Equivalence Symbols

Written by Jerry Ratzlaff on . Posted in Nomenclature & Symbols for Engineering, Mathematics, and Science

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Equivalence Symbols

This is a list of the most common equivalence symbols:

SymbolDefinitionExample
\(=\) 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