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