Math Symbols - List of Symbols, Solved Examples (2024)

Math is all about numbers, symbols, and formulas. Math symbols are used for different purposes from one mathematical field to another. Using symbols to represent mathematical information makes it easier to understand expressions as these symbols show the relationship between quantities. In this article, let us look at the common ones that we use across different branches of mathematics.

1.Common Math Symbols
2.Constants Used as Math Symbols
3.Math Symbols Used in Logic
4.Venn Diagram and Set Theory Symbols
5.Numeral Symbols
6.Geometry and Algebra Symbols
7.Greek Alphabets and Combinatorics Symbols
8.Solved Examples
9. Practice Questions
10. FAQs on Math Symbols

Common Math Symbols

If we write the words"adding 4 to 2 gives 6" repeatedly, it might complicate things. These words also occupymore space and take time to write. Instead, we can save time and space by using symbols. The language and vocabulary of mathematics contain a large number of symbols and this list is endless — some being more technical than others. We have at least 10,000+ symbols and there are some that we rarely use. The most common symbols are listed in the following table:

SymbolsMeaningMath Symbols Examples
+Add5 + 4 = 9
- Subtract5 - 4 = 1
=Equal to1+1 = 2
\(\equiv\)Identically equal to(a+b)2 \(\equiv\) a2 + 2ab +b2
\(\approx\)Approximately equal to\(\pi \approx 3.14\)
\( \neq\)Not equal to5 + 4 \(\neq\) 1
\(\times\)Multiply5 \(\times\) 4 = 20
\(\div\)Divide10 \(\div\) 2 = 5
\(<\)Less than10 \(<\) 20
\(>\)Greater than20 \(>\) 10
\(\leq\)Less than or equal tox +y \(\leq\) z
\(\geq\)Greater than or equal tox +y \(\geq\) z
\(\% \)Percentage50% = \(\begin{align}\frac{50}{100}\end{align}\)
\(.\)Decimal point or Period\(\begin{align}\frac{1}{2} = 0.5\end{align}\)
\(-\)

Vinculum

It seperates the Numerator and Denominator

\(\begin{align}\frac{2}{3}\end{align}\)
\( \sqrt{} \)Square root\(\sqrt{4} = 2\)
\( \sqrt[3]{ x}\)Cube root of x\(\sqrt[3]{ 27} = 3\)
\(\sqrt[n]{ x}\)nth root of \(x\)\(\sqrt[4]{16} = 2\)
\(()\)Parentheses\(2+(5-3) = 2 +2 = 4\)
\([\:\:]\)Square brackets\(\begin{align}
&3\times[2 +(5 -2)] +1 \\
&3 \times[2+3] +1 \\
&3 \times5+1\\
&16
\end{align}\)
\(\{\}\)Flower bracket\(\begin{align}
&16 \div \{3\times[2 +(5 -2)] +1\} \\
&16 \div \{3 \times[2+3] +1\} \\
&16 \div \{3 \times5+1\}\\
&16 \div \{16\} \\
&1
\end{align}\)
\(\in\)Belongs to0 \(\in\) Whole number
\(\not\in\)Does not belong to\(\frac{1}{2} \not\in\) Natural numbers
\(\therefore\)Therefore\(x+1 = 2 \therefore x = 1\)
\(\because\)Because\(\begin{align}\frac{1}{2} \!\div\! 0.5 \!= \!1 (\because\! \frac{1}{2} \!=\! 0.5)\end{align}\)
\(\infty\)Infinity

Infinity is countless,

\(\begin{align}\frac{1}{3}\end{align}\) when written in decimal form,

is endless \(0.333.....\)

\(!\)Factorial\( 5!\ \!\!=\! 5 \!\times\! 4 \!\times\!3 \!\times\! 2\! \times\! 1\)

Constants Used as Math Symbols

We use constants in mathematics to refer to non-varying objects. These constants can include key mathematical sets, key numbers, key mathematical infinities, and other key mathematical objects (such as the identity matrix). These mathematical constants most often take the form of an alphabet letter — or a derivative of it. The following table lists some of the most commonly-used constants, along with their name, meaning, and usage.

Symbol NameExplanation
0 (Zero)Additive identity of common numbers
1 (One)Multiplicative identity of common numbers
2 (Square root of 2)A positive number whose square is 2. Approximately equals 1.41421.
e (Euler's constant)The base of the natural logarithm. Limit of the sequence (1 + (1/n)n ). Approximately equals 2.71828
\(\pi\) (Pi, Archimedes’ constant)The ratio of a circle’s circumference to its diameter. Half-circumference of a unit circle. Approximately equals 3.14159
\(\phi\) (Phi, golden ratio)Ratio between a larger number and p smaller number q when (p+q)/p = p/q. Positive solution to the equation y2-y-1 = 0 .
i (Imaginary unit)The principal root of -1. The foundational component of a complex number.

The following table shows the math symbols used in logic.

SymbolsMeaningMath Symbols Examples
\(\exists\)There exists at least one

∃ x: P(x)∃ x: F(x)

There exists at least one element of p(x), \(x\),

such that F(x) is True.

\(\exists!\)There exists one and only one

∃! x: F(x)

means that there is exactly one \(x\)

such that F(x) is true.

\(\forall\)For all\( \forall n >1; n^2 > 1\)
\(\neg\)Logical NotStatement A is true only if \(\neg\) is false
\(x \neq y \iff\neg(x=y)\)
\(\lor\)Logical OR

The statement A \(\lor\) B is true

if A or B is true;

if both are false,

the statement is false.

\(\land\)Logical And

The statement A\(\land\) B is true

if A and B are both true;

else it is false.

\(\implies\)Implies

x = 2

\(\implies\) x2 = 4

\(\iff\)If and only ifx +1 = y +1 \(\iff\) x = y
\(\text{|}\) or \(\text{:}\)Such that{ \(x\) | \(x\) > 0 } = {1,2,3,...}

Venn Diagram and Set Theory Symbols

The following table shows the math symbols used in venn diagrams and set theory.

SymbolsMeaningMath Symbols Examples
\(\cap\)Intersection

A = {2,3,4}

B = {4,5,6}

A \(\cap\) B = {4}

\(\cup\)UnionA = {2,3,4} B = {4,5,6} A \(\cup\) B = {2,3,4,5,6}
\(\varnothing\)Empty set

A set with no elements

\(\varnothing\) = { }

\(\in\)Is a member of2 \(\in\) \(\mathbb{N}\)
\(\notin\)is not a member of0 \(\notin\) \(\mathbb{N}\)
\(\subset \)Is a subset\(\mathbb{N} \subset \mathbb{I}\)
\(\supset\)Is a superset\(\mathbb{R} \supset \mathbb{W}\)
\(\text{P(A)}\)The power set of AP({1,2}) = { {}, {1}, {2}, {1,2} }
\(A= B\)

Equality

(same elements in set A and Set B)

A = {1,2}; B = {1,2}

\(\implies \) A = B

\( A \times B\)

Cartesian product

Set of ordered pairs from A and B

A ={5,6}; B = {7,8}

\(\implies \)\( A \times B\) = {(5,7),(5,8),(6,7),(6,8)}

\(\text{|A|}\)Cardinality is the number of elements in set A|{1,2,3,4}| = 4

Numeral Symbols

The numeralsymbols with their examples and corresponding Hindu-Arabic numerals are listed here in the table.

SymbolsMeaningMath Symbols Examples
Roman Numeral I Value = 1I = 1 , II = 2 , III = 3
Roman Numeral VValue = 5IV = 4 (5-1)
VI = 6 (5+1)
VII = 7 (5+2)
VIII = 8 (5+3)
Roman numeral XValue = 10

IX = 9 (10-1)
XI = 11 (10+1)
XII = 12 (10+2)
XIII = 13 (10+3)

Roman Numeral LValue = 50

XLIX = 49(50-1)
LI = 51(50+1)
LIX = 59 (50+9)
LXI = 61 (50+11)

Roman Numeral CValue = 100 (Century)CC = 200 (100+100)
CCLIX = 259 (100+100+50+9)
Roman Numeral DValue = 500DCLI = 651 (500+100+50+1)
DCCIV = 704 (500+100+100+4)
Roman Numeral MValue = 1000

MM = 2000 (1000+1000)
MMCCLV = 2255(1000+1000+100+100+50+5)

R or \(\mathbb{R}\)Real numbers\(\frac{1}{2} , \frac{1}{4}, 0.5\)\(\sqrt{2},\sqrt{3}\)
Z or \(\mathbb{Z}\)Integer-100,-20,5,10,....
N or \(\mathbb{N}\)Natural numbers1,2,3,...500,...
Q or \(\mathbb{Q}\)Rational Numbers\(-\frac{1}{2}, \frac{1}{4}, 0.5\)
P or \(\mathbb{P}\)Irrational Numbers\(\sqrt{2},\sqrt{3}\)
C or \(\mathbb{C}\)Complex numbers5+2i

Geometry and Algebra Symbols

The table given below shows the commonly used geometrical symbols. The mathematical symbols with names and examples are also listed in the table.

SymbolsMeaningMath Symbols Examples
\(\angle\)Mention the angle\(\angle ABC\)
\(\Delta \)Triangle symbol\(\Delta \text{PQR}\)
\(\cong\)Congruent to\(\Delta \text{PQR} \cong \Delta \text{ABC}\)
\(\sim\)Similar to\(\Delta \text{PQR} \sim\Delta \text{ABC}\)
\(\perp\)Is perpendicular withAB \(\perp\) PQ
\(\parallel \)Is parallel withAB \(\parallel\) CD
\(^\circ\)Degree\(60^\circ\)
\(\overline{\rm AB}\)Line segment ABA line from Point A to Point B
\(\overrightarrow{\rm AB}\)Ray ABA line starting from Point A and extends through B
\(\overleftrightarrow{\rm AB}\)Line ABAn infinite line passing through points A and B
\(\frown \atop AB \)Arc A to B\(\frown \atop AB = 60^\circ \)
\(^c\)Radians symbol\(360^\circ = 2 \pi \:^c \)

Algebra Symbols

The following table below shows the commonly used algebraicsymbols. The mathematical symbols with names and examples are also listed in the table.

SymbolsMeaningMath Symbols Examples
\(x,y\)Variables\(x =5\), \(y=2\)
\(+\)Add\(2x +3x = 5x\)
\(-\)Subtract\(3x-x = 2x\)
\(.\)Product\(2x .3x =6x\)
\(-\)Division\(\frac{2x}{3y}\)
\(\equiv\)Identically equal to\( (a+b)^2 \equiv a^2 + 2ab +b^2 \)
\(\neq\)Not equal to\(a + 5 = b+1 \implies a \neq b\)
\(=\)Equal to\(a = 5\)

\(\propto\)

Proportional to\(x \propto y \implies x= ky \)
\(f(x)\)Function maps values of \(\)x to \(f(x)\)\( f(x) = x +3 \)

Greek Alphabets and Combinatorics Symbols

The table below shows the Greek alphabets that are used asmathematical symbols. Their names, usage, and examples are also listed in the table.

SymbolsMeaningMath Symbols Examples
\(\alpha\)AlphaUsed to denote angles, coefficients
\(\beta\)BetaUsed to denote angles, coefficients
\(\gamma\)GammaUsed to denote angles, coefficients
\(\Delta\)DeltaDiscriminant symbol
\(\varepsilon\)EpsilonUsed to represent Universal Set
\(\iota\)IotaRepresents imaginary number
\(\lambda\)LambdaRepresents constant
\(\pi\)Pi\(\pi \approx 3.14\)
\(\Sigma\)SigmaRepresents the sum
\(\theta\)ThetaRepresents angles
\(\rho\)RhoStatistical constant
\(\phi\)PhiDiameter symbol

Combinatorics Symbols

The table below shows the combinatorics symbols that are commonly used.

SymbolsMeaningMath Symbols Examples
\( n! \)\( n\) factorial\( n! = n \times (n-1) \times (n-2) \times..... \times 2 \times 1\)

\({n \choose x} \)

or

\(^n{C_r}\)

Combination\(\begin{align}^n{C_r} =\\ \frac{{^n{P_r}}}{{r!}} &= \frac{{\left\{ {\frac{{n!}}{{\left( {n - r} \right)!}}} \right\}}}{{r!}} \\&= \frac{{n!}}{{r!\left( {n - r} \right)!}} \\^5{C_3} &= \frac{5!}{3!(5-3)!} = 10 \end{align}\)
\(^n{P_r} \)Permutation\begin{align}^n{P_r} &\!=\! \left( n \right) \!\times\! \left( {n - 1} \right) \times \!... \!\!\times \!\left( {n \!- \!r \!+\! 1} \right) \\
^6{P_4} &= 6 \times 5 \times 4 \times 3 = 360\end{align}

Related Articles on Math Symbols

Check out the following pages related to math symbols.

  • Arithmetic
  • Algebraic expressions
  • Divisibility rules
  • Vectors

Important Notes

Here is a list of a few points that should be remembered while studying math symbols:

  • Using symbols to represent information makes it easier to understand mathematical expressions.
  • We have at least 10,000+ symbols and there are some that we rarely use.
  • We use constants in mathematics to refer to non-varying objects.

FAQs on Math Symbols

What is U in Math Symbols?

The math symbol U is used to denote the set made by combining the elements of two sets. Hence, the union of two sets P and Q will be the set of elements in P and Q. The special symbol used to denote the set is ∪ that looks like "U".

How Many Mathematical Symbols are there?

There are more than 10000 math symbols. Some of the basic ones are =,+,−,≠,±, * and so on. There are complex symbols like \(\alpha\), \(\varepsilon\) and so on.

What is the Math Symbol Used for the Period Of a Wave?

The math symbol that is used for the period of a wave is λ. It is also known as wavelength which is measured in units of distance.

What are the Uses of the Addition Math Symbol?

The addition symbol (+) is usually used while adding two or more numbers, for example, 5 + 5. Apart from this, the (+) symbol can also be used to indicate a positive number, for example, +7.

List Some of the Common Arithmetic Math Symbols.

Some of the common arithmetic math symbols are: plus sign (+) used for addition, minus sign (-) used for subtraction, asterisk sign (*) or times sign (×) used for multiplication, and division sign (÷) or slash sign (/) used for division.

Math Symbols - List of Symbols, Solved Examples (2024)
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