# Equivalence Symbols

### Mathematics Symbols

### Mathematics Terms

- See algebra, geometry, trigonometry

### Nomenclature & Symbols for Engineering, Mathematics, & Science

- See A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

### Postulates and theorems

- See geometry postulates
- See geometry theorems

## Equivalence Symbols

This is a list of the most common equivalence symbols:

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

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

\(\ne\) | not equal to | \(5+5 \ne 9\) |

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

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

\(\overset{\underset{\mathrm{\land}}{}}{=}\) | estimates | |

\(\overset{\underset{\mathrm{\lor}}{}}{=}\) | equiangular to | \(\triangle ABC \overset{\underset{\mathrm{\lor}}{}}{=} \triangle XYZ\) |

\(\overset{\underset{\mathrm{\frown}}{}}{=}\) | corresponds to | |

\(\triangleq\) | equiangular or equal to | \(\triangle ABC \triangleq \triangle XYZ\) |

\(\overset{\underset{\mathrm{def}}{}}{=}\) | equal to by defination | \(a \overset{\underset{\mathrm{def}}{}}{=} b\) |

\(\overset{\underset{\mathrm{m}}{}}{=}\) | measured by | \(a \overset{\underset{\mathrm{m}}{}}{=} b\) |

\(\overset{\underset{\mathrm{?}}{}}{=}\) | questioned equal to | \(a \overset{\underset{\mathrm{?}}{}}{=} b\) |

\(\sim\) | similar to | \(\triangle ABC \sim \triangle XYZ\) |

\(\nsim\) | not similar to | \(a \nsim b\) |

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

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

\(\ncong\) | congruent but not equivalent in size and shape | \(\triangle ABC \ncong \triangle XYZ\) |

\(\doteq\) | approaches the limit | |

\(\doteqdot\) | geometrically equal to | |

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

\(\fallingdotseq\) | approximately equal to or the image of | |

\(\risingdotseq\) | image of or approximately equal to | |

\(\bumpeq\) | difference between | \(a \bumpeq b\) |

\(\Bumpeq\) | geometrically equivalent to | |

\(\asymp\) | equivalent to | \(a \asymp b\) |

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

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

\(:\) | ratio | \(4\) to \(5\) or \(4:5\) or \(4/5\) |

\(::\) | porportion | \(4/5 :: 20/25\) scale factor \(4\) |

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

\(\gg\) | much greater than | \(500 \gg 4\) |

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

\(\ll\) | much less than | \(4 \ll 500\) |

\(\ge\) | greater than or equal to | \(\measuredangle XYZ \ge \measuredangle ABC\) |

\(\le\) | less than or equal to | \(\measuredangle ABC \le \measuredangle XYZ\) |

\(\geqq\) | greater than over equal to | \(a \geqq b\) |

\(\leqq\) | less than over equal to | \(a \leqq b\) |

\(\gneqq\) | greater than but not equal to | \(5 \gneqq 4\) |

\(\lneqq\) | less than but not equal to | \(4 \lneqq 5\) |

\(\gtrsim\) | greater than or equivalent to | \(b \gtrsim a\) |

\(\lesssim\) | less than or equivalent to | \(a \lesssim b\) |

\(\gnsim\) | greater than but not equivalent to | \(5 \gnsim 4\) |

\(\lnsim\) | less than but not equivalent to | \(4 \lnsim 5\) |

\(\gtrless\) | greater than or less than | \(b \gtrless a\) |

\(\lessgtr\) | less than or greater than | \(a \lessgtr b\) |

\(\succ\) | succeeds or higher rank than | \(b \succ a\) |

\(\prec\) | precedes or lower rank than | \(a \prec b\) |

\(\nsucc\) | does not succeed or not higher rank than | \(a \nsucc b\) |

\(\nprec\) | does not precede or not lower rank than | \(b \nprec a\) |

\(\succcurlyeq\) | succeeds or equal to | \(b \succcurlyeq a\) |

\(\preccurlyeq\) | precedes or equal to | \(a \preccurlyeq b\) |

\(\succsim\) | succeeds or equivalent to | \(b \succsim a\) |

\(\precsim\) | precedes or equivalent to | \(a \precsim b\) |

\(\gtreqless\) | greater than or equal to or less than | \(b \gtreqless a\) |

\(\lesseqgtr\) | less than or equal to or greater than | \(a \lesseqgtr b\) |

\(\Rightarrow\) | 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 |