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Mathematical Symbols

List of all mathematical symbols and signs - meaning and examples.

Basic math symbols

Geometry symbols

Algebra symbols

Probability & statistics symbols

Set theory symbols

Logic symbols

Calculus & analysis symbols

Number symbols

Greek symbols

Roman numerals

Basic math symbols

Symbol Symbol Name Meaning / definition Example

= equals sign

equality 5 = 2+3

≠ not equal sign inequality 5 ≠ 4

> strict inequality greater than 5 > 4

< strict inequality less than 4 < 5

≥ inequality greater than or equal to 5 ≥ 4

≤ inequality less than or equal to 4 ≤ 5

( ) parentheses calculate expression inside ...view middle of the document...

141592654...

is the ratio between the circumference and diameter of a circle c = π•d = 2•π•r

rad radians radians angle unit 360º = 2π rad

grad grads grads angle unit 360º = 400 grad

Algebra symbols

Symbol Symbol Name Meaning / definition Example

x x variable unknown value to find when 2x = 4, then x = 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 f(x) ∝ g(x)

∞ lemniscate

infinity symbol

≪ 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

⌊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

∑ 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 = 0.527721566...

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 Symbols

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

( ) parentheses 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 A A-1 = I

rank(A) matrix rank rank of matrix A rank(A) = 3

dim(U) dimension dimension of matrix A rank(U) = 3

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...

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