Mathematic Symbols
This is a list of mathematic symbols:
Algebra Symbols
| Symbol | Definition | Example |
|---|---|---|
| \(=\) | 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
| Symbol | Definition | Example |
|---|---|---|
| \(\triangle\) | 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
| Symbol | Definition | Example |
|---|---|---|
| \(+\) | 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
| Symbol | Definition | Example |
|---|---|---|
| \(\left(\; \right)\) | 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
| Symbol | Definition | Example |
|---|---|---|
| \(=\) | 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
| Symbol | Definition | Example |
|---|---|---|
| \(\triangle\) | 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
| Symbol | Definition | Example |
|---|---|---|
| \(\{ \; \}\) | 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 | \(|B|=\{3\}\) |