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Symbols in Algebra

Introduction

Many people today find math to be challenging. Algebraic symbols that are significant and have names must be understood, nevertheless. A branch of mathematics called algebra deals with symbols and the rules for manipulating them. These symbols are used in algebra to represent variables, which are quantities without fixed values. In algebra, equations express relationships between variables in a manner similar to how sentences describe relationships between particular words.

Let us look at the various symbols used in algebra in this article, how they represent values, and what they mean when they are used in notations or equations.

What are Symbols in Algebra?

Definition

Symbols in algebra provide mathematical equations and expressions consistency. Symbols in Algebra are used to represent variables, quantities without fixed values, and equations that express relationships between variables, like how sentences describe relationships between particular words.

Writing, interpreting, and performing computations using algebraic symbols and signs is quicker and simpler. It would be pointless to spend time and effort explaining the meanings of the various symbols in words. Different algebraic symbols and signs are used, and it will be easier to conduct and comprehend calculations if you are familiar with the meanings of the various algebraic symbols.

Frequently Used Symbols in Algebra

The table below shows some of the most frequently used symbols in Algebra.

Algebraic SymbolSymbol NameMeaningExample
=equal signequality4 + 5 = 9
4 + 5 is equal to 9
xx variableunknown quantitywhen 5x=20,
then x=4
not equal signinequality5 ≠ 7
+plus signaddition3 + 6 = 9
minus signsubtraction10 – 7 = 3
Xtimes signmultiplication3 × 9 = 27
.multiplication dotmultiplication2 ⋅ 10 = 20
*asteriskmultiplication4 * 3 = 12
÷divide sign / obelusdivision20 ÷ 4 = 5
/slashdivision30/5 = 6
radical signsquare root√36 =6
3cube rootcube root3√8=2
nnth root
<less thaninequality5 < 8
>greater thaninequality10 > 7
less than or equal toinequalitya≤c
means that a = c or a < c
greater than or equal toinequalitya≥c
means that a = c or a > c
( )parenthesesgrouping of expressions or numbers( 4 × 5 ) + 6 = 20 + 6
[ ]square bracketsgrouping of expressions or numbers5 [ ( 3 × 2 ) ] = 5 × 6
{ }curly bracketsgrouping of expressions or numbers3 { ( 5 × 2 ) } = 3 × 10
±plus – minus signboth addition and subtraction operations6 ± 4 = 10 and 2
6 + 4 = 10
6 – 4 = 2
minus – plus signboth subtraction and addition operations8 ± 3 = 11 and 5
8 + 3 = 11
8 – 3 = 5
^caretexponent3 ^ 2 = 9
approximately equal toapproximatione≈2.71828
therefore signconclusionx = y
∴ y = x
!factorialmultiply all the integers and positives between the number that appears in the formula and the number 1.5! = 5 × 4 × 3 × 2 × 1
5! =120
4! = 4 × 3 × 2 × 1
4! =24
|   |Vertical barsAbsolute value| – 8 | = | 8 | = 8
f ( x )Function of xFor any number x, f x depends on the value of xf ( x ) = 2x-5
f ( x ) = x+6
SigmaSum of all values in the given range$\sum_{i=1}^{8}$2i
=2 (1) + 2 (2) + 2 (3) + 2 (4) + 2 (5) + 2 (6) + 2 (7) + 2 (8)
DeltaChangem=$\frac{∆y}{∆x}$
f∘gf composition g or
f composed with g of x
Composition of Functionsf ( x ) = 2x
g ( x ) = x + 6
( f∘g )( x ) = 2 ( x + 6 )

Common Mathematical Constants

Constants are symbols used in algebra to represent essential mathematical elements. Natural numbers, integers, reals, and complex numbers are frequently represented as constants. The names, applications, and examples of the most common symbols are listed in the tables below.

Mathematical ConstantMeaning
π ( Pi )The ratio of a circle’s circumference and diameter
Half-circumference of a unit circle.
An irrational number and approximately 3.1416
e ( Euler’s Number ) Approximately 2.718
The base of the natural algorithm
φ ( Phi, golden ratio)Approximately 1.618
The ratio between two positive numbers a > b such that $\frac{a+b}{a}=\frac{a}{b}$
i ( Imaginary unit )The square root of -1 or $\sqrt{-1}$
A solution to the quadratic equation (x2+1=0)

Symbols for Sets

There are some sets of numbers that appear more frequently in algebra. Numerous variations of alphabetical letters, many of which are in the blackboard bold typeface, are commonly used to indicate these sets.

SymbolMeaningExample
ZSet of all integers
This set includes all whole numbers and negative numbers.
{ … -4, -3, -2, -1, 0, 1, 2, 3 , 4 }
Z+Set of all positive integers{ 1, 2, 3, 4, 5, 6, 7, … }
ZSet of all negative integers{ -1, -2, -3, -4, -5, -6, -7, … }
NSet of all natural numbers
This set includes numbers from 1 and ends at infinity
{1,2,3,4, 5, 6, 7, 8, 9, 10, 11, 12, 13, … }
R


R+

R
Set of all real numbers
This set includes all numbers except complex numbers.

Set of all positive real numbers

Set of all negative real numbers
All rational and irrational numbers.


Q



Q+

Q
Set of all rational numbers
All rational numbers can be written as the quotient of two integers with a non-zero denominator.

Set of all positive rational numbers

Set of all negative rational numbers
Q={$\frac{a}{b}$, b≠0}

5/3 , ½ , 10/3, 5, 4, 0.54, 0.234
-½ , -0.05, -7, -3.25, -8.75 
Q’Set of all irrational numbers
This set includes all real numbers that cannot be expressed as a fraction and can neither terminate nor repeat when in decimal form.
$\sqrt{2}$, π, $\sqrt{72}$, 3, $\sqrt{10}$
CSet of all complex numbers
This set includes the set of real numbers and a set of imaginary numbers.
3 + 2i
5 + $\sqrt{-15}$

Common Relational Symbols

Relational symbols, frequently associated with ideas like equality comparison, are used in algebra to indicate the relationship between two mathematical elements. The most typical of these are detailed in the tables below. 

SymbolMeaning
c = dc is equal to d
c ≈ dc is approximately equal to d
c ≠ dc is not equal to d
c ≡ dc is equivalent to d
c < dc is less than d
c > dc is greater than d
c ≤ dc is less than or equal to d
c ≥ dc is greater than or equal to d
c ≪ dc is much smaller than d
c ≫ dc is much greater than d
c ≻ dc succeeds d
c ∣ dinteger c divides integer d
c ∤ dinteger c does not divide integer d
c ⊥ dintegers c and d are coprime

Common Delimiters

Delimiters are mathematical symbols that indicate the division between various distinct mathematical elements. Common delimiters like parentheses, brackets, and braces are among them.

SymbolMeaning
( ) , [ ] , { }Order of Operation
Example: { [ ( 2 + 3 ) + 4 ] } – 10 
.Decimal separator
Example: 1.25 + 2. 50 = 3.75
,Object separator
Example: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
[ a, b ]Closed interval from a to b
a ≤ x ≤ b
( a, b )Open interval from a to b
a < x < b
( a, b ]Left open interval from a to b
a < x ≤ b
[ a, b )Right open interval from a to b
a ≤ x < b

Common Math Operators 

Operators are symbols that are used to indicate mathematical operations. The table below shows some of the commonly used operators.

SymbolMeaningExample
a + bAddition 
a plus b
5 + 3 = 8
-6 + -7 = -13
10 + 4 = 14
a – bSubtraction
a minus b
20 – 18 = 2
5 – 10 = -5
25 – 12 = 13
a × b, a ⋅ bMultiplication
a times b
4 × 5 = 20  
9 ⋅ 3 = 27
a ÷ bDivision
a divided by b
10 ÷ 2 = 5
24 ÷ 6 = 4
a/bFraction
a over b
½=0.50 
±plus – minus sign
both addition and subtraction operations
6 ± 4 = 10 and 2
6 + 4 = 10
6 – 4 = 2
minus – plus sign
both subtraction and addition operations
8 ± 3 = 11 and 5
8 + 3 = 11
8 – 3 = 5
aSquare root of a$\sqrt{16} = \sqrt{4⋅4}$
3aCube root of a38 = 2
naNth root of a532 = 2
| a |Absolute value of a| -7 | = | 7 | = 7

Linear Algebra Symbols

The table below shows some examples of symbols used in linear algebra.

SymbolName
̇dot
Xcross
X ⊗ Ytensor product
[ ]brackets
( )Parentheses
| A |determinant
ATtranspose
det ( A )determinant
A Hermitian matrix
A-1inverse matrix
rank ( A )matrix rank
dim ( U )dimension
∥A∥double vertical bars
⟨x,y⟩inner product

Summary

Definition

Symbols in algebra provide mathematical equations and expressions consistency. Symbols in Algebra are used to represent variables, quantities without fixed values, and equations that express relationships between variables, like how sentences describe relationships between particular words.

There are thousands of symbols available, but there are some that are rarely used. Common symbols are relational symbols, mathematical constants, delimiters, etc.

Frequently Asked Questions on Symbols on Algebra ( FAQs)

Why do we use symbols in algebra?

It is quicker and simpler to write, interpret, and perform computations using algebraic symbols and signs. It would be pointless to spend time and effort explaining the meanings of the various symbols in words. Different algebraic symbols and signs are used, and it will be easier to conduct and comprehend calculations if you are familiar with the meanings of the various algebraic symbols.

What are some examples of commonly used symbols in algebra?

The table below shows some of the most frequently used symbols in Algebra.

Algebraic SymbolSymbol NameMeaningExample
=equal signequality4 + 5 = 9
4 + 5 is equal to 9
xx variableunknown quantitywhen 5x=20,
then x=4
not equal signinequality5 ≠ 7
+plus signaddition3 + 6 = 9
minus signsubtraction10 – 7 = 3
Xtimes signmultiplication3 × 9 = 27
.multiplication dotmultiplication2 ⋅ 10 = 20
*asteriskmultiplication4 * 3 = 12
÷divide sign / obelusdivision20 ÷ 4 = 5
/slashdivision30/5 = 6
radical signsquare root√36 =6
3cube rootcube root3√8=2
nnth root
<less thaninequality5 < 8
>greater thaninequality10 > 7
less than or equal toinequalitya≤c
means that a = c or a < c
greater than or equal toinequalitya≥c
means that a = c or a > c
( )parenthesesgrouping of expressions or numbers( 4 × 5 ) + 6 = 20 + 6
[ ]square bracketsgrouping of expressions or numbers5 [ ( 3 × 2 ) ] = 5 × 6
{ }curly bracketsgrouping of expressions or numbers3 { ( 5 × 2 ) } = 3 × 10
±plus – minus signboth addition and subtraction operations6 ± 4 = 10 and 2
6 + 4 = 10
6 – 4 = 2
minus – plus signboth subtraction and addition operations8 ± 3 = 11 and 5
8 + 3 = 11
8 – 3 = 5
^caretexponent3 ^ 2 = 9
approximately equal toapproximatione≈2.71828
therefore signconclusionx = y
∴ y = x
!factorialmultiply all the integers and positives between the number that appears in the formula and the number 1.5! = 5 × 4 × 3 × 2 × 1
5! =120
4! = 4 × 3 × 2 × 1
4! =24
|   |Vertical barsAbsolute value| – 8 | = | 8 | = 8
f ( x )Function of xFor any number x, f x depends on the value of xf ( x ) = 2x-5
f ( x ) = x+6
SigmaSum of all values in the given range$\sum_{i=1}^{8}$2i
=2 (1) + 2 (2) + 2 (3) + 2 (4) + 2 (5) + 2 (6) + 2 (7) + 2 (8)
DeltaChangem=$\frac{∆y}{∆x}$
f∘gf composition g or
f composed with g of x
Composition of Functionsf ( x ) = 2x
g ( x ) = x + 6
( f∘g )( x ) = 2 ( x + 6 )

What are examples of relational symbols or operators in Algebra?

Relational symbols, frequently associated with ideas like equality comparison, are used in algebra to indicate the relationship between two mathematical elements. The most typical of these are detailed in the tables below.

SymbolMeaning
c = dc is equal to d
c ≈ dc is approximately equal to d
c ≠ dc is not equal to d
c ≡ dc is equivalent to d
c < dc is less than d
c > dc is greater than d
c ≤ dc is less than or equal to d
c ≥ dc is greater than or equal to d
c ≪ dc is much smaller than d
c ≫ dc is much greater than d

What are the different kinds of brackets used in algebra?

Using brackets in algebra designates groups of numbers that must be evaluated together, and any numbers contained within brackets must first be evaluated.

The different kinds of brackets are parentheses or round brackets, (  ), curly or braced brackets, { }, and square or box brackets [ ].

The order of operation of brackets can be illustrated as [ { ( ) } ].  

How many symbols in algebra are there?

It is quicker and simpler to write, interpret, and perform computations using algebraic symbols and signs. There are thousands of symbols available, but there are some that are rarely used. Common symbols are relational symbols, mathematical constants, delimiters, etc. The tables below show some of the frequently used symbols. 

Common Mathematical Constant

Mathematical ConstantMeaning
π ( Pi )The ratio of a circle’s circumference and diameter
Half-circumference of a unit circle.
An irrational number and approximately 3.1416
e ( Euler’s Number ) Approximately 2.718
The base of the natural algorithm
φ ( Phi, golden ratio)Approximately 1.618
The ratio between two positive numbers a > b such that $\frac{a+b}{a}=\frac{a}{b}$
i ( Imaginary unit )The square root of -1 or $\sqrt{-1}$
A solution to the quadratic equation (x2+1=0)

Common Relational Symbols

SymbolMeaning
c = dc is equal to d
c ≈ dc is approximately equal to d
c ≠ dc is not equal to d
c ≡ dc is equivalent to d
c < dc is less than d
c > dc is greater than d
c ≤ dc is less than or equal to d
c ≥ dc is greater than or equal to d
c ≪ dc is much smaller than d
c ≫ dc is much greater than d
c ≻ dc succeeds d
c ∣ dinteger c divides integer d
c ∤ dinteger c does not divide integer d
c ⊥ dintegers c and d are coprime

Common Math Operators

SymbolMeaningExample
a + bAddition 
a plus b
5 + 3 = 8
-6 + -7 = -13
10 + 4 = 14
a – bSubtraction
a minus b
20 – 18 = 2
5 – 10 = -5
25 – 12 = 13
a × b, a ⋅ bMultiplication
a times b
4 × 5 = 20  
9 ⋅ 3 = 27
a ÷ bDivision
a divided by b
10 ÷ 2 = 5
24 ÷ 6 = 4
a/bFraction
a over b
½=0.50 
±plus – minus sign
both addition and subtraction operations
6 ± 4 = 10 and 2
6 + 4 = 10
6 – 4 = 2
minus – plus sign
both subtraction and addition operations
8 ± 3 = 11 and 5
8 + 3 = 11
8 – 3 = 5
aSquare root of a$\sqrt{16} = \sqrt{4⋅4}$
3aCube root of a38 = 2
naNth root of a532 = 2
| a |Absolute value of a| -7 | = | 7 | = 7

What are symbols in algebra?

Symbols in algebra provide mathematical equations and expressions consistency. Symbols in Algebra are used to represent variables, quantities without fixed values, and equations that express relationships between variables, like how sentences describe relationships between particular words. 

It is quicker and simpler to write, interpret, and perform computations using algebraic symbols and signs. It would be pointless to spend time and effort explaining the meanings of the various symbols in words. Different algebraic symbols and signs are used, and it will be easier to conduct and comprehend calculations if you are familiar with the meanings of the various algebraic symbols.

There are thousands of symbols available, but there are some that are rarely used. Common symbols are relational symbols, mathematical constants, delimiters, etc.

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