# Equivalence Symbols

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

This is a list of the most common equivalence symbols:

SymbolDefinitionExample
$$=$$ 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