## Math Algebra Symbols with Examples

Symbol | Symbol Name | Symbol Meaning | Example |
---|---|---|---|

x |
x Variable | unknown value to find | when 3x = 9, thenx = 3 |

≡ | Congruence Relation | identical to | 5 ≡ 2 (mod 3) |

≜ | Is Equal By Definition | is equal by definition | a≜b |

Is Equal By Definition | is equal by definition | AB | |

:= | Is Equal By Definition | is equal by definition | a:=b |

~ | Approximately Equal | is similar to | ∆ABC ~ ∆DEF means triangle ABC is similar to triangle DEF. |

≈ | Approximately Equal | approximation | |

∝ | Is Proportional to | is proportional to | y∝ x means, when y = kx, k constant |

∞ | Lemniscate | infinity symbol | 1 / 0 = ∞ |

≪ | Much Less Than | x ≪ y means x is much less than y. | 0.001≪ 1000000 |

≫ | Much Greater Than | x ≫ y means x is much greater than y. | 1000000≫ 0.001 |

( ) | Parentheses | calculate expression inside first | 3 * (3+3) = 18 |

[ ] | Brackets | calculate expression inside first | [(1+1)*(1+1)] = 4 |

{ } | Braces | set | {..., -3,-2,-1,0,1,2,3, ... } |

⌊x⌋ |
Floor Brackets | rounds number to lower integer | ⌊5.4⌋= 5 |

⌈x⌉ |
Ceiling Brackets | rounds number to upper integer | ⌈5.4⌉= 6 |

x! |
Exclamation Mark | factorial | 3! = 1*2*3 = 6 |

| x | |
Single Vertical Bar | absolute value | | -8 | = 8 |

f (x) |
Function of x | maps values of x to f(x) | f (x) = 2x+3 |

(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
∈ (3,9) |

[a,b] |
Closed Interval | [a,b] = {x | a ≤ x ≤ b} |
x
∈ [3,9] |

∆ | Delta | change / difference | ∆t = t_{1 }- t_{0} |

∆ | Discriminant | Δ = b^{2} - 4ac |
∆ = 5^{2}-4(1)(4), = 25 - 16 , = 9 |

∑ | 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 = 0.527721566... | |

φ | Golden Ratio | golden ratio constant | |

π | pi Constant | π = 3.141592654...is the ratio between the circumference and diameter of a circle |