MATHS SYMBOLS by Brijesh Sharma

MATHS SYMBOLS Math is all about numbers, symbols and Maths formulas. These symbols are required for different operations. These symbols are used in different mathematical fields. From representing the equation to telling the relationship between the two numbers. All mathematical symbols are used in mathematical operations for various concepts. There are so many mathematical symbols which are important for students. To make it easier for you we’ve given here the mathematical symbols table with definitions and examples. From addition, subtraction to geometry to algebra etc, there are various types of symbols. Find all the symbols in the tables given below:

Basic Maths Symbols In Mathematics, it's all about numbers, symbols and formulas. Here we're discussing the foundation of Mathematics. In simple words, without symbols, we cannot do arithmetic. Mathematical symbols and symbols are considered to represent a value. Basic mathematical symbols are used to express mathematical ideas. The relationship between the symbol and the value refers to the basic mathematical requirement. With the help of symbols, certain concepts and ideas are clearly explained. Here is a list of commonly used mathematical symbols with words and meanings. Also, an example is given to understand the use of mathematical symbols. Symbol

Symbol Name

Meaning / definition

Example

equals sign

equality

10 = 2+8 10 is equal to 2+8

≠

not equal sign

inequality

2≠8 2 is not equal to 8

≈

approximately equal

approximation

sin (0.01) ≈ 0.01, x ≈ y means is approximately equal to y

strict inequality

greater than

8>2 8 is greater than 2

strict inequality

less than

2<8 2 is less than 8

≥

inequality

greater than or equal to

8 ≥ 2, x ≥ y means x is greater than or equal to y

≤

inequality

less than or equal to

2 ≤ 8, x ≤ y means is less than or equal to y

()

parentheses

calculate expression inside first

2 × (4+8) = 24

[]

brackets

calculate expression inside first

[(2+3)×(4+6)] = 50

plus sign

addition

2 + 8 = 10

−

minus sign

subtraction

8-2=6

plus - minus

both plus and minus operations

2 ± 8 = 10 or -6

minus - plus

both minus and plus operations

2∓8 = -6 or 10

asterisk

multiplication

2*8 = 16

times sign

multiplication

2 × 8 = 16

⋅

multiplication dot

multiplication

2 sdot; 8 = 16

division sign / obelus

division

8÷2=4

division slash

division

8/2=4

—

horizontal line

division / fraction

6—2=3

mod

modulo

remainder calculation

7 mod 2 = 1

period

decimal point, decimal separator

3.84 = 3+84/100

ab;

power

exponent

23=8

a^b

caret

exponent

2^3=8

√a

square root

√⋅√a =a

√4=±2

3√a

cube root

3√a⋅3√a⋅3√a⋅& =a

3√8=2

4√a

fourth root

4√a ⋅ 4√a ⋅ 4√a ⋅ 4√a =a

4√16=±2

n√a

n-th root (radical)

percent

1%=1/100

10%× 80=8

‰

per-mile

1‰=1/1000=0.1%

10‰ × 80=0.8

ppm

per-million

1ppm=1/1000000

10ppm × 80=0.0008

ppb

per-billion

1ppb=1/1000000000

10ppb × 80=8×10&minussup7;

ppt

per-trillion

1ppt=10&minussup12;

10ppt × 80=8×10&minussup10;

Geometry Symbols

for n=3,n√8=2

There are geometry symbols which are used in mathematics. Here we’re mentioning each and every geometry symbols which are necessary for students to know. Symbol Symbol Name Meaning / definition ∠

formed by two rays

Example

∠ABC=30°

measured angle

ABC=30°

spherical angle

AOB=30°

∟

right angle

=90°

α=90°

degree

1 turn=360°

α=60°

deg

degree

1 turn=360deg

α=60deg

′

prime

arcminute, 1°=60′

α=60°59′

″

double prime

arcsecond, 1′=60″

α=60°59′ 59″

line

infinite line

line segment

line from point A to point B

ray

line that start from point A

⊥

perpendicular

perpendicular lines (90° angle)

AC ⊥ BC

∥

parallel

parallel lines

AB ∥ CD

≅

congruent to

equivalence of geometric shapes and size

∆ABC≅∆XY Z

∼

similarity

same shapes, not same size

∆ABC∼∆XY Z

triangle

triangle shape

;ΔABC ≅ΔBCD

∣x−y∣

distance

distance between points x and y

∣x−y∣=5

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

grad

gradians ∕ gons

grads angle unit

360°;=400 grad

gradians ∕ gons

grads angle unit

360°=400g

Algebra Symbols Algebra is a mathematical component of symbols and rules to deceive those symbols. In algebra, those symbols represent non-fixed values, called variables. How sentences describe the relationship between certain words, in algebra, mathematics describes the relationship between variables. A

Symbol Name

Meaning / definition

Example

x variable

unknown value to find

when 2χ=4, then χ=2

≡

equivalence

identical to

≜

equal by definition equal by definition

≔

equal by definition equal by definition

∽

approximately equal

weak approximation

11∽10

≈

approximately equal

approximation

sin(0.01) ≈ 0.01

∝

proportional to

y ∝ x when y=kx, k constant

∞

lemniscate

infinity symbol

≪

much less than

1≪1000000

⁽⁾

much grataer than

1000000 ≫1

⁽⁾

parentheses

calculate expression inside first

2 *(3+5) = 16

[]

brackets

calculate expression inside first

[ (1+2)*(1+5) ] = 18

{}

braces

set

⌊χ⌋

floor brackets

rounds number to lower integer

⌊4.3⌋ = 4

⌈χ⌉

ceiling brackets

rounds number to upper integer

⌈4.3⌉ = 5

χ!

exclamation mark

factorial

4! =1*2*3*4 = 24

|χ|

vertical bars

absolute value

| -5 | = 5

Af(χ )

function of x

maps values of x to f(x)

f(x)=3x+5

(f°g)

function composition

(f°g)(x)=f(g(x))

f(x)=3x,g(x)=x-1⇒(f° g)(x)=3(x-1)

(a,b)={ x | a < x < b }

x∈(2,6)

(a,b) open interval

[a,b]

closed interval

[a,b]={x | a≤ x ≤b }

x&isin[2,6]

delta

change / difference

Δ=t1-t0

discriminant

Δ=b²-4ac

∑

sigma

summation - sum of all values in range of series

∑∑

sigma

double summation

∏

capital pi

product - product of all values in range of series

∏x1=x1∙x2∙...∙xn

e constant / Euler's number

e = 2.718281828...

e =lim (1+1/x)x,x→∞

Euler-Mascheroni constant

γ= 0.5772156649...

golden ratio

golden ratio constant

pi constant

π = 3.141592654... is the ratio between the circumference and diameter of a circle

∑x1=x1+x2+...+xn

c=π⋅d=2⋅π⋅r

Linear Algebra Symbol These are the linear Algebraic Symbols. It's also a part of mathematics. These symbols are generally used in higher standard. Here's the list of all linear algebra symbols which are helpful for you guys. Symbol

Symbol Name

Meaning/definition

Example

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

|A|

determinant

determinant of matrix A

det(A)

determinant

determinant of matrix A

∥x∥

double vertical bars

norm

transpose

matrix transpose

(AT ) ij = ( A )

A†

Hermitian matrix

matrix conjugate transpose

(A† ) ij = ( A )

Hermitian matrix

matrix conjugate transpose

(A* ) ij = ( A )

A-1

inverse matrix

AA-1=/

rank(A)

matrix rank

rank of matrix A

rank(A)= 3

dim(U)

dimension

dimension of matrix A

dim(U)= 3

Probability and Statistics Symbols Probability and statistics are also a part of mathematics. As you’ve already studied probability and statistics from the junior classes. So here’s the list of the most important probability and statistics symbols. Symbol

Symbol Name

Meaning / definition

Example

P(A)

probability function

probability of event A

P(A)= 0.5

P(A ∩ B)

probability of events intersection

probability that of events A and B

P(A ∩ B)= 0.5

P(A ∪ B)

probability of events union

probability that of events A or B

P(A ∪ B)= 0.5

P(A | B)

conditional probability function

probability of event A given event B occured

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)

population mean

mean of population values

μ= 10

E( X )

expectation value

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

covariance

covariance of random variables X and Y

cov( X,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

∑

summation

summation - sum of all values in range of series

∑∑

double summation

mode

value that occurs most frequently in population

mid-range

MR =( xmax+xmin)/2

sample median

half the population is below this value

lower / first quartile

25 % of population are below this value

median / second quartile

50% of population are below this value = median of samples

upper / third quartile

75% of population are below this value

sample mean

average / arithmetic mean

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

sample variance

population samples variance estimator

s2= 4

sample standard deviation

population samples standard deviation estimator

standard score

Zx=(x-x)/ Sx

distribution of X

distribution of random variable X

X ~ N (0,3)

distribution of X

distribution of random variable X

X ~ N (0,3)

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)=λe-λx x≥0

gamma(c, gamma distribution λ)

f(x)=λ c xc-1 e-λx / Γ ( c ) x≥0

χ2(k)

chi-square distribution f(x)=xk/2-1 e-x/2 / ( 2k/2Γ )(k/2) )

F (k1,k2)

F distribution

Bin( n,p )

binomial distribution

F(k) = nCk pk(1-p)n-k

Poisson( λ)

Poisson distribution

F(k) = λke-λ / k !

Geom( p )

geometric distribution

F(k) = p( 1-p)k

HG( N ,K ,n )

hyper-geometric distribution

Bern( p )

Bernoulli distribution

Greek Alphabet Letters

s= 2

Mathematicians often use Greek letters in their work to represent flexibility, consistency, functions and more. Some of the Greek symbols commonly used in Maths are listed below Upper Case Letter

Lower Case Letter

Greek Letter Name

English Equivalent

Letter Name Pronounce

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

m-yoo

noo

x-ee

Omicron

o-mee-c-ron

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

Frequently Asked Questions (FAQs) Q1. What do math symbols mean? Ans. It means all the symbols which show the quantities or the relationship between two quantities. Q2. What is the value of pi? Ans. The value of pi is 22/7 and 3.14. It is a Greek alphabet. It is an irrational number. While solving NCERT Solutions you'll find many questions about where you've to use them. Q3. What is the * symbol called?

Ans. In English, the * symbol generally means asterisk, but in Mathematics it is generally used to represent multiplication between two quantities.

The Original Source for this from- https://www.pw.live/maths-symbols