Math Symbols
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.
Common Math Symbols
If we write the words "adding 4 to 2 gives 6" repeatedly, it might complicate things. These words also occupy more 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:
| Symbols | Meaning | Math Symbols Examples |
|---|---|---|
| + | Add | 5 + 4 = 9 |
| - | Subtract | 5 - 4 = 1 |
| = | Equal to | 1+1 = 2 |
| \(\equiv\) | Identically equal to | (a+b)2 \(\equiv\) a2 + 2ab +b2 |
| \(\approx\) | Approximately equal to | \(\pi \approx 3.14\) |
| \( \neq\) | Not equal to | 5 + 4 \(\neq\) 1 |
| \(\times\) | Multiply | 5 \(\times\) 4 = 20 |
| \(\div\) | Divide | 10 \(\div\) 2 = 5 |
| \(<\) | Less than | 10 \(<\) 20 |
| \(>\) | Greater than | 20 \(>\) 10 |
| \(\leq\) | Less than or equal to | x +y \(\leq\) z |
| \(\geq\) | Greater than or equal to | x +y \(\geq\) z |
| \(\% \) | Percentage | 50% = \(\begin{align}\frac{50}{100}\end{align}\) |
| \(.\) | 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 to | 0 \(\in\) 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 Name | Explanation |
|---|---|
| 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. |
Math Symbols Used in Logic
The following table shows the math symbols used in logic.
| Symbols | Meaning | Math 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 Not | Statement 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 if | x +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.
| Symbols | Meaning | Math Symbols Examples |
|---|---|---|
| \(\cap\) | Intersection |
A = {2,3,4} B = {4,5,6} A \(\cap\) B = {4} |
| \(\cup\) | Union | A = {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 of | 2 \(\in\) \(\mathbb{N}\) |
| \(\notin\) | is not a member of | 0 \(\notin\) \(\mathbb{N}\) |
| \(\subset \) | Is a subset | \(\mathbb{N} \subset \mathbb{I}\) |
| \(\supset\) | Is a superset | \(\mathbb{R} \supset \mathbb{W}\) |
| \(\text{P(A)}\) | The power set of A | P({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 numeral symbols with their examples and corresponding Hindu-Arabic numerals are listed here in the table.
| Symbols | Meaning | Math Symbols Examples |
|---|---|---|
| Roman Numeral I | Value = 1 | I = 1 , II = 2 , III = 3 |
| Roman Numeral V | Value = 5 | IV = 4 (5-1) VI = 6 (5+1) VII = 7 (5+2) VIII = 8 (5+3) |
| Roman numeral X | Value = 10 |
IX = 9 (10-1) |
| Roman Numeral L | Value = 50 |
XLIX = 49 (50-1) |
| Roman Numeral C | Value = 100 (Century) | CC = 200 (100+100) CCLIX = 259 (100+100+50+9) |
| Roman Numeral D | Value = 500 | DCLI = 651 (500+100+50+1) DCCIV = 704 (500+100+100+4) |
| Roman Numeral M | Value = 1000 |
MM = 2000 (1000+1000) |
| 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 numbers | 1,2,3,...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 numbers | 5+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.
| Symbols | Meaning | Math 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 with | AB \(\perp\) PQ |
| \(\parallel \) | Is parallel with | AB \(\parallel\) CD |
| \(^\circ\) | Degree | \(60^\circ\) |
| \(\overline{\rm AB}\) | Line segment AB | A line from Point A to Point B |
| \(\overrightarrow{\rm AB}\) | Ray AB | A line starting from Point A and extends through B |
| \(\overleftrightarrow{\rm AB}\) | Line AB | An 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 algebraic symbols. The mathematical symbols with names and examples are also listed in the table.
| Symbols | Meaning | Math 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 as mathematical symbols. Their names, usage, and examples are also listed in the table.
| Symbols | Meaning | Math Symbols Examples |
|---|---|---|
| \(\alpha\) | Alpha | Used to denote angles, coefficients |
| \(\beta\) | Beta | Used to denote angles, coefficients |
| \(\gamma\) | Gamma | Used to denote angles, coefficients |
| \(\Delta\) | Delta | Discriminant symbol |
| \(\varepsilon\) | Epsilon | Used to represent Universal Set |
| \(\iota\) | Iota | Represents imaginary number |
| \(\lambda\) | Lambda | Represents constant |
| \(\pi\) | Pi | \(\pi \approx 3.14\) |
| \(\Sigma\) | Sigma | Represents the sum |
| \(\theta\) | Theta | Represents angles |
| \(\rho\) | Rho | Statistical constant |
| \( \phi\) | Phi | Diameter symbol |
Combinatorics Symbols
The table below shows the combinatorics symbols that are commonly used.
| Symbols | Meaning | Math 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.
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.
Solved Examples
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Example 1. Which math symbol is used to denote the relationship between the two parallel lines AB and CD?
Solution:
The relationship between the two parallel lines AB and CD can be denoted using the parallel symbol as AB || CD.
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.