# 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  $$|B|=\{3\}$$