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 | 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 | | 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 = 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 = 0.527721566… | |

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 |

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