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 | ||
Integral sign | The integral of ... | integration | ||
Double integral sign | The double integral of ... | integration | ||
Triple integral sign | The triple integral of ... | integration | ||
Line integral sign | The line integral of ... | integration | ||
Surface integral sign | The surface integral of ... | integration | ||
- | 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 | |
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 | ||
^ | 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 = | |
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 S = {x : x < 3} |
| | Vertical line | ... such that ... ...it is true that ... | Symbol following logical quantifier or used in defining a set | S = {x | x < 3} |
:: | Double colon | ... averaged with ... | arithmetic mean | 3 :: 11 = 7 |
lemniscate | ... infinity ... increases without limit | Infinite summations Infinite sequence Limit | ||
( ) | 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 | |
~ | Similarity sign | ... is similar to ... | Indicates two objects are geometrically similar | |
Approximate equal sign | ... is approximately equal to ... | Indicates two values are close to each other | x + y | |
Inequality sign | ... is not equal to ... | Indicates two values are different | x | |
< | 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 | |
> | 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 = | |
Perpendicularity symbol | ... is perpendicular to ... | Geometry | L | |
// | Parallel symbol | ... is parallel to ... | Geometry | L // M |
Angle symbol | Angle ... | Geometry | ||
Existential quantifier | For some ... There exists a(n) ... | Logical statements | ||
Universal quantifier | For all ... For every ... | Logical statements | ||
¬ | Logical negation symbol | not ... | Logical statements | ¬(¬A) |
logical implication symbol | ... implies ... If ... then ... | Logical statements | A | |
logical equivalence symbol | ... is logically equivalent to ... ... if and only if .. | Logical statements | A | |
Three dots | ... therefore ... ... it follows that ... | Logical statements or mathematical proofs | x = y and y = z | |
Element-of symbol | ... is an element of a set ... | Sets | a | |
Not-element-of symbol | ... is not an element of a set ... | Sets | b | |
Subset symbol | ... is a subset of ... | Sets | A | |
Proper subset symbol | ... is a proper subset of ... | Sets | A | |
Union symbol | ... union ... | Sets | A | |
Intersection symbol | ... intersect ... ... intersected with ... | Sets | A | |
Null symbol | The null set The empty set | Sets | ||
Hebrew aleph (uppercase) | Aleph ... | Transfinite cardinal | ||
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 | |
λ | Greek lambda (lowercase) | ... lambda ... | Wavelength Ratio Eigenvalue Lebesgue measure | |
µ | Greek mu (lowercase) | micro- (10-6) | Prefix multiplier | C = 0.001 µF |
Greek pi (lowercase) | ... pi ... | General science | ||
Greek omega (uppercase) | ... omega ... | Volume of an object Ohms (resistance) | R2 = 330 | |
Greek omega (lowercase) | ... omega ... | Transfinite ordinal Angular velocity Period | ||
Enhanced or bold N | The set of natural numbers | Number theory Set theory | ||
Enhanced or bold Z | The set of integers | Number theory Set theory | ||
Enhanced or bold Q | The set of rational numbers | Number theory Set theory | ||
Enhanced or bold R | The set of real numbers | Number theory Set theory | What is the cardinality of |
This was last updated in June 2021
Next Steps
How improving your math skills can help in programming
Reskilling the analytics team: Math, science and creativity
How an 18th century math puzzle solves 21st century problems
Dig Deeper on Data center careers, staffing and certifications
-
null set
By: Rahul Awati
-
permittivity of free space
By: Robert Sheldon
-
logical negation symbol
By: Rahul Awati
-
operator
By: Rahul Awati
What does ∑ mean in math?
Simple sum
The symbol Σ (sigma) is generally used to denote a sum of multiple terms. This symbol is generally accompanied by an index that varies to encompass all terms that must be considered in the sum. For example, the sum of first whole numbers can be represented in the following manner: 1 2 3 ⋯.
What does ∈ mean in math?
The symbol ∈ indicates set membership and means “is an element of” so that the statement x∈A means that x is an element of the set A. In other words, x is one of the objects in the collection of (possibly many) objects in the set A.
What does ε mean in math?
ε: “Error term” in regression/statistics; more generally used to denote an arbitrarily small, positive number. ∈ (Variant Epsilon) This version of epsilon is used in set theory to mean “belongs to” or “is in the set of”: x ∈ X; similarly used to indicate the range of a parameter: x ∈ [0, 1].
What does Ǝ mean in math?
∃! (mathematics) The symbol used in predicate calculus, etc, to represent the unique existential quantifier, meaning "there exists exactly one".