Mathematical Symbols (2024)

By

• TechTarget Contributor

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	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
^	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
, 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 ?

This was last updated in June 2021

See Also

LeoTaurus CompatibilityFrom Taurus to Scorpio: 4 Zodiac signs who make controlling partnersAccording to your zodiac sign know about your Friends & enemies

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

Related Terms

digital leadership

Digital leadership is the strategic use of a company's digital assets and emerging technologies to achieve business goals. A ... Seecompletedefinition

disaster recovery team

A disaster recovery team is a group of individuals focused on planning, implementing, maintaining, auditing and testing an ... Seecompletedefinition

MCSA (Microsoft Certified Solutions Associate)

MCSA (Microsoft Certified Solutions Associate) was a certification program offered by Microsoft and intended for people seeking ... Seecompletedefinition

Dig Deeper on Data center careers, staffing and certifications

• lambdaBy: NickBarney
• glyphBy: KatieTerrell Hanna
• reactanceBy: RobertSheldon
• first-order logicBy: RahulAwati

As someone deeply immersed in mathematics, I possess a comprehensive understanding of the various mathematical symbols, their meanings, applications, and significance across multiple mathematical domains. My expertise extends from basic arithmetic operations like addition, subtraction, multiplication, and division to advanced concepts such as integrals, derivatives, set theory, logic, and algebraic expressions.

Each symbol in mathematics serves a distinct purpose, representing operations, relationships, quantities, sets, logic, and more. Here's a breakdown of the concepts and symbols outlined in the provided article:

1. Basic Arithmetic Operations:

   • Addition (+): Denotes combining quantities.
   • Subtraction (-): Represents the difference between two quantities.
   • Multiplication (*, x, ·): Indicates the product of quantities.
   • Division (/, ÷): Signifies the quotient of two values.

2. Advanced Mathematical Concepts:

   • Exponents (^): Represents raising a number to a power.
   • Factorial (!): Indicates the product of all positive integers up to a certain value.
   • Square Root (√): Denotes the square root of a number.
   • Summation (∑): Signifies the sum of a sequence of values.
   • Integral (∫): Represents the antiderivative or area under a curve.
   • Inequality Signs (<, >, ≤, ≥): Used to compare values.

3. Set Theory:

   • Symbols for denoting sets and their elements: {}, |, ∈, ∉, ⊆, ⊂.
   • Union (∪) and Intersection (∩) symbols: Represent set operations.

4. Logic Symbols:

   • Logical operators like ¬ (negation), ∧ (logical AND), ∨ (logical OR), ⇒ (logical implication), ⇔ (logical equivalence).
   • Quantifiers (∃ for existential quantification, ∀ for universal quantification).

5. Geometry and Trigonometry:

   • Symbols for angles, perpendicularity, parallelism, similarity, and degree measurements.

6. Special Symbols:

   • Absolute value (| |), increment (∆), null set (∅), Greek letters (θ, φ, λ, π, ω, etc.), Hebrew aleph (ℵ), and various prefix multipliers.

7. Mathematical Relationships and Equations:

   • Equal sign (=), proportionality (∝), approximate equal sign (≈), not equal to sign (≠), and mathematical implications.

Understanding these symbols and their applications is crucial across various fields, including physics, engineering, computer science, economics, and more. They serve as the foundational language of quantitative reasoning and problem-solving.

This knowledge is instrumental in fields like data analysis, scientific research, programming, and engineering, where mathematical concepts are fundamental to problem-solving and decision-making.

If you have any specific questions or require further insights into any of these mathematical symbols or concepts, feel free to ask!