Mathematical symbols
This list of commonly used mathematical symbols explains what each math symbol is, how it is used and provides a sample expression.
Symbol | What it is | How it is read | How it is used | Sample expression |
+ | Addition sign Logical OR symbol |
... plus ... ... or ... |
Sum of a few values Logical disjunction |
3 + 5 = 8 ¬(A + B) = ¬A * ¬B |
* | Multiplication sign Logical AND symbol |
... times ... ... and ... |
Product of two values Logical conjunction |
3 x 5 = 15 ¬(A * B) = ¬A + ¬B |
x | Multiplication sign | ... times ... | Product of two values | 3 x 5 = 15 |
· | Multiplication sign | ... times ... | Product of two values | 3 · 5 = 15 |
summation sign | The summation of ... | Sum of many or infinitely many values |
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Integral sign | The integral of ... | integration | x2 dx = x3/3 + c | |
Double integral sign | The double integral of ... | integration | f(x,y) dx dy | |
Triple integral sign | The triple integral of ... | integration | f(x,y,z) dx dy dz | |
Line integral sign | The line integral of ... | integration | F dx | |
Surface integral sign | The surface integral of ... | integration | F(x,y,z) dx dy | |
- | Subtraction sign Minus sign |
... minus ... Negative... |
Difference of two values, negative number |
3 - 5 = -2 |
± | Plus/minus sign | ... plus or minus ... | Expression of range, error, or tolerance |
500 kbps ± 10% |
dot product sign | ... dot ... | Scalar (dot) product of two vectors |
A B = B A | |
x | Cross product sign | ... cross ... | Vector (cross) product of two vectors |
A x B = - (B x A) |
Product sign | The product of ... | Product of three up to infinitely many values |
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^ | Carat | ... to the power of ... | exponent | 2 ^ 5 = 32 |
! | Exclamation | ... factorial | Product of all positive integers up to a certain value |
5! = 120 |
Surd | ... root of ... | Algebraic expressions | z = (x + y) | |
Square root symbol | The square root of ... | Algebraic expressions | ||
... | Continuation sign | ... and so on up to ... ... and so on indefinitely |
Extension of sequence | S = {1, 2, 3, ...} |
/ | Slash | ... divided by ... ... over ... |
Division | 3/4 = 0.75 |
÷ | Division sign | ... divided by ... | Division | 3 ÷ 4 = 0.75 |
Percent symbol | ... percent ... | Proportion | 0.032 = 3.2 | |
Per mil symbol | ... per mil ... | Proportion | 0.032 = 32 | |
: | Colon, ratio sign |
... is to ... ... such that ... ... it is true that ... |
Division or ratio, symbol following logical quantifier or used in defining a set |
2:4 = 20:40 x : x > 4 and x < 5 x : x < 0 or x > -1 S = {x : x < 3} |
| | Vertical line | ... such that ... ...it is true that ... |
Symbol following logical quantifier or used in defining a set |
x | x > 4 and x < 5 x | x < 0 or x > -1 S = {x | x < 3} |
:: | Double colon | ... averaged with ... | arithmetic mean | 3 :: 11 = 7 |
lemniscate | ... infinity ... increases without limit |
Infinite summations Infinite sequence Limit |
x : x < | |
( ) | Parentheses | ...quantity... ...list... ...set of coordinates... ...open interval |
Denotes a quantity, list, set of coordinates, or an open interval |
(x + y) + z (a1, a2, a3, a4) (x,y,z) (3,5) |
[ ] | Square brackets | ... the quantity ... ... the closed interval ... |
Denotes a quantity or a closed interval |
w + [(x + y) + z] [3,5] |
( ] | Hybrid brackets | ... the half-open interval ... | Denotes a half-open interval |
(3,5] |
[ ) | Hybrid brackets | ... the half-open interval ... | Denotes a half-open interval |
[3,5) |
{ } | Curly brackets | ... the quantity ... ... the SET ... |
Denotes a quantity or a SET | E = {2, 4, 6, 8, ...} |
= | Equal sign | ... equals ... | Indicates two values are the same |
-(-5) = 5 2z2 + 4z - 6 = 0 |
proportionality sign | ... is proportional to ... | Indicates two variables change in direct proportion |
x y | |
~ | Similarity sign | ... is similar to ... | Indicates two objects are geometrically similar |
ABC ~ DEF |
Approximate equal sign |
... is approximately equal to ... | Indicates two values are close to each other |
x + y z | |
Inequality sign | ... is not equal to ... | Indicates two values are different |
x y | |
< | Inequality sign | ... is less than ... | Indicates value on left is smaller than value on right |
3 < 5 x < y |
Inequality sign | ... is less than or equal to ... ... is at most equal to ... |
Indicates value on left is smaller than or equal to value on right |
x y | |
> | Inequality sign | ... is greater than ... | Indicates value on left is larger than value on right |
5 > 3 x > y |
≥ | Inequality sign | ... is greater than or equal to ... | Indicates value on left is larger than or equal to value on right |
x ≥ y |
| | | absolute value sign | The absolute value of ... | Distance of value from origin in number line, plane, or space |
| -3 | = 3 |
increment sign, Triangle symbol |
the change in ... triangle ... |
Indicates a small change, Denotes vertices of triangle |
m = y / x ABC = DEF |
|
Perpendicularity symbol |
... is perpendicular to ... | Geometry | L M | |
// | Parallel symbol | ... is parallel to ... | Geometry | L // M |
Angle symbol | Angle ... | Geometry | ABC = DEF | |
Existential quantifier | For some ... There exists a(n) ... |
Logical statements | x : x > 4 and x < 5 | |
Universal quantifier | For all ... For every ... |
Logical statements | x : x < 0 or x > -1 | |
¬ | Logical negation symbol |
not ... | Logical statements | ¬(¬A) A |
logical implication symbol |
... implies ... If ... then ... |
Logical statements | A B | |
logical equivalence symbol |
... is logically equivalent to ... ... if and only if .. |
Logical statements | A B | |
Three dots | ... therefore ... ... it follows that ... |
Logical statements or mathematical proofs |
x = y and y = z x = z |
|
Element-of symbol |
... is an element of a set ... |
Sets | a A | |
Not-element-of symbol |
... is not an element of a set ... |
Sets | b A | |
Subset symbol | ... is a subset of ... | Sets | A B | |
Proper subset symbol | ... is a proper subset of ... | Sets | A B | |
Union symbol | ... union ... | Sets | A B = B A | |
Intersection symbol | ... intersect ... ... intersected with ... |
Sets | A B = B A | |
Null symbol | The null set The empty set |
Sets | = { } | |
Hebrew aleph (uppercase) |
Aleph ... | Transfinite cardinal | 1 + 0 = 1 | |
º | Degree symbol | ... degree(s) | Angular measure Temperature |
T = +20 ºC |
θ | Greek theta (lowercase) |
... theta ... | Angular variable | θ = 90º |
φ | Greek phi (lowercase) |
... phi ... | Angular variable | = 45º |
λ | Greek lambda (lowercase) |
... lambda ... | Wavelength Ratio Eigenvalue Lebesgue measure |
= 70 cm = 3:1 |
µ | Greek mu (lowercase) |
micro- (10-6) | Prefix multiplier | C = 0.001 µF |
Greek pi (lowercase) |
... pi ... | General science | 3.14159 | |
Greek omega (uppercase) |
... omega ... | Volume of an object Ohms (resistance) |
R2 = 330 | |
Greek omega (lowercase) |
... omega ... | Transfinite ordinal Angular velocity Period |
= 36,000 rad/s = 1/60 s |
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, N | Enhanced or bold N | The set of natural numbers | Number theory Set theory |
= {0, 1, 2, 3, ...} |
, Z | Enhanced or bold Z | The set of integers | Number theory Set theory |
= {0, 1, -1, 2, -2, 3, -3, ...} |
, Q | Enhanced or bold Q | The set of rational numbers | Number theory Set theory |
= {a/b | a and b are in } |
, R | Enhanced or bold R | The set of real numbers | Number theory Set theory |
What is the cardinality of ? |