# Math Symbols

Go back to  'Pre-number Math'

 1 Introduction to Mathematical Symbols 2 List of Mathematical Symbols 3 Important Notes on Math Symbols 4 Practice Questions on Math Symbols 5 Challenging Questions on Math Symbols 6 Maths Olympiad Sample Papers 7 Frequently Asked Questions (FAQs)

## 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 $$\equiv$$ 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 $$\sqrt{4} = 2$$
$$\sqrt{ x}$$ Cube root of x $$\sqrt{ 27} = 3$$
$$\sqrt[n]{ x}$$ nth root of $$x$$ $$\sqrt{16} = 2$$
$$()$$ 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

$$\implies$$ 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 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)
XI = 11 (10+1)
XII = 12 (10+2)
XIII = 13 (10+3)

Roman Numeral L Value = 50

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

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)
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 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. Challenging Question
1. 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)

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.

## 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.

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus