Exhaustive List Of Math Symbols & Their Meaning [+ Downloadable Chart For Classroom]

1. Basic math symbols
2. Algebra symbols
3. Geometry symbols
4. Set theory symbols
5. Calculus & analysis symbols

1. Basic Math Symbols

2. Algebra Symbols

Symbol	Symbol Name	Meaning / definition	Example
x	x variable	unknown value to find	when 2x = 4, then x = 2
≡	equivalence	identical to	n/a
≜	equal by definition	equal by definition	n/a
:=	equal by definition	equal by definition	n/a
~	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	n/a
≪	much less than	much less than	1 ≪ 1000000
≫	much greater than	much greater than	1000000 ≫ 1
( )	parentheses	calculate expression inside first	2 * (3+5) = 16
[ ]	brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
{ }	braces	set	n/a
⌊x⌋	floor brackets	rounds number to lower integer	⌊4.3⌋ = 4
⌈x⌉	ceiling brackets	rounds number to upper integer	⌈4.3⌉ = 5
x!	exclamation mark	factorial	4! = 1*2*3*4 = 24
| x |	single vertical bar	absolute value	| -5 | = 5
f (x)	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 ∈ [2,6]
∆	delta	change / difference	∆t = t1 - t0
∆	discriminant	Δ = b2 - 4ac	n/a
∑	sigma	summation - sum of all values in range of series	∑ xi= x1+x2+...+xn
∑∑	sigma	double summation
∏	capital pi	product - product of all values in range of series	∏ xi=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...	n/a
φ	golden ratio	golden ratio constant	n/a
π	pi constant	π = 3.141592654...is the ratio between the circumference and diameter of a circle	c = π⋅d = 2⋅π⋅r

3. Geometry Symbols

Symbol	Symbol Name	Meaning / definition	Example
∠	angle	formed by two rays	∠ABC = 30°
	measured angle	n/a	ABC = 30°
	spherical angle	n/a	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	n/a
AB	line segment	line from point A to point B	n/a
	ray	line that start from point A	n/a
	arc	arc from point A to point B	= 60°
⊥	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
c	radians	radians angle unit	360° = 2π c
grad	gradians / gons	grads angle unit	360° = 400 grad
g	gradians / gons	grads angle unit	360° = 400 g

4. Set Theory Symbols

Symbol	Symbol Name	Meaning / definition	Example
{ }	set	a collection of elements	A = {3,7,9,14}, B = {9,14,28}
|	such that	so that	A = {x | x∈, x<0}
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	n/a
	power set	all subsets of A	n/a
A=B	equality	both sets have the same members	A={3,9,14}, B={3,9,14}, A=B
Ac	complement	all the objects that do not belong to set A	n/a
A'	complement	all the objects that do not belong to set A	n/a
A\B	relative complement	objects that belong to A and not to B	A = {3,9,14}, B = {1,2,3}, A \ B = {9,14}
A-B	relative complement	objects that belong to A and not to B	A = {3,9,14}, B = {1,2,3}, A - B = {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	n/a
A×B	cartesian product	set of all ordered pairs from A and B	n/a
|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
	aleph-null	infinite cardinality of natural numbers set	n/a
	aleph-one	cardinality of countable ordinal numbers set	n/a
Ø	empty set	Ø = {}	A = Ø
	universal set	set of all possible values	n/a
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	= {...-3,-2,-1,0,1,2,3,...}	-6 ∈
	rational numbers set	= {x | x=a/b, a,b∈ and b≠0}	2/6 ∈
	real numbers set	= {x | -∞ < x <∞}	6.343434 ∈
	complex numbers set	= {z | z=a+bi, -∞<a<∞,      -∞<b<∞}	6+2i ∈

5. Calculus & Analysis Symbols

Symbol	Symbol Name	Meaning / definition	Example
	limit	limit value of a function	n/a
ε	epsilon	represents a very small number, near zero	ε → 0
e	e constant / Euler's number	e = 2.718281828...	e = lim (1+1/x)x , x→∞
y '	derivative	derivative - Lagrange's notation	(3x3)' = 9x2
y ''	second derivative	derivative of derivative	(3x3)'' = 18x
y(n)	nth derivative	n times derivation	(3x3)(3) = 18
	derivative	derivative - Leibniz's notation	d(3x3)/dx = 9x2
	second derivative	derivative of derivative	d2(3x3)/dx2 = 18x
	nth derivative	n times derivation	n/a
	time derivative	derivative by time - Newton's notation	n/a
	time second derivative	derivative of derivative	n/a
Dx y	derivative	derivative - Euler's notation	n/a
Dx2y	second derivative	derivative of derivative	n/a
	partial derivative	n/a	∂(x2+y2)/∂x = 2x
∫	integral	opposite to derivation	∫ f(x)dx
∬	double integral	integration of function of 2 variables	∫∫ f(x,y)dxdy
∭	triple integral	integration of function of 3 variables	∫∫∫ f(x,y,z)dxdydz
∮	closed contour / line integral	n/a	n/a
∯	closed surface integral	n/a	n/a
∰	closed volume integral	n/a	n/a
[a,b]	closed interval	[a,b] = {x | a ≤ x ≤ b}	n/a
(a,b)	open interval	(a,b) = {x | a < x < b}	n/a
i	imaginary unit	i ≡ √-1	z = 3 + 2i
z*	complex conjugate	z = a+bi → z*=a-bi	z* = 3 + 2i
z	complex conjugate	z = a+bi → z = a-bi	z = 3 + 2i
∇	nabla / del	gradient / divergence operator	∇f (x,y,z)
	vector	n/a	n/a
	unit vector	n/a	n/a
x * y	convolution	y(t) = x(t) * h(t)	n/a
	Laplace transform	F(s) = {f (t)}	n/a
	Fourier transform	X(ω) = {f (t)}	n/a
δ	delta function	n/a	n/a
∞	lemniscate	infinity symbol	n/a