There are tons of symbols in the language of Mathematics - some are easy, while some are complex. Mathematical symbols are used for different purposes in the subject. Using these math symbols, you can form phrases, words, and sentences and represent the relationship between numbers and quantities. Also, mathematical symbols are the only thing that helps us perform mathematical operations.
I hope you already know what mathematics is, right? It is the science and study of measuring, calculating, structure, shape, and quantity. It involves shapes, numerical calculations, and logical thinking. We have dimensions like trigonometry, algebra, and geometry that are solely based on Mathematical symbols and numbers.
For example, we use the pi math symbol (π) to represent the numbers and value 3.17. Also, we use Euler's constant math symbol (e) to represent the value 2.71828... Therefore, understanding the math symbols and their uses is highly essential if you want to ace and build a higher foundation in the subject.
We have compiled this post to help you understand and know about the math symbols in detail! Below, we will share a complete list of all mathematical symbols, from basic to logic to calculus to more. Also, we will be giving solved examples at the end to help you practice and understand the math symbols more efficiently. Keep Reading, and remember to stick till the end!
Basic & Common Math Symbols
Let's start our lesson with some commonly used mathematical symbols. These
common symbols are the key mathematical objects, honestly, and we can't do mathematics without them. Imagine, without symbols; math would be like; adding 5 to 10 gives 15. Annoying and complicated, right? But with mathematical symbols, it's just: 5 + 10 = 15. Here, we saved a lot of time, space, and effort. Here is our list of some common and basic symbols:
Math Symbols | Meaning | Math Symbol Examples |
+ | Add | 4 + 4 = 8 |
- | Subtract / Minus | 4 - 4 = 0 |
= | Equal to | 2 + 2 = 4 |
≡ | Ideantically equal to | (a+b)2 ≡ a2 + 2ab +b2 |
≈
| Approximately equal to | Π ≈ 3.14 |
≠ | Not equal to | 4 + 5 ≠ 10 |
× | Multiply | 2 × 4 = 8 |
÷ | Division sign | 6 ÷ 3 = 2 |
< | Less than | 5 < 7 |
> | Greater than | 10 > 2 |
≤ | Less than or equal to | x +y ≤ z |
≥ | Greater than or equal to | x +y ≥ z |
% | Percentage | 60% = 60/100 |
. | Decimal Point or Period | ⅔ = 0.6 |
_ | Vincullum: Separates the numerator and denominator | 2 - 3 |
√ | Square Root | √16 = 4
|
() | Parentheses | 2+(5−3)=2+2=4 |
[ ] | Square Brackets | 6×[3+(5−4)]+1 |
∞ | Infinity | Infinity means countless |
Constants Used As Math Symbols
We use the mathematical constants symbols to represent the numbers that don't vary and stay the same. Key mathematical infinities, key mathematical sets, key mathematical objects, and key numbers are included in constants symbols. Here is a list of all the most commonly used constants and their explanation:
Math Symbol Name | Explanation |
0 (Zero) | Additive identity of common numbers |
1 (One) | Multiplicative identity of common numbers |
√2 (Square root of 2) | A positive number whose square is 2. Approximately equals 1.41421.
|
e (Euler's constant) | The base of the natural logarithm. Approximately equals 2.71828 |
π (Pi, Archimedes’ constant) | The ratio of a circle’s circumference to its diameter. Half-circumference of a unit circle. Approximately equals 3.14159 |
Φ (Phi, golden ratio) | Ratio between a larger number and p smaller number q when (p+q)/p = p/q. Positive solution to the equation y2-y-1 = 0 . |
i (Imaginary unit) | The principal root of -1. The foundational component of a complex number. |
Logic Math Symbols
Here is a list of all logical-mathematical symbols along with their meaning and examples:
Symbol | Meaning | Math Symbols Examples |
∃ | 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. |
∃! | There exists one and only one | ∃! x: F(x) means that there is exactly one X such that F(x) is true. |
∀ | For all | ∀n>1 ; n2>1 |
¬ | Logical Not | Statement A is true only if ¬ is false x≠y⟺¬(x=y) |
∨ | Logical OR | The statement A ∨ B is true if A or B is true; if both are false, the statement is false. |
∧ | Logical And | The statement A ∧ B is true
if A and B are both true; else it is false. |
⟹ | Implies | x = 2 ⟹ x2 = 4 |
⟺ | If and only If | x +1 = y +1 ⟺ x = y |
| or : | Such that | { X | X > 0 } = {1,2,3,...} |
Math Symbols for Venn Diagram and Set Theory
Here is a list of symbols used in the Venn Diagram and Set Theory:
Symbol | Meaning | Examples |
|
|
|
∩ | Intersection | A = {2,3,4} B = {4,5,6} A∩B = {4} |
∪ | Union | A = {2,3,4} B = {4,5,6} A∪B = {2,3,4,5,6} |
∅ | Empty Set | A set with no elements ∅ = { } |
∈ | Is a member of | 2 ∈ N |
∉ | Is not a member of | 0 ∉ N |
⊂ | Is a subset | N ⊂ I |
⊃ | Is a super set | R ⊃ W |
P(A) | The Power Set of A | P ({1,2}) = { {}, {1}, {2}, {1,2} } |
A=B | Equality (Same elements) | A = {1,2}; B = {1,2} ⟹ A = B |
A×B | Cartesian Product | A = {5,6}; B = {7,8} ⟹ A×B = {(5,7),(5,8),(6,7),(6,8)} |
|A| | Cardinality is the number of elements in set A | |{1,2,3,4}| = 4 |
Common Numeral Math Symbols
These
Roman numerals are commonly used in our day-to-day lives. Here are some common numeral symbols and their Hindu, Arabic, and Roman versions:
Name | European | Roman | Hindu Arabic | Hebrew |
zero | 0 | n/a | 0 | n/a |
one | 1 | I | ١ | א |
two | 2 | II | ٢ | ב |
three | 3 | III | ٣ | ג |
four | 4 | IV | ٤ | ד |
five | 5 | V | ٥ | ה |
six | 6 | VI | ٦ | ו |
seven | 7 | VII | ٧ | ז |
eight | 8 | VIII | ٨ | ח |
nine | 9 | IX | ٩ | ט |
ten | 10 | X | ١٠ | י |
eleven | 11 | XI | ١١ | יא |
twelve | 12 | XII | ١٢ | יב |
thirteen | 13 | XIII | ١٣ | יג |
fourteen | 14 | XIV | ١٤ | יד |
fifteen | 15 | XV | ١٥ | טו |
sixteen | 16 | XVI | ١٦ | טז |
seventeen | 17 | XVII | ١٧ | יז |
eighteen | 18 | XVIII | ١٨ | יח |
nineteen | 19 | XIX | ١٩ | יט |
twenty | 20 | XX | ٢٠ | כ |
thirty | 30 | XXX | ٣٠ | ל |
forty | 40 | XL | ٤٠ | מ |
fifty | 50 | L | ٥٠ | נ |
sixty | 60 | LX | ٦٠ | ס |
seventy | 70 | LXX | ٧٠ | ע |
eighty | 80 | LXXX | ٨٠ | פ |
ninety | 90 | XC | ٩٠ | צ |
one hundred | 100 | C | ١٠٠ | ק |
Geometry Math Symbols
Below, we are sharing a list of mathematical symbols used in geometry, along with their explanation and examples:
Symbols | Meaning | Math Symbol Examples |
∠ | Mention the angle | ∠ABC |
Δ | Triangle symbol | ΔPQR |
≅ | Congruent to | ΔPQR ≅ ΔABC |
∼ | Similar to | ΔPQR ∼ ΔABC |
⊥ | Is perpendicular with | AB ⊥PQ |
∥ | Is parallel with | AB ∥ CD |
∘ | Degree | 90∘ |
¯¯ AB | Line Segment AB | A line from Point A to Point B |
−−→ AB | Ray AB | A line starting from Point A and extends through B |
←→ AB | Line AB | An infinite line passing through points A and B |
⌢ AB | Arc A to B | ⌢ AB=90∘ |
c | Radians Symbol | 360∘=2πc |
Algebraic Math Symbols
Mathematical symbols are a lifesaver when they include in Algebra. Algebra itself is a complex dimension, and it would have been a nightmare without math symbols. Here is a list of all algebraic math symbols with their meaning and examples:
Algebraic Math Symbols | Meaning | Math Symbol Examples |
x,y | Variables | X = 5, y = 2 |
+ | Add | 2x + 3x = 5x |
− | Subtract | 3x−x = 2x |
. | Product | 2x.3x = 6x |
− | Division | 2x − 3y |
≡ | Identically equal to | (a+b)2 ≡ a2 + 2ab + b2 |
≠ | Not equal to | A + 5 = b + 1⟹ a ≠ b |
= | Equal to | A = 7 |
∝ | Proportional to | X ∝ y ⟹ x = ky |
f (x) | Function maps values of x to f(x) | F (x) = x + 3 |
Greek Alphabets and Combinatorics Symbols
The table below includes all the commonly used mathematical symbols for Greek Alphabets and Combinatorics symbols. You will also see their examples and usage in the table.
Greek Alphabets as Mathematics Symbols:
Math Symbols | Meaning | Math Symbol Examples |
|---|
α | Alpha | Used to denote angles and coefficients |
β | Beta | Used to denote angles and coefficients |
γ | Gamma | Used to denote angles and coefficients |
Δ | Delta | Discriminant symbol |
ε | Epsilon | Used to represent an Universal Set |
ι | lota | Represents an imaginary number |
λ | Lambda | Represents constant |
π | Pi | π ≈ 3.14 |
Σ | Sigma | Represents the sum |
θ | Theta | Represents angles |
ρ | Rho | Statistical constant |
ϕ | Phi | Diameter symbol |
Combinatorics Mathematics Symbols:
Math Symbols | Meaning | Math Symbols Examples |
n! | n factorial | n! = n × (n−1) × (n−2) ×.....× 2×1 |
(n/c) or nCr | Combination |
|
nPr | Permutation |
|
Calculus & Analysis Math Symbols
Calculus is full of different math symbols that help us solve and understand the concept. Here is a list of all mathematical symbols used in calculus, along with their names and meanings:
Math Symbol | Symbol Name | Meaning | Math Symbols Example |
ε | Epsilon | Represents a very small number | ε → 0
|
limx→a | limit | Limit value of a function | limx→a(3x+1)= 3 × a + 1 = 3a + 1 |
y ‘ | derivative | Derivative - Lagrange’s notation | (5x3)’ = 15x2 |
e | e constant / Euler’s number | e = 2.718281828… | e = lim (1+1/x)x , x→∞ |
y(n) | nth derivative | n times derivation | nth derivative of 3xn = 3 n (n-1)(n-2)….(2)(1)= 3n! |
y” | second derivative | derivative of derivative | (4x3)” = 24x |
D2x | second derivative | derivative of derivative | n/a |
∫ | Integral | Opposite to derivation | n/a |
∭ | Triple integral | Integration of function of 3 variables | n/a |
∬ | Double integral(a,b) | Integration of function of 2 variables | n/a |
∯ | Closed surface integral | n/a | n/a |
∮ | Closed contour / Line integral | n/a | n/a |
[a,b] | Closed Interval | [a,b] = {x | a ≤ x ≤ b} | n/a |
∰ | Closed volume integral | n/a | n/a |
(a,b) | Open interval | (a,b) = {x | a < x < b} | n/a |
i | Imaginary unit | i ≡ √-1 | z = 3 + 2i |
z | Complex conjugate | z = a+bi → z = a-bi | z = 3 + 2i |
Notational Mathematical Symbols in Probability and Statistics
Here is the list of all the math symbols used in the dimension of probability and statistics:
Math Symbol | Symbol Name | Meaning | Math Symbols Example |
P(A) | Probability function | probability of event A | P(A) = 0.5 |
P(A ⋂ B) | probability of events intersection | probability that of events A and B | P(A⋂B) = 0.5
|
P(A ⋃ B) | probability of events union | probability that of events A or B | P(A⋃B) = 0.5
|
P(A | B) | conditional probability function | probability of event A given event B occured | P(A | B) = 0.3
|
f (x) | probability density function (pdf) | P(a ≤ x ≤ b) = ∫ f (x) dx |
|
F(x) | cumulative distribution function (cdf) | F(x) = P(X≤ x) |
|
μ | population mean | mean of population values | μ = 10
|
E(X) | expectation value | expected value of random variable X | E(X) = 10
|
E(X | Y) | conditional expectation | expected value of random variable X given Y | E(X | Y=2) = 5
|
∑ | summation | summation - sum of all values in range of series |
|
∑∑ | double summation | double summation |
|
Mo | mode | value that occurs most frequently in population |
|
Frequently Asked Questions
What is the pi symbol?
Pi is a constant in Maathematics, and its value is equal to approximately 3.14. It is represented by the π, and it defines the ratio of circle circumference to its diameter.
What are the symbols for basic arithmetic operations?
The symbols for basic arithmetic operations are as follows:
+ for Addition
- for Subtraction
x for Multiplication
÷ for Division
Why do we use Math Symbols?
We use Math symbols because they have played a great role in making Mathematics an universal language. Also, it has made the concepts and dimensions of mathematics easy to understand and time-saving!
Final Words
We hope that this post helped you understand the importance of Math symbols and their usage. If you still have questions, you can request the help of a professional
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