Maths Symbols

Basic 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.

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)		for n=3,n√8=2
%	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

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	Example
∠	formed by two rays	∠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
AB	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≅∆XYZ
∼	similarity	same shapes, not same size	∆ABC∼∆XYZ
Δ	triangle	triangle shape	;ΔABC ≅ΔBCD
∣x−y∣	distance	distance between points x and y	∣x−y∣=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
grad	gradians ∕ gons	grads angle unit	360°;=400 grad
g	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
χ	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	proportional to	y ∝ x when y=kx, k constant
∞	lemniscate	infinity symbol
≪	much less than	much less than	1≪1000000
⁽ ⁾	much grataer than	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)	open interval	(a,b)={ x | a < x < b }	x∈(2,6)
[a,b]	closed interval	[a,b]={x | a≤ x ≤b }	x&isin[2,6]
Δ	delta	change / difference	Δ=t1-t0
Δ	discriminant	Δ=b²-4ac
∑	sigma	summation - sum of all values in range of series	∑x1=x1+x2+...+xn
∑∑	sigma	double summation
∏	capital pi	product - product of all values in range of series	∏x1=x1∙x2∙...∙xn
e	e constant / Euler's number	e = 2.718281828...	e =lim (1+1/x)x,x→∞
γ	Euler-Mascheroni constant	γ= 0.5772156649...
φ	golden ratio	golden ratio constant
π	pi constant	π = 3.141592654... is the ratio between the circumference and diameter of a circle	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
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	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)
μ	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
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
∑	summation	summation - sum of all values in range of series
∑∑	double summation	double summation
Mo	mode	value that occurs most frequently in population
MR	mid-range	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=(x-x)/ Sx
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)
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, λ)	gamma distribution	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

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
Α	α	Alpha	a	al-fa
Β	β	Beta	b	be-ta
Γ	γ	Gamma	g	ga-ma
Δ	δ	Delta	d	del-ta
Ε	ε	Epsilon	e	ep-si-lon
Ζ	ζ	Zeta	z	Ze-ta
Η	η	Eta	h	eh-ta
Θ	θ	Theta	th	te-ta
Ι	ι	Iota	i	io-ta
Κ	κ	Kappa	k	ka-pa
Λ	λ	Lambda	l	lam-da
Μ	μ	Mu	m	m-yoo
Μ	μ	Mu	m	m-yoo
Ν	ν	Nu	n	noo
Ν	ν	Nu	n	noo
Ξ	ξ	Xi	x	x-ee
Ο	ο	Omicron	o	o-mee-c-ron
Π	π	Pi	p	pa-yee
Ρ	ρ	Rho	r	row
Σ	σ	Sigma	s	sig-ma
Τ	τ	Tau	t	ta-oo
Υ	υ	Upsilon	u	oo-psi-lon
Φ	φ	Phi	ph	f-ee
Χ	χ	Chi	ch	kh-ee
Ψ	ψ	Psi	ps	p-see
Ω	ω	Omega	o	o-me-ga