**Introduction to Mathematical Symbols **

Math symbols are short forms to represent the information and data we have.

For example, writing the words "adding 4 to 2 gives 6" repeatedly complicates things.

These words also occupy more space and take time to write.

When our problems have more steps, it can get very confusing.

Instead, we can save time and space by using symbols.

They also gives a better and clear understanding of the problem.

Let's look at an example.

Zach and Cody were asked by their Math teacher to add four and six and show the result on the board.

Zach wrote the following:

**Adding four and six gives us ten.**

Cody wrote the same information but as following:

**4 + 6 = 10**

Zach was not pleased as Cody was quicker in completing this task.

Cody wrote much quicker since he used Math symbols to show the information.

Which do you think is a better way to represent the information?

I hope you agree that Cody's way of using Math symbols is a better way.

It is quicker, simple and easy to understand.

**List of Mathematical Symbols**

You can see the **Common Math Symbols** **List **below.

The list of math symbols is endless.

We have at least 10,000+ symbols and there are some that we rarely use.

Let us look at the common ones we use across different branches of mathematics.

**Basic Symbols**

The commonly used mathematical symbols with names are listed here in the table below

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} \(\equiv\) a^{2} + 2ab +b^{2} |

\(\approx\) | 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 | \( \sqrt[3]{ 27} = 3\) |

\( \sqrt[n]{ x}\) | n^{th} 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 | \( 5!\ \!\!=\! 5 \!\times\! 4 \!\times\!3 \!\times\! 2\! \times\! 1\) |

**Logic Symbols**

The table below shows the math symbols list for logic and data.

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 exist 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 \(\implies\) x |

\(\iff\) | 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 table below shows the math symbols list for logic and data.

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),(6,7)} |

\(\text{|A|}\) | 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 Symbols**

The table below shows the commonly used geometrical symbols.

The mathematical symbols with names and examples are 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 table below shows the commonly used algebraic symbols.

The mathematical symbols with names and examples are 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**

The table below shows the Greek alphabets that are used as mathematical symbols.

Their names, usage and examples are 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} |

**Practice Questions **

**Here are a few activities for you to practice.**

**Select/Type your answer and click the "Check Answer" button to see the result.**

- If A and B are independent events with P(A) = 0.6 and P(B) = 0.3, find the following

P(A\(\cup\)B)

P(A \(\cap\)B)

P(A | B)

**Maths Olympiad Sample Papers**

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

You can download the FREE grade-wise sample papers from below:

- IMO Sample Paper Class 1
- IMO Sample Paper Class 2
- IMO Sample Paper Class 3
- IMO Sample Paper Class 4
- IMO Sample Paper Class 5
- IMO Sample Paper Class 6
- IMO Sample Paper Class 7
- IMO Sample Paper Class 8
- IMO Sample Paper Class 9
- IMO Sample Paper Class 10

To know more about the Maths Olympiad you can **click here**

**Frequently Asked Questions (FAQs)**

## 1. How many mathematical symbols are there?

There are more than 10000 math symbols.

Some of the basic ones are \(=, \:+,\:-,\:\neq, \:\pm \:\pi,\:^\circ,\:\theta \) and so on.

There are complex symbols like \( \iiint,\:\:\lim_{x \to 1},\:\:\liminf\limits_{x\to 0},\: \:\frac{\partial^{k} f}{\partial x^k}\) and so on.

## 2. What are the symbols in math?

Symbols make mathematics explanations easy.

They help to transform the text-based learning to equation or expression-based learning.

The commonly used mathematical symbols in Geometry, Algebra, Arithmetic etc. are shown under the List of Mathematical Symbols.