# Equivalence Symbols

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

## 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
Symbol Definition Example