Mathematic Symbols

Written by Jerry Ratzlaff on . Posted in Geometry

This is a list of mathematic symbols:

Algebra 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 \(a \approx b\)
\(>\) 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 \(a+b+c=1\;\Rightarrow\;c+b+a=1\)
\(\Leftrightarrow\) is equivalent to if in only if (iff) \(a=b+1\;\Leftrightarrow\;b=a+1\)
\(\therefore\) therefore \( a=b\; \therefore\; b=a \)
\( \sum\) sigma, summation or sum of all \( \sum_{n=4}^8 n = 4+5+6+7+8=30 \)
\(\left(\; \right)\) parentheses, calculate expression inside first \( 5\times \left(5+4\right) = 45\)
\(\left[\; \right]\) brackets, calculate expression inside first \( \left[ \left(5+4\right) \times \left(9+4\right) \right] = 117\)
\(\{ \; \}\) set, a collection \(A = \{4, 5, 9 \} \)
\(\lfloor x \rfloor\) rounds number to lower integer \(\lfloor 5.4 \rfloor = 5\)
\(\lceil x \rceil\) rounds number to upper integer \(\lceil 5.4 \rceil = 6\)
\(\left | x \right |\) absolute value \(\left | -5 \right | = 5 \)
\(\left \| x \right \|\) normal  
\(x!\) factorial \(5!=5\;x\;4\;x\;3\;x\;2\;x\;1=120 \)
\(a^n\) power, an exponent \(5^4 = 3125\)
\(a\wedge b\) caret, an exponent \(5\wedge4 = 3125\)
\( \sqrt a\) Square root - \(\sqrt a \;\times\; \sqrt a = a\) \(\sqrt 9= 3\)
\(^3\sqrt a\) cube root - \(^3\sqrt a \;\times\; ^3\sqrt a \;\times\; ^3\sqrt a = a\) \(^3\sqrt 9 = 2.08008382305\)
\(^4\sqrt a\) 4th root - \(^4\sqrt a \;\times\; ^4\sqrt a \;\times\; ^4\sqrt a \;\times\; ^4\sqrt a = a\) \(^4\sqrt 9 = 1.73205080757\)
\( ^n\sqrt a\) n-th root \(n=5\;\), \(\;^n\sqrt 9 = 1.55184557391\)
\(\gamma\) Euler-Mascheroni constant \(\gamma = 0.5772156649...\)
\(\Phi\) golden ratio \(1 : 1.6180339887...\)
\(\pi\) \(\pi = 3.141592654... \) \(C = \pi \cdot d = 2 \cdot \pi \cdot r\)

 

Angle and Line Symbols

SymbolDefinitionExample
\(\triangle\) triangle \(\triangle ABC \)
\(\angle\) angle \(\angle ABC = 60^\circ\)
\(\measuredangle\) measured angle \(\angle ABC = 60^\circ\)
\(\sphericalangle\) spherical angle \(\angle AOC = 60^\circ\)
\(\overleftrightarrow {AB}\) infinite line distance  
\(\overline {AB}\) line segment from A to B  
\(\overrightarrow {AB}\) start line at point A  
\(\overset{\frown} {AB}\) arc from A to B  
\(|A-B|\) distance between A and B \(|A-B| = 9\)
\(\parallel\) parallel to \(\overline {AB} \parallel \overline {XY} \)
\(\nparallel\) not parallel to \(\overline {AB} \nparallel \overline {XY} \)
\(\perp\) perpendicular lines \(\overline {AB} \perp \overline {XY} \)

 

Basic Math Symbols

SymbolDefinitionExample
\(+\) addition \(5+4=9\)
\(-\) subtraction \(5-4=1\)
\(\mp\) plus - minus, both plus and minus operations \(5\mp4=9\) and \(1\)
\(\pm\) minus - plus, both minus and plus operations \(5\mp4=1\) and \(9\)
\(*\) multiplication \(5*4=20\)
\(\times\) multiplication \(5\times4=20\)
\(\bullet\) multiplication \(5\bullet4=20\)
\(\div\) division \(5\div 4=1.25\)
\(/\) division \(5/4=1.25\)
\(-\) horizontal line is for division / fraction \(\frac {5} {4} =1.25\)
\(.\) decimal point \(5.4\)
\(=\) equal \(5+4=9\)
\(\left(\; \right)\) parentheses, calculate expression inside first \( 5\times \left(5+4\right) = 45\)
\(\left[\; \right]\) brackets, calculate expression inside first \( \left[ \left(5+4\right) \times \left(9+4\right) \right] = 117\)
\(a^n\) power, an exponent \(5^4 = 3125\)
\( \sqrt a\) Square root - \(\sqrt a \;\times\; \sqrt a = a\) \(\sqrt 9= 3\)
 % percent, \(1\)% \(= 1/100 \) \(5\)% \(\times 4 = 0.2 \)

 

Bracket Symbols

SymbolDefinitionExample
\(\left(\; \right)\) parentheses, calculate expression inside first \( 5\times \left(5+4\right) = 45\)
\(\left[\; \right]\) brackets, calculate expression inside first \( \left[ \left(5+4\right) \times \left(9+4\right) \right] = 117\)
\(\{ \; \}\) set, a collection \(a = {4, 5, 9 } \)
\(\lfloor a \rfloor\) rounds number to lower integer \(\lfloor 5.4 \rfloor = 5\)
\(\lceil a \rceil\) rounds number to upper integer \(\lceil 5.4 \rceil = 6\)
\(\left | a \right |\) absolute value \(\left | -5 \right | = 5 \)
\(\left \| x \right \|\) normal  

 

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 \(a \not\equiv b\)
\(\overset{\underset{\mathrm{\Delta}}{}}{=}\) delta equal to  
\(\overset{\underset{\mathrm{def}}{}}{=}\) 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 \(a \sim b\)
\(\approx\) approximately equal to \(a \approx b\)
\(\cong\) congruent, equivalent in size and shape \(\triangle ABC \cong \triangle XYZ\)
\(\ncong\) not equivalent in size and shape \(\triangle ABC \ncong \triangle XYZ\)
\(:=\) 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 \(a\le b\)
\(\geqq\) greater than over equal to \(a\geqq b\)
\(\leqq\) less than over equal to \(a\leqq b\)
\(\gneqq\) greater than but not equal to \(a\gneqq b\)
\(\lneqq\) less than but not equal to \(a\lneqq b\)
\(\Rightarrow\) 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

 

Geometry Symbols

SymbolDefinitionExample
\(\triangle\) triangle \(\triangle ABC \)
\(\bigcirc\) circle  
\(\odot A\) circle with center A  
\(\angle\) angle \(\angle ABC = 60^\circ\)
\(\measuredangle\) measured angle \(\measuredangle ABC = 60^\circ\)
\(\sphericalangle\) spherical angle \(\sphericalangle AOC = 60^\circ\)
\(^\circ\) degree 1 circle \(= 360^\circ\)
' arcminute \(1^\circ = 60^\prime\)
" arcsecond \(1'=60^{\prime\prime}\)
\(r \;or\; rad\) radiant, \(1 \;rad = 180^\circ /\pi \;\) and \(\;1^\circ = \pi / 180 \;rads\) \(360^\circ = 2\pi\; rad\) or about \(57.2958^\circ\)
\(g \;or\; grad\) gradian, four hundredth (1/400) of a full circle \( 360^\circ = 400\; grad\)
\(\overleftrightarrow {AB}\) infinite line distance  
\(\overline {AB}\) line segment from endpoint A to B  
\(\overrightarrow{AB}\) start line at point A  
\(\overset{\frown}{AB}\) arc with endpoints A and B  
\(\overset{\frown}{ABC}\) arc with endpoints A and C  
m\(\overset{\frown}{AB}\) measure arc with endpoints A and B  
\(|A-B|\) distance between points A and B \(|A-B| = 9\)
\(\parallel\) parallel to \(\overline {AB} \parallel \overline {XY} \)
\(\nparallel\) not parallel to \(\overline {AB} \nparallel \overline {XY} \)
\(\perp\) perpendicular lines \(\overline {AB} \perp \overline {XY} \)
\(\sim\) similarity to \(\triangle ABC \sim \triangle XYZ\)
\(\cong\) congruent, equivalent in size and shape \(\triangle ABC \cong \triangle XYZ\)
\(\ncong\) is not congruent to \(\triangle ABC \ncong \triangle XYZ\)
\(\therefore\) therefore \( a=b\; \therefore\; b=a \)
\(\pi\) \(\pi = 3.141592654... \) \(C = \pi \cdot d = 2 \cdot \pi \cdot r\)

 

Set Symbols

SymbolDefinitionExample
\(\{ \; \}\) set, a collection \(A= \{ 1, 2, 3, 4 \}\) ,  \(B= \{ 3, 4, 5, 6 \} \)
\(\varnothing\) empty set \(A=\{ \varnothing\} \)
\(\cap\) intersection, belonging to set A or B \(A\cap B =\{3, 4\}\)
\(\cup\) union, belonging to set A or B \(A\cup B =\{1, 2, 3, 4, 5, 6\}\)
     
\(\subset\) strict subset, A is subset of B \(\{3, 4\} \subset \{3, 4, 5, 6\}\)
\(\subseteq\) subset, A subset of B, A included in B \(\{3, 4\} \subseteq \{3, 4\}\)
\(\nsubseteq\) not subset, A not subset of B \(\{6, 7\} \nsubseteq \{3, 4, 5, 6\}\)
     
 \(\supset\) strict superset, A superset of B, B not equal to A \(\{3, 4, 5, 6\} \supset \{3, 4\}\)
 \(\supseteq\) superset, A subset of B, A includes B \(\{3, 4, 5, 6\} \supseteq \{3, 4, 5, 6\}\)
\(\nsupseteq\) not superset, A not superset of B \(\{3, 4, 5, 6\} \nsupseteq \{6, 7\}\)
     
\(\in\) belongs to \(B=\{3, 4, 5, 6\}\) ,  \(3\in B\)
\(\notin\) does not belong to \(B=\{3, 4, 5, 6\}\) ,  \(1\notin B\)
     
= equality, both sets the same A=B \(\{3, 4, 5, 6\} = \{3, 4, 5, 6\}\)
\(-\) relative complement, belongs to B but not A \(A-B = \{5, 6\}\)
\(\ominus\) symmetric difference, belongs to A or B gut no matches \(A \ominus B = \{1, 2, 5, 6\}\)
\(|\;|\) cardinality, element of set B  \(|B|=\{3\}\)