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250 LearnersLast updated on December 11, 2025
Math Symbols
Math is based on numbers, symbols, and formulas. Symbols, signs, or characters are used to represent numbers, operations, relationships between two or more values, and more. These symbols help us solve problems quickly. In this article, we will explore them in detail.
What are the Common Math Symbols?
Symbols save us from writing long and complicated equations, which in turn saves a lot of time and space. The symbols mentioned below are used in algebra.
|
Symbols |
Meaning |
How to use |
|
+ |
Add |
2 + 2 = 4 |
|
- |
Subtract |
3 - 2 = 1 |
|
= |
Equal to |
2 + 1 = 3 |
|
\(\equiv\) |
Identically equal to |
(a - b)2 \(\equiv\) a2- 2ab + b2 |
|
≈ |
Approximately equal to () |
e ≈ 2.71828 |
|
\(\neq\) |
Not equal to |
3 + 1 \(\neq\) 6 |
|
× |
Multiply |
5 × 2 = 10 |
|
÷ |
Divide |
9 ÷ 3 = 3 |
|
< |
Less than |
3 < 6 |
|
> |
Greater than |
6 > 3 |
|
\(\leq\) |
Less than or equal to |
5 - 2 \(\leq\) 3 |
|
\(\geq\) |
Greater than or equal to |
8 - 1 \(\geq\) 4 |
|
% |
20% = 20/100 = 0.20 |
|
|
. |
Decimal point or period |
13 = 0.333… Here, the dot after 0 is the decimal point. |
|
– |
Vinculum (—, it separates the numerator and denominator) |
\(3 \over 5\) |
|
\(\sqrt {}\) |
Square root |
\(\sqrt 9 = \pm 3\) |
|
\(\sqrt [3] {{}}\) |
Cube root |
\(\sqrt [3] {64} = 4\) |
|
\(\sqrt [n] {}\) |
nth root |
\(\sqrt [2]{25} = 5\) |
|
( ) |
Parentheses |
1 + (3 - 2) = 1 + 1 = 2 |
|
[ ] |
Square brackets |
2 × [3 + (2 - 1)] + 2 2 × [3 +1] + 2 2 × 4 + 2 = 10 |
|
{ } |
Curly braces |
20 ÷ {2 × [3 + (2 - 1)] + 2} 20 ÷ {2 × [3 +1] + 2} 20 ÷ {2 × 4 + 2} 20 ÷ 10 = 2 |
|
\(\in \) |
Belongs to |
1 \(\in \) whole number |
|
∉ |
Does not belong to |
1/3 ∉ natural numbers |
|
∴ |
Therefore |
x + 3 = 5 |
|
∵ |
Because |
14/0.25 = 1 (∵ 1/4 = 0.25) |
|
∞ |
Infinity |
1,2,3,4,.... ∞ |
|
! |
Factorial |
4! = 4 × 3 × 2 × 1 = 24 |
|
∑ |
Summation (sum of a series) |
∑(i=1 to n) i |
|
∏ |
Product (multiplying a series) |
\(\prod _{i =1} ^ \pi = { 1\times 2 \times 3 \times 4 \times ..... \times n}\) |
Math Symbols Used for Constants
Constants are values that don’t change. In the table below, some of the math symbols used for constants are given, along with their values and descriptions.
| Symbol | Name | Approx. Value | Description |
| π | PI | 3.14159 | The ratio of a circle's circumference to its diameter |
| e |
Euler's Number |
2.71828 | Base of natural logarithms |
| i | Imaginary Unit | √(-1) | Used in complex numbers. |
| ϕ (phi) | Golden Ratio | 1.61803 | Used in geometry, art, and architecture |
| γ | Euler–Mascheroni Constant | ~0.57721 | Used in number theory and analysis |
| ℵ₀ | Aleph-null (Aleph-zero) | — |
Represents the cardinality of the set of natural numbers. |
| ∞ | Infinity | — | Used to represent an unbounded quantity. Infinity cannot be a fixed value. |
Math Symbols Used in Logic
The following table shows the math symbols used in logic.
| Symbol | Meaning | Example |
| ¬ | Not (negation) | ¬ P means "not P" |
| ∧ | And (conjunction) | P ∧ Q means "P and Q" |
| ∨ | Or (disjunction) | P ∨ Q means "P or Q" |
| ⇒ | Implies (if...then) | P ⇒ Q means "if P then Q" |
| ⇔ | If and only if (biconditional) | P ⇔ Q means "P if and only if Q" |
| ∀ | For all (universal quantifier) | ∀ x ∈ A, P(x) means "for all x in A, P(x) is true" |
| ∃ | There exists (existential quantifier) | ∃ x ∈ A such that P(x) |
| ∃! | Unique existence | ∃! (5x = 10) can be read as “there exists a unique x such that 5x = 10". |
| ⊤ | True (tautology) | P ∨ ¬ P is always ⊤ |
| ⊥ | False (contradiction) | P ∧ ¬ P is ⊥ |
| ⊢ | Provable | P ⊢ Q means, in a proof, Q is logically derived from P. |
| ⊨ | Satisfies (semantic entailment) | P ⊨ Q means if P is true, then Q is also true. |
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Numeric Symbols
In the following table, you’ll find a collection of numeric symbols with examples of their use. Their Hindu-Arabic equivalents are also mentioned according.
| Roman Numeral | Value | Math Symbols Examples |
| I | 1 | I = 1, II = 2, III =3 |
| v | 5 |
IV = 4 (5-1) VI = 6 (5+1) |
| X | 10 |
IX = 9 (10-1) XI = 11 (10+1) |
| L | 50 | XLIX = 49(50-1) |
| C | 100 | CC = 100+100 = 200 |
| D | 500 | DCL = 500+100+50 = 650 |
| M | 1000 | MCLI = 1000+100+50+1 = 1151 |
| R | Real Number | 5, -4.2, 0, 2 |
| Z | Integers | -99, -15, 8, 10 |
| N | Natural Numbers | 1, 2, 3,... |
| Q | Ratio Number | 45, 0.6 |
| P | Irrational Number | 5, 7 |
| C | Complex Number | 3+7i |
Math Symbols Used in Geometry
Symbols play an important role in geometry . In the following table, the commonly used geometrical symbols are listed, along with their names and examples:
| Symbol | Meaning | Example |
| ∠ | Angle | ∠ABC means angle ABC |
| ° | Degree (unit of angle measure) | 90° is a right angle |
| ‖ | Parallel | AB ‖ CD means AB is parallel to CD |
| ⊥ | Perpendicular | AB ⊥ CD, means AB is perpendicular to CD |
| ≅ | Congruent (same size and shape) | ∆ABC ≅ ∆DEF (triangles are congruent) |
| ≈ | Approximately equal | ∠A ≈ 90° means angle A is about 90 degrees |
| ∼ | Similar (same shape, different size) | ∆ABC ∼ ∆DEF |
| △ | Triangle | △ABC means triangle ABC |
| □ | Square | □ABCD means square ABCD |
| ∥ | Parallel lines (alternative symbol) | l ∥ m means line l is parallel to m |
| m∠ | Measure of an angle | m∠ABC = 45° |
| π | Pi (ratio of circumference to diameter) | π ≈ 3.1416 |
Math Symbols Used in Venn Diagrams and Set Theory
The table below shows the mathematical symbols commonly used while working with Venn diagrams and set theory. They often denote the relationship between two or more sets.
| Symbol | Meaning | Example |
| ⊆ | Subset | A ⊆ B |
| ∅ | Empty Set | X = { } (null set or void set) |
| ∩ | Intersection | A ∩ B |
| ∪ | Union | A ∪ B |
| ⊂ | Proper Subset | A ⊂ B |
| ℕ | Natural Number | {0, 1, 2, 3, …} or {1, 2, 3, …} |
| ℤ | Integer | {…, −2, −1, 0, 1, 2, …} |
| ℚ | Rational numbers | Numbers expressible as p/q |
| ℝ | Real Number | All rational + irrational numbers |
| ℂ | Complex Number | Numbers in the form a + bi |
| ℙ | Prime Number | {2, 3, 5, 7, 11, …} (sometimes used) |
Math Symbols used in Combinatorial
Combinatorics deals with counting and arranging objects. In the table given below, the symbols that are used to solve combinatorics problems are mentioned:
| Symbol | Meaning | Example |
| n! | Factorial of n (product of all positive integers up to n) | \(5! = 5 × 4 × 3 × 2 × 1 = 120\) |
| C(n, k) | Combination | C(5,2) = 10 |
| P(n, k) | Permutation: arranging k items from n in order | P(5, 2) = 5 × 4 = 20 |
| ∑ | Summation (adding a series of terms) | \(∑ni=1=1+2+3+4+......+n\) |
| ∏ | Product (multiplying a series of terms) | \(∏ni=1=1×2×3×....×n\) |
| ∈ | Element of a set | a \(∈ \)A means "a belongs to A" |
| ⊆ | Subset | A ⊆ B is read as "A is a subset of B" |
| ∅ | Empty set | A = ∅ means A has zero elements in the set |
| ∩ | Intersection of sets | A ∩ B means the elements in A ∩ B are present in both A and B |
| ∪ | Union of sets | A ∪ B means elements in A or B or both |
Tips and Tricks to Master Math Symbols
For students, remembering and using all the mathematical symbols correctly can sometimes be confusing. Here are some tips and tricks that help to learn students math symbols easily.
- Group and categorize symbols by topic, instead of trying to memorize all symbols at once. Organize them into clusters like arithmetic (+, -, ×, ÷), logic (∧, ∨, ⇒), sets (∈, ∪, ∩), geometry (∠, ⊥, ∥), Greek letters (α, β, λ …), etc.
- Whenever you solve math problems, try writing out each step using the appropriate symbol, rather than substituting with words. For instance, if you have to combine sets, instead of writing elements in both A and B, use A ∩ B.
- Be more careful with similar but different symbols. Some common pitfalls would be confusing = vs ≈, or misusing < and >.
-
Introduce symbols slowly Teach math symbols one at a time. Let children see how each symbol is used, practice it, and become comfortable with it. When they feel ready, introduce the next symbol.
-
Color-Code Symbols Give each math symbol its own color, like green for +, red for –, and blue for =. Using the same colors every time helps kids see the symbols clearly and makes learning more fun.
Common Mistakes and How to Avoid Them While Using Math Symbols
While working with math symbols, students tend to make mistakes. Here are some common mistakes to avoid:
Mistake 1
Confusion between = and ≈
Sometimes, students tend to get confused between the equal to (=) symbol and the approximately (≈) symbol. Remember that ‘=’ means equality. For example, \(3 + 1 = 4\). On the other hand, ‘’ is used to indicate approximate value. For example, 1.29999 ≈ 1.3.
Mistake 2
Not understanding factorial notation (n!)
Students can wrongly assume that factorial involves an addition operation instead of multiplication. When it's a factorial operation, remember that only multiplication is involved. For example, \(5! = 5 × 4 × 3 × 2 × 1 = 120 \).
Mistake 3
Confusing < with >
We can get confused with the direction of the symbol when dealing with the greater than or lesser than symbols. Always remember that the symbol pointing to the left (<) is lesser than the symbol, and that which points to the right (>) is greater than the symbol. For example, 5 < 8 represents 5 is lesser than 8 and 8 > 5 represents 8 is greater than 5.
Mistake 4
Not using ± symbol correctly
Students can get confused with the ± symbol if they don’t know how to use it. This symbol is used when a value can be both positive and negative. For example, \(36 = ±6\).
Mistake 5
Wrong order of operations and forgetting parentheses
Students may forget the order of operations when solving equations with parentheses. The standard order to follow is PEMDAS where P is parentheses, E is exponents, MD is multiplication and division, and AS is addition and subtraction.
Real Life Applications of Math Symbols
Math symbols are used widely in various fields like physics, engineering, and so on. Some of the key applications are mentioned below:
- Math symbol ‘+’ is used while adding up prices, bills, and in everyday calculations. For example, when we need to add the numbers 5 and 10, we use the ‘+’ symbol. So, \(5 + 10 = 15\).
- In construction, symbols like ‘α’ and ‘θ’ are used to represent angles.
- In statistics and data analysis, ‘Σ’ is used to indicate summation. For example, it is used to calculate the mean.
- Percentage symbol is used while calculating interest rates. It is also used for giving discounts and in other financial situations.
- In computer science, databases, programming, and logic circuits, ∧ (logical AND) is used in building algorithms and digital systems.
Solved Examples on Math Symbols
Problem 1
A square has an area of 25 cm^2. What is the side length?
5 cm
Explanation
We can find the side of a square by using the formula:
Area = side2
So, side = \(\sqrt {25}\) \(= 5\)
This concludes that each side of the square is 5 cm.
Problem 2
Which is greater, 0.75 or 0.7?
0.75 is greater.
Explanation
Compare 0.75 and 0.7 to determine which is greater.
So 0.75 > 0.7
So, 0.75 is greater.
Problem 3
A $400 jacket is 14% off. What is the sale price?
$344.
Explanation
14% of 400 \(= (14/100) × 400 = 56\)
Subtracting the discount from the original price gives:
Sale price = \(400 − 56 = 344\)
Problem 4
Find the circumference of a circle with radius 5 cm.
The circumference is approximately 31.5 cm.
Explanation
Circumference formula:
\(C = 2\pi r \)
\(C = 2 × \pi × 5 = 10 × 3.1415 \approx 31.42 \space cm \)
The circumference is approximately 31.42 cm
Problem 5
You buy a pen for $1 and a book for $2.5. How do you pay in total to the shopkeeper?
You pay $3.50.
Explanation
Pen = $1 and Book = $2.5
\(1 + 2.5 = 3.50\)
So, the total is 3.50.
FAQs on Math Symbols
1.What are math symbols?
2.How many math symbols are there?
3.What is the meaning of ∞ ?
4.Are math symbols the same worldwide?
5.Can a symbol have different meanings depending on context?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
