Online Calculators & Tools

List of mathematical algebra symbols and signs.

Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|

x | x variable | unknown value to find | when 2x = 4, then x = 2 |

= | equals sign | equality | 5 = 2+3 5 is equal to 2+3 |

≠ | not equal sign | inequality | 5 ≠ 4 5 is not equal to 4 |

≡ | 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 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 | | vertical bars | 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 (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 = t_{1}- t_{0} |

∆ | discriminant | Δ = b^{2} - 4ac | |

∑ | sigma | summation - sum of all values in range of series | ∑ x_{i}= x_{1}+x_{2}+...+x_{n} |

∑∑ | sigma | double summation | |

∏ | capital pi | product - product of all values in range of series | ∏x_{i}=x_{1}∙x_{2}∙...∙x_{n} |

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 |

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 | |

A^{T} | transpose | matrix transpose | (A^{T}) = (_{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 | dim(U) = 3 |