Math Symbols – Definition with Examples

What Are Math Symbols?

Math symbols are concise marks, signs, or notations representing mathematical operations, quantities, relations, and functions. These symbols help to represent mathematical concepts and equations concisely. 

Math symbols turn a lengthy explanation into a quick, easy calculation, helping you easily find the answer.

Example: Imagine you’re planning to find the area of a garden. Instead of writing “length times width” every time, math symbols let you simply jot down “l × w.” So, if your garden is 10 meters long and 4 meters wide, instead of saying “ten meters multiplied by four meters,” you can quickly see that 10 × 4 = 40 square meters.

Symbols vary across different areas of mathematics, enabling precise communication of mathematical concepts and abstract ideas.

Math Symbols for Arithmetic Operations

Arithmetic is a fundamental branch of mathematics focused on numbers and their relationships. It encompasses basic operations like addition, subtraction, multiplication, and division, which are integral to our daily activities.

Symbols	Math Symbol Names	Meaning	Examples
$+$	Plus sign	Addition	$1 + 2$
$-$	Minus sign	Subtraction	$3 – 2$
$\times$	Times sign	Multiplication	$5 \times 8$
$\div$	Division sign (obelus)	Division	$9 \div 3$

Commonly Used Mathematical Symbols

The mathematics vocabulary is rich in a wide variety of symbols. Compiling all math symbols here is not possible, but the table below shows the list of math symbols that are commonly used, their names, definitions, and examples.

Symbols	Meaning	Examples
$=$	Equal to sign (Is equal to)	$1 + 2 = 3$
$\neq$	Not equal to	$5 + 4 \neq 2$
$\pm$	Both plus and minus	$3(x \pm y) = 3x \pm 3y$
	Sometimes used to indicate a range	$3 \pm 1$ means numbers from 2 to 4.
$\mp$	Both minus and plus	$-\;2(a \pm b)= -\;2a \mp 2b$
$\equiv$	Identical to	$(a + b)^{2} ≡ a^{2} + 2ab + b^{2}$
$\approx$	Almost equal to (approximately equal to)	$\pi \approx 3.14$
$\neq$	Not equal to	$5 + 4 \neq 2$
$.$	Multiplication dot	$(5).(4) = 20$
$/$	Division slash	$8 \div 2 = 4$
$\lt$	Strictly less than	$5 \lt 10$
$\gt$	Strictly greater than	$10 \gt 5$
$\le$	Less than or equal to	$x \le 3$
$\ge$	Greater than or equal to	$x \ge 3$
$\ll$	Much less than	$0.001 \ll 1,000,000$
$\gg$	Much greater than	$1000 gg y$
$\%$	Percentage	$\frac{50}{100} = 50\%$
$.$	Period, decimal point	$0.75$
$\overline{}$	Vinculum (the line separating the numerator & denominator)	$\frac{1}{2}$
$\propto$	Proportional to	$x \propto y$
$\ln$	Natural logarithm (log to the base e)	$\ln 1 = log_{e} 1 = 0$
$\sqrt{}$	Square root	$\sqrt{4} = 2$
$3\sqrt{}$	Cube root	$3\sqrt{27} = 3$
$n\sqrt{}$	nth root	$5\sqrt{32} = 2$
$\left( \right)$	Parentheses (Round brackets)	$(a + b)^{2}$
$\left[ \right]$	Square brackets (brackets)	$\left[a-(b+3)\right]^{2}$
$\left\{ \right\}$	Curly brackets (Braces)	$\left\{[a-(b+3)]^{2}\right\}^{3}$
$\in$	Belongs to	$x \in A$
$\notin$	Does not belong to	$x \notin A$
$\therefore$	Therefore	$\therefore x = 1$
$\because$	Because	$b = 2 \because b = a$ and $a = 2$
$\infty$	Infinity	$x \rightarrow \infty$
$\Sigma$	Sigma (summation of all values in the given range)	$^{3}\Sigma_{i=1}\; i = 1 + 2 + 3 = 6$

Geometry Symbols

Geometry is a branch of mathematics that deals with the properties and relationships of points, lines, angles, surfaces, and solids. Understanding concepts such as length, width, area, volume, and perimeter is essential for solving geometric problems. 

Symbols often represent specific terms in geometry to facilitate easier communication and problem-solving. These symbols are shorthand for complex geometric terms, making calculations and explanations more efficient. In daily life, these geometric symbols are ubiquitous, helping to quantify and describe the world around us in terms of shape, size, and position.

The table below lists the most commonly used geometric symbols, accompanied by examples to illustrate their application.

Symbols	Meaning	Examples
$\angle$	angle	$∠XYZ$
$\measuredangle$	measured angle	$\measuredangle\;LMN = 45^{\circ}$
$\triangle$	triangle	$\triangle\;DEF$
$\cong$	Congruent to	$\triangle\; PQR \cong \triangle \;ABC$
$\sim$	Similar to	$\triangle \; PQR \sim \triangle \;ABC$
$\perp$	is perpendicular to	$CD \perp XY$
$∟$	right angle	$∟\;A$
$\parallel$	is parallel to	$AB \parallel CD$
$\circ$	Degree	$50^{\circ}$
(x, y)	Ordered pair (represents coordinates of a point)	(1, 2)
$\overline{AB}$	Line segment	Line segment CD
$\overleftrightarrow{AB}$	Line	Line AB
$\overrightarrow{AB}$	Ray	Ray AB

Math Symbols in Set Theory, Probability, and Combinatorics

Symbol	Meaning	Formula	Example
!	Factorial	n!= n.(n-1).(n-2)…3.2.1	3! = 3.2.1 = 6
nPr	Number of permutations of n distinct objects, taken r at a time	nPr $= \frac{n!}{(n-r)!}$	3P2 $= \frac{3!}{(3-2)!} = 6$
nCr	Number of combinations of n distinct objects, taken r at a time	nCr $= \frac{n!}{(n-r)!}$	3C2 $= \frac{3!}{(3-2)!2!} = 3$
P( )	Probability of an event	P(A) $= \frac{n(A)}{n(S)}$	P(B) $= 1$
{}	Empty set	–	A $= \left\{\right\}$
∅	Empty set	–	B = ∅
$\cup$	Union of sets	$A \cup B = \left\{\text{x | x is in A or B}\right\}$	$A \cup B$
$\cap$	Intersection of sets	$A\cap B = \left\{\text{x | x is in A and B}\right\}$	$A\cap B$

Mathematical Constants Used as Math Symbols

In mathematics, ‘constants’ refer to entities that maintain fixed values, unlike variables that can change. Constants can encompass essential numbers, fundamental sets, specific concepts of infinity, and pivotal mathematical objects like the identity matrix. Often represented by letters of the alphabet or their variations, these constants are integral to mathematical expressions and equations. Below is a curated table detailing the most frequently encountered constants, including their names, definitions, and applications.

Symbol	Description	Value
e	Euler’s constant; the base of the natural logarithm	e ≈  2.71828
π	Pi: The ratio of a circle’s circumference to its diameter	π  ≈ 3.14159
i	The square root of -1	$i = \sqrt{-\;1}$
φ	Golden ratio	φ ≈  1.61803
$\sqrt{2}$	Pythagoras’ Constant	$\sqrt{2}$ ≈ 1.41421

Math Symbols Used in Logic (Boolean Algebra)

Symbols	Meaning	Examples
^	and	p ^ q
∨	or	p ∨ q
∃	there exists	∃ x
∀	for all	n2 > 1          ∀ n > 1
⟹	implies	x = 2 ⟹ x2 = 4
⟺	if and only if	x + 1 = y + 1 ⟺ x = y
| or :	such that	A = { x | x is a natural number. } A = {1, 2, 3,…}

Numeric Symbols in Different Number Systems

Numbers serve as abstract symbols to denote arithmetic values, enabling us to count, measure, and categorize objects. When dealing with large quantities, such as 4,657, verbal descriptions become cumbersome. To address this, numerical symbols are employed for more efficient communication. The table below presents these quantities alongside their equivalents in Hindu-Arabic and Roman numeral systems, illustrating the diverse ways we represent numbers.

Number Name	Hindu-Arabic Numerals	Roman numeral	Binary
Zero	0	Did not exist	0000
One	1	I	0001
Two	2	II	0010
Three	3	III	0011
Four	4	IV	0100
Five	5	V	0101
Six	6	VI	0110
Seven	7	VII	0111
Eight	8	VIII	1000
Nine	9	IX	1001
Ten	10	X	1010
Eleven	11	XI	1011
Twelve	12	XII	1100
Thirteen	13	XIII	1101
Fourteen	14	XIV	1110
Fifteen	15	XV	1111
Sixteen	16	XVI	10000
Seventeen	17	XVII	10001
Eighteen	18	XVIII	10010
Nineteen	19	XIX	10011
Twenty	20	XX	10100
Thirty	30	XXX	11110
Forty	40	XL	101000
Fifty	50	L	110010
Sixty	60	LX	111100
Seventy	70	LXX	1000110
Eighty	80	LXXX	1010000
Ninety	90	XC	1011010
Hundred	100	C	1100100

Importance of Mathematical Symbols

Mathematical symbols serve as a foundational tool in mathematics, streamlining communication and understanding across various aspects of the discipline. Here’s an organized overview of their significance:

• Simplifying Language: Mathematical symbols streamline the expression of relationships and statements.
• Denoting Quantities: They provide a concise way to represent numerical values.
• Facilitating Discussion: Symbols ease the referencing and analysis of mathematical concepts.
• Clarifying Operations: They specify the operations to be performed, reducing errors.
• Universal Communication: Symbols transcend language barriers, enabling global understanding.

Facts about Math Symbols

Conclusion

In this article, we learned about the different math symbols and their crucial role in simplifying and conveying complex mathematical concepts. These symbols form the backbone of mathematical communication, enabling precise and efficient problem-solving. To further our understanding, let’s solve a few examples and practice MCQs on these symbols for better comprehension.

Solved Examples on Math Symbols

1. Express using different math symbols:

i) the sum of a and b

ii) eight times y

iii) x to the power of 5

Solution:

i) The expression “sum of a and b” refers to the addition of the terms “a” and “b.”

Sum of a and b $= a + b$

ii) eight times y

Eight $= 8$

Here, y is a variable.

“Eight times x” refers to the multiplication of 8 and x.

Eight times $y = 8 \times y = 8y$

We can skip the multiplication symbol when we multiply a constant and a variable.

iii) x to the power of 5 means the base is x and the exponent is 5

x to the power of $5 = x^{5}$

2. Identify the meanings of the math symbols.

i) %

ii) $\triangle$

iii) ( )

iv) <

v) e

Solution:

i) % – Percentage

ii) $\triangle$ Triangle

iii) ( ) – Parentheses OR round brackets

iv) < – strictly less than

v) e – The e symbol in math represents the Euler’s constant.

3. Interpret the meanings using the math symbols.

i) $3 + 6$

ii) $x \neq 1$

iii) $a \parallel b$

Solution:

Expression	Meaning
$3 + 6 \lt 10$	The sum of 3 and 6 is strictly less than 10.
$x \neq 1$	The value of the variable x is not equal to 1.
$a \parallel b$	The line a is parallel to the line b.

4. What are and-or symbols in logic? Give simple examples.

Solution:

In mathematics and logic, the “and” symbol is represented by ∧ and the “or” symbol by ∨. Here’s a simple example using these symbols:

Example 1:

Statement: “It is raining and cold.”

Mathematical Expression: Let statement p represent “It is raining” and q represent “It is cold.” The expression becomes p∧q.

Example 2: 

Statement: “You can have tea or coffee.”

Mathematical Expression: Let statement a represent “You can have tea” and 

b represent “You can have coffee.” The expression becomes a∨b.

Practice Problems on Math Symbols

Frequently Asked Questions about Math Symbols