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

Pranalika Mahanta

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  • India
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The concept of mathematics is completely based on the relationship between numbers and symbols. These math symbols are used to perform different mathematical operations and represent various mathematical concepts.And although students sometimes find it challenging to use complex math symbols to solve math problems, these symbols are used to refer math quantities and help in easy denotation. There are a lot of math symbols applied in any given mathematical concept ranging from simple addition and subtraction to complicated operations like integration. This is the main reason why students find math symbols confusing to understand and difficult to remember. Since there are so many notations that are important for students to understand, we have put down a list of common math symbols, their concise definition and how to use them.(You can also download this chart to use in the classroom and distribute it among the students)Let’s first divide the types of math symbols you’ll need as per the syllabus:
  1. Basic math symbols
  2. Algebra symbols
  3. Geometry symbols
  4. Set theory symbols
  5. Calculus & analysis symbols

1. Basic Math Symbols

SymbolSymbol NameMeaning / definitionExample
=equals signequality5 = 2+35 is equal to 2+3
not equal signinequality5 ≠ 45 is not equal to 4
approximately equalapproximationsin(0.01) ≈ 0.01,x ≈ y means x is approximately equal to y
>strict inequalitygreater than5 > 45 is greater than 4
<strict inequalityless than4 < 54 is less than 5
inequalitygreater than or equal to5 ≥ 4,x ≥ y means x is greater than or equal to y
inequalityless than or equal to4 ≤ 5,x ≤ y means x is less than or equal to y
( )parenthesescalculate expressions inside first2 × (3+5) = 16
[ ]bracketscalculate expressions inside first[(1+2)×(1+5)] = 18
+plus signaddition1 + 1 = 2
minus signsubtraction2 − 1 = 1
±plus - minusboth plus and minus operations3 ± 5 = 8 or -2
±minus - plusboth minus and plus operations3 ∓ 5 = -2 or 8
*asteriskmultiplication2 * 3 = 6
×times signmultiplication2 × 3 = 6
multiplication dotmultiplication2 ⋅ 3 = 6
÷division sign / obelusdivision6 ÷ 2 = 3
/division slashdivision6 / 2 = 3
modmoduloremainder calculation7 mod 2 = 1
.perioddecimal point, decimal separator2.56 = 2+56/100
abpowerexponent23 = 8
a^bcaretexponent2 ^ 3 = 8
√asquare root√a ⋅ √a  = a√9 = ±3
3√acube root3√a ⋅ 3√a  ⋅ 3√a  = a3√8 = 2
4√afourth root4√a ⋅ 4√a  ⋅ 4√a  ⋅ 4√a  = a4√16 = ±2
n√an-th root (radical) n/afor n=3, n√8 = 2
%percent1% = 1/10010% × 30 = 3
per-mille1‰ = 1/1000 = 0.1%10‰ × 30 = 0.3
ppmper-million1ppm = 1/100000010ppm × 30 = 0.0003
ppbper-billion1ppb = 1/100000000010ppb × 30 = 3×10-7
pptper-trillion1ppt = 10-1210ppt × 30 = 3×10-10
Download the printable chart here- Basic Math Symbols

2. Algebra Symbols

SymbolSymbol NameMeaning / definitionExample
xx variableunknown value to findwhen 2x = 4, then x = 2
equivalenceidentical ton/a
equal by definitionequal by definitionn/a
:=equal by definitionequal by definitionn/a
~approximately equalweak approximation11 ~ 10
approximately equalapproximationsin(0.01) ≈ 0.01
proportional toproportional toy ∝ x when y = kx, k constant
lemniscateinfinity symbol n/a
much less thanmuch less than1 ≪ 1000000
much greater thanmuch greater than1000000 ≫ 1
( )parenthesescalculate expression inside first2 * (3+5) = 16
[ ]bracketscalculate expression inside first[(1+2)*(1+5)] = 18
{ }bracesset n/a
⌊x⌋floor bracketsrounds number to lower integer⌊4.3⌋ = 4
⌈x⌉ceiling bracketsrounds number to upper integer⌈4.3⌉ = 5
x!exclamation markfactorial4! = 1*2*3*4 = 24
| x |single vertical barabsolute value| -5 | = 5
f (x)function of xmaps 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]
deltachange / difference∆t = t1 - t0
discriminantΔ = b2 - 4ac n/a
sigmasummation - sum of all values in range of series∑ xi= x1+x2+...+xn
∑∑sigmadouble summation
capital piproduct - product of all values in range of series∏ xi=x1∙x2∙...∙xn
ee constant / Euler's numbere = 2.718281828...e = lim (1+1/x)x , x→∞
γEuler-Mascheroni constantγ = 0.5772156649...n/a
φgolden ratiogolden ratio constantn/a
πpi constantπ = 3.141592654...is the ratio between the circumference and diameter of a circlec = π⋅d = 2⋅π⋅r
Download the printable chart here- Algebra Symbols

3. Geometry Symbols

SymbolSymbol NameMeaning / definition Example
angleformed by two rays∠ABC = 30°
anglemeasured angle n/aangleABC = 30°
anglespherical angle n/aAOB = 30°
right angle= 90°α = 90°
°degree1 turn = 360°α = 60°
degdegree1 turn = 360degα = 60deg
primearcminute, 1° = 60′α = 60°59′
double primearcsecond, 1′ = 60″α = 60°59′59″
linelineinfinite line n/a
ABline segmentline from point A to point B n/a
rayrayline that start from point A n/a
arcarcarc from point A to point Barc = 60°
perpendicularperpendicular lines (90° angle)AC ⊥ BC
parallelparallel linesAB ∥ CD
congruent toequivalence of geometric shapes and size∆ABC ≅ ∆XYZ
~similaritysame shapes, not same size∆ABC ~ ∆XYZ
Δtriangletriangle shapeΔABC ≅ ΔBCD
|x-y|distancedistance between points x and y| x-y | = 5
πpi constantπ = 3.141592654...is the ratio between the circumference and diameter of a circlec = πd = 2⋅πr
radradiansradians angle unit360° = 2π rad
cradiansradians angle unit360° = 2π c
gradgradians / gonsgrads angle unit360° = 400 grad
ggradians / gonsgrads angle unit360° = 400 g
Download the printable chart here- Geometric Symbol

4. Set Theory Symbols

SymbolSymbol NameMeaning / definitionExample
{ }seta collection of elementsA = {3,7,9,14}, B = {9,14,28}
|such thatso thatA = {x | x\mathbb{R}, x<0}
A⋂Bintersectionobjects that belong to set A and set BA ⋂ B = {9,14}
A⋃Bunionobjects that belong to set A or set BA ⋃ B = {3,7,9,14,28}
A⊆BsubsetA is a subset of B. set A is included in set B.{9,14,28} ⊆ {9,14,28}
A⊂Bproper subset / strict subsetA is a subset of B, but A is not equal to B.{9,14} ⊂ {9,14,28}
A⊄Bnot subsetset A is not a subset of set B{9,66} ⊄ {9,14,28}
A⊇BsupersetA is a superset of B. set A includes set B{9,14,28} ⊇ {9,14,28}
A⊃Bproper superset / strict supersetA is a superset of B, but B is not equal to A.{9,14,28} ⊃ {9,14}
A⊅Bnot supersetset A is not a superset of set B{9,14,28} ⊅ {9,66}
2Apower setall subsets of A n/a
\mathcal{P}(A)power setall subsets of A n/a
A=Bequalityboth sets have the same membersA={3,9,14}, B={3,9,14}, A=B
Accomplementall the objects that do not belong to set A n/a
A'complementall the objects that do not belong to set A n/a
A\Brelative complementobjects that belong to A and not to BA = {3,9,14}, B = {1,2,3}, A \ B = {9,14}
A-Brelative complementobjects that belong to A and not to BA = {3,9,14}, B = {1,2,3}, A - B = {9,14}
A∆Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = {3,9,14}, B = {1,2,3}, A ∆ B = {1,2,9,14}
A⊖Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = {3,9,14}, B = {1,2,3}, A ⊖ B = {1,2,9,14}
a∈Aelement of, belongs toset membershipA={3,9,14}, 3 ∈ A
x∉Anot element ofno set membershipA={3,9,14}, 1 ∉ A
(a,b)ordered paircollection of 2 elements n/a
A×Bcartesian productset of all ordered pairs from A and B n/a
|A|cardinalitythe number of elements of set AA={3,9,14}, |A|=3
#Acardinalitythe number of elements of set AA={3,9,14}, #A=3
symbolaleph-nullinfinite cardinality of natural numbers set n/a
symbolaleph-onecardinality of countable ordinal numbers set n/a
Øempty setØ = {}A = Ø
\mathbb{U}universal setset of all possible values n/a
\mathbb{N}0natural numbers / whole numbers  set (with zero)0 = {0,1,2,3,4,...}0 ∈ \mathbb{N}0
\mathbb{N}1natural numbers / whole numbers  set (without zero)\mathbb{N}1 = {1,2,3,4,5,...}6 ∈ \mathbb{N}1
\mathbb{Z}integer numbers set\mathbb{Z} = {...-3,-2,-1,0,1,2,3,...}-6 ∈ \mathbb{Z}
\mathbb{Q}rational numbers set\mathbb{Q} = {x | x=a/b, a,b\mathbb{Z} and b≠0}2/6 ∈ \mathbb{Q}
\mathbb{R}real numbers set\mathbb{R} = {x | -∞ < x <∞}6.343434 ∈ \mathbb{R}
\mathbb{C}complex numbers set\mathbb{C} = {z | z=a+bi, -∞<a<∞,      -∞<b<∞}6+2i\mathbb{C}
Download the printable chart here- Set Theory Symbols

5. Calculus & Analysis Symbols

SymbolSymbol NameMeaning / definitionExample
lim_{x\to x0}f(x)limitlimit value of a function n/a
εepsilonrepresents a very small number, near zeroε 0
ee constant / Euler's numbere = 2.718281828...e = lim (1+1/x)x , x→∞
y 'derivativederivative - Lagrange's notation(3x3)' = 9x2
y ''second derivativederivative of derivative(3x3)'' = 18x
y(n)nth derivativen times derivation(3x3)(3) = 18
\frac{dy}{dx}derivativederivative - Leibniz's notationd(3x3)/dx = 9x2
\frac{d^2y}{dx^2}second derivativederivative of derivatived2(3x3)/dx2 = 18x
\frac{d^ny}{dx^n}nth derivativen times derivation n/a
\dot{y}time derivativederivative by time - Newton's notation  n/a
time second derivativederivative of derivative  n/a
Dx yderivativederivative - Euler's notation  n/a
Dx2ysecond derivativederivative of derivative  n/a
\frac{\partial f(x,y)}{\partial x}partial derivative  n/a∂(x2+y2)/∂x = 2x
integralopposite to derivation ∫ f(x)dx
double integralintegration of function of 2 variables ∫∫ f(x,y)dxdy
triple integralintegration 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
iimaginary uniti ≡ √-1z = 3 + 2i
z*complex conjugatez = a+biz*=a-biz* = 3 + 2i
zcomplex conjugatez = a+biz = a-biz = 3 + 2i
nabla / delgradient / divergence operatorf (x,y,z)
vector n/a n/a
unit vector n/a n/a
x * yconvolutiony(t) = x(t) * h(t) n/a
Laplace transformF(s) = {f (t)} n/a
Fourier transformX(ω) = {f (t)} n/a
δdelta function n/a n/a
lemniscateinfinity symbol n/a
Download the printable chart here- Calculus & Analysis SymbolsThese are some of the most commonly used math symbols that your students need to learn in order to solve math questions. To help your students better memorise these symbols, you can download these math symbol charts and distribute them among your students as well as stick it in the classroom. Use these charts and math symbols in your classroom to help your students clearly understand mathematical concepts and perform tasks. You can also quiz your students on these symbols and hold fun contests in the class.If you are interested in introducing Prodigy in your class, you can sign up for a free demo here: https://india.prodigygame.com/get-started/