Equivalence Symbols
Tags: Nomenclature and Symbols
Equivalence SymbolsThis 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 |
| Symbol | Definition | Example |
Tags: Nomenclature and Symbols