# Equivalence Symbols

This is a list of the most common equivalence symbols:

Symbol | Definition | Example |
---|---|---|

\(=\) | equal to | \(5+4=9\) |

\(\ne\) | not equal to | \(5\ne4\) |

\(\equiv\) | identical to | \(a \equiv b\) |

\(\not\equiv\) | not identical to | \(a \not\equiv b\) |

\(\sim\) | similar to | \(a \sim b\) |

\(\approx\) | approximately equal to | \(a \approx b\) |

\(\cong\) | congruent, equivalent in size and shape | \(\triangle ABC \cong \triangle XYZ\) |

\(:=\) | is defined to be | \(a := \{2, 4, 6, 8 \}\;\) means \(\;a\;\) is defined to be set \(\;\{2, 4, 6, 8 \} \) |

\(\therefore\) | therefore | \( a=b\; \therefore\; b=a \) |

\(\because\) | because | \( a=b\; \because\; b=a \) |

\(>\) | greater than | \(5>4\) |

\(\gg\) | much greater than | \(50000 \gg 4\) |

\(<\) | less than | \(4<5\) |

\(\ll\) | much less than | \(4 \ll 50000\) |

\(\ge\) | greater than or equal to | \(a\ge b\) |

\(\le\) | less than or equal to | \(a\le b\) |

\(\Rightarrow\) | implies if then - \(\; a \Rightarrow b\;\) means if \(\;a\;\) is true then \(\;b\;\) is also true, if \(\;a\;\) is false then nothing is said about \(\;b \) | \( a = 3 \Rightarrow a3 = 9\;\) is true, but \(\;a3 = 9 \Rightarrow a = 3\;\) is in general false since \(\;a\;\) could be \(\;−3\) |

\(\rightarrow\) | same as above | same as above |

\(\Leftrightarrow\) | if and only if - \(\;a \Leftrightarrow b\;\) means \(\;a\;\) is true if \(\;b\;\) is true and \(\;a\;\) is false if \(\;b\;\) is false | \(a + 2 = b - 5 \Leftrightarrow a = b - 7\) |

\(\leftrightarrow\) | same as above | same as above |