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

Pranalika Mahanta

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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

 Symbol Symbol Name Meaning / definition Example = equals sign equality 5 = 2+35 is equal to 2+3 ≠ not equal sign inequality 5 ≠ 45 is not equal to 4 ≈ approximately equal approximation sin(0.01) ≈ 0.01,x ≈ y means x is approximately equal to y > strict inequality greater than 5 > 45 is greater than 4 < strict inequality less than 4 < 54 is less than 5 ≥ inequality greater than or equal to 5 ≥ 4,x ≥ y means x is greater than or equal to y ≤ inequality less than or equal to 4 ≤ 5,x ≤ y means x is less than or equal to y ( ) parentheses calculate expressions inside first 2 × (3+5) = 16 [ ] brackets calculate expressions inside first [(1+2)×(1+5)] = 18 + plus sign addition 1 + 1 = 2 − minus sign subtraction 2 − 1 = 1 ± plus - minus both plus and minus operations 3 ± 5 = 8 or -2 ± minus - plus both minus and plus operations 3 ∓ 5 = -2 or 8 * asterisk multiplication 2 * 3 = 6 × times sign multiplication 2 × 3 = 6 ⋅ multiplication dot multiplication 2 ⋅ 3 = 6 ÷ division sign / obelus division 6 ÷ 2 = 3 / division slash division 6 / 2 = 3 mod modulo remainder calculation 7 mod 2 = 1 . period decimal point, decimal separator 2.56 = 2+56/100 ab power exponent 23 = 8 a^b caret exponent 2 ^ 3 = 8 √a square root √a ⋅ √a  = a √9 = ±3 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) n/a for n=3, n√8 = 2 % percent 1% = 1/100 10% × 30 = 3 ‰ per-mille 1‰ = 1/1000 = 0.1% 10‰ × 30 = 0.3 ppm per-million 1ppm = 1/1000000 10ppm × 30 = 0.0003 ppb per-billion 1ppb = 1/1000000000 10ppb × 30 = 3×10-7 ppt per-trillion 1ppt = 10-12 10ppt × 30 = 3×10-10

## 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, -∞
 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
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