X,Y )  covariance  covariance of random variables X and Y  cov( X,Y )= 4 
corr( X,Y )  correlation  correlation of random variables X and Y 
corr( X,Y )= 0.6

ρ x,y  correlation  correlation of random variables X and Y  ρ x,y= 0.6 
X ~  distribution of X  distribution of random variable X  X ~ N (0,3) 
X ~  distribution of X  distribution of random variable X  X ~ N (0,3) 
Mo  mode 
value that occurs most frequently in population


MR  midrange 
MR =( xmax+xmin)/2


Md  sample median 
half the population is below this value


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 
x=(2+5+9) /3=5.333

s2  sample variance  population samples variance estimator  s2= 4 
s  sample standard deviation  population samples standard deviation estimator  s= 2 
Zx  standard score  Zx=(xx)/ Sx  
HG( N ,K ,n ) 
hypergeometric distribution


Bern( p ) 
Bernoulli distribution


N(μσ2)  normal distribution  gaussian distribution  X ~ N (0,3) 
U( a,b )  uniform distribution  equal probability in range a,b  X ~ U (0,3) 
exp(λ)  exponential distribution 
f(x)=λeλx x≥0


gamma(c, λ)  gamma distribution 
f(x)=λ c xc1 eλx / Γ ( c ) x≥0


χ2(k)  chisquare distribution 
f(x)=xk/21 ex/2 / ( 2k/2Γ )(k/2) )


F (k1,k2)  F distribution  
Bin( n,p )  binomial distribution 
F(k) = nCk pk(1p)nk


Poisson( λ )  Poisson distribution 
F(k) = λkeλ / k !


Geom( p )  geometric distribution 
F(k) = p( 1p)k

Advanced Math Symbols: Calculus
Various math symbols have appeared in calculus. All the symbols of mathematics with names and definitions can be found here. Examine all of the mathematical symbols utilized during calculus.
Calulas Symbols  
Symbol  Symbol Name in Maths  Math Symbols Meaning  Example 
∫  integral  opposite to derivation 
∫xn dx = xn + 1/n + 1 + C

ε  epsilon  represents a very small number, nearzero  ε → 0 
limx→a  limit  limit value of a function 
limx→a(3x+1)= 3 × a + 1 = 3a + 1

y ‘  derivative  derivative – Lagrange’s notation  (5×3)’ = 15×2 
e  e constant / Euler’s number  e = 2.718281828… 
e = lim (1+1/x)x , x→∞

y(n)  nth derivative  n times derivation 
nth derivative of 3xn = 3 n (n1)(n2)….(2)(1)= 3n!

y”  second derivative  derivative of derivative  (4×3)” = 24x 
second derivative 
derivative of derivative


dy/dx  derivative 
derivative – Leibniz’s notation


nth derivative 
n times derivation


Second derivative of time  derivative of derivative 
If y = 4t2, then


Single derivative of time  derivative by time – Newton’s notation  y = 5t, then  
D2x  second derivative  derivative of derivative 
y” + 2y + 1 = 0
⇒ D2y + 2Dy + 1 = 0 
Dx  derivative  derivative – Euler’s notation  dy/x – 1 = 0 ⇒ Dy – 1 = 0 
δ  delta function 
Dirac Delta function


partial derivative  Differentiating a function with respect to one variable considering the other variables as constant 
∂(x2+y2)/∂x = 2x


∭  triple integral 
integration of the function of 3 variables


∬  double integral  integration of the function of 2 variables 
∬(x3+y3)dx dy

∯  closed surface integral  Double integral over a closed surface 
∭V (⛛.F)dV = ∯S (F.n̂) dS

∮  closed contour / line integral  Line integral over closed curve  ∮C 2/z dz 
[a,b]  closed interval  [a,b] = {x  a ≤ x ≤ b}  sin x ∈ [ – 1, 1] 
∰  closed volume integral  Volume integral over a closed threedimensional domain 
∰ (x2 + y2 + z2) dx dy dz

(a,b)  open interval  (a,b) = {x  a < x < b} 
f is continuous within (0, 1)

z*  complex conjugate  z = a+bi → z*=abi 
If z = 3 + 2i then z* = 3 – 2i

i  imaginary unit  i ≡ √1  z = 3 + 2i 
∇  nabla / del  gradient / divergence operator  ∇f (x,y,z) 
vector 
A quantity with magnitude and direction


x * y  convolution  Modification in a function due to the other function. 
y(t) = x(t) * h(t)

∞  lemniscate  infinity symbol 
3x ≥ 0; x ∈ (0, ∞)

Set Theory Symbols
Set theory is a theory of mathematics that was designed to explain the groupings of items. Sets have proven to be an invaluable tool for describing some of mathematics’ most complex structures. They are primarily used to specify a wide range of realworld applications. Let us look at the many sorts of symbols employed during mathematics set theory, as well as their meanings and examples.
Set Theory Symbols  
Math Symbols  Symbol Name  Meaning  Example 
A = B  equality  both sets have the same members  A={6,4,17}, B={6,4,17}, A=B 
{ }  set  a collection of elements  A = {3,7,9,14}, B = {9,14,28} 
A ∩ B  intersection  objects that belong to set A and set B  A ∩ B = {9,14} 
A ∪ B  union  objects that belong to set A or set B 
A ∪ B = {3,7,9,14,28}

A ⊆ B  subset  A is a subset of B. set A is included in set B. 
{9,14,28} ⊆ {9,14,28}

A ⊂ B  proper subset / strict subset  A is a subset of B, but A is not equal to B. 
{9,14} ⊂ {9,14,28}

A ⊄ B  not subset  set A is not a subset of set B 
{9,66} ⊄ {9,14,28}

A ⊇ B  superset  A is a superset of B. set A includes set B 
{9,14,28} ⊇ {9,14,28}

A ⊃ B  proper superset / strict superset  A is a superset of B, but B is not equal to A. 
{9,14,28} ⊃ {9,14}

A ⊅ B  not superset  set A is not a superset of set B 
{9,14,28} ⊅ {9,66}

2A  power set 
all subsets of A


power set 
all subsets of A


A×B  cartesian product  set of all ordered pairs from A and B 
A×B = {(a,b)a∈A , b∈B}

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  A = {3,9,14}, B = {1,2,3}, AB = {9,14} 
A – B  relative complement  objects that belong to A and not to B  A = {3,9,14}, B = {1,2,3}, AB = {9,14} 
A ∆ B  symmetric difference  objects that belong to A or B but not to their intersection 
A = {3,9,14},
B = {1,2,3}, A ∆ B = {1,2,9,14} 
A ⊖ B  symmetric difference  objects that belong to A or B but not to their intersection 
A = {3,9,14},
B = {1,2,3}, A ⊖ B = {1,2,9,14} 
a∈A  element of, belongs to 
set membership 
A={3,9,14}, 3 ∈ A

x∉A  not element of  no set membership 
A={3,9,14}, 1 ∉ A

(a,b)  ordered pair 
collection of 2 elements


complex numbers set

6+2i ∈  
A  cardinality  the number of elements of set A 
A={3,9,14}, A=3

#A  cardinality  the number of elements of set A 
A={3,9,14}, #A=3

  vertical bar  such that  A={x3<x<14} 
alephnull 
infinite cardinality of natural numbers set


alephone 
cardinality of countable ordinal numbers set


Ø  empty set  Ø = { }  C = {Ø} 
universal set 
set of all possible values


0  natural numbers / whole numbers set (with zero)  0 = {0,1,2,3,4,…}  0 ∈ 0 
1  natural numbers / whole numbers set (without zero)  1 = {1,2,3,4,5,…}  6 ∈ 1 
integer numbers set

6 ∈  
rational numbers set

2/6 ∈  
real numbers set

6.343434∈ 
Mathematical Language and Symbols
Roman numerals are employed in a variety of applications and are frequently seen in our daily lives. The followings are the most popular Roman and European numeric symbols used in mathematics.
Numerical Symbols  
Name  European  Roman 
zero  0  n/a 
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 
forty  40  XL 
fifty  50  L 
sixty  60  LX 
seventy  70  LXX 
eighty  80  LXXX 
ninety  90  XC 
one hundred  100  C 