Table of Contents
Mathematical Symbols
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.
Mathematical Symbols
Maths symbols are used to perform mathematical operations and make it easier to solve mathematical problems for students. Mathematical symbols are the basic building blocks for solving huge mathematical problems. Without using mathematical symbols, we can’t think of doing math or solving problems.
Each symbol has a special meaning along with the role it plays in solving any equation or problem. There are many symbols in mathematics, from basic ones to complex ones. But, in order to understand complex symbols and solve equations using those symbols, you must know about the basic symbols and their meanings. In this article, let us discuss the basic math symbols and how to use them. Scroll down to find out more.
Basic Mathematical Symbols
In Mathematics, it’s all about numbers, symbols and formulas. Here we’re discussing the foundation of Mathematics. In simple words, without symbols, we cannot do arithmetic. Mathematical symbols and symbols are considered to represent a value.
Basic mathematical symbols are used to express mathematical ideas. The relationship between the symbol and the value refers to the basic mathematical requirement. With the help of symbols, certain concepts and ideas are clearly explained. Here is a list of commonly used mathematical symbols with words and meanings. Also, an example is given to understand the use of mathematical symbols.
Symbol | Name | Description and Meaning | Example |
+ | Addition | plus | 4 + 3 = 7 |
– | Subtraction | minus | 11 – 5 = 6 |
× | Multiplication | times | 2 × 4 = 8 |
. | Multiplication dot | times | 6 ∙ 2 = 12 |
* | Asterisk | times | 3 * 5 = 15 |
÷ | Division | divided by | 8 ÷ 4 = 2 |
/ | Division | divided by | 9 ⁄ 3 = 3 |
– | horizontal line | division / fraction | 8/2 = 4 |
= | Equality | is equal to | 2 + 6 = 8 |
< | Comparison | is less than | 17 < 45 |
> | Comparison | is greater than | 19 > 6 |
∓ | minus – plus | minus or plus | 5 ∓ 9 = -4 and 14 |
± | plus – minus | plus or minus | 5 ± 9 = 14 and -4 |
. | decimal point | period | 12.05 = 12 +(5/100) |
mod | modulo | mod of | 16 mod 5 = 1 |
ab | exponent | power | 73 = 343 |
√a | square root | √a · √a = a | √16 = ±4 |
3√a | cube root | 3√a ·3√a · 3√a = a | 3√81 = 3 |
4√a | fourth root | 4√a ·4√a · 4√a · 4√a = a | 4√625 = ± 5 |
n√a | n-th root (radical) | n√a · n√a · · · n times = a | for n = 5, n√32 = 2 |
% | percent | 1 % = 1/100 | 25% × 60 = 25 /100 × 60 = 15 |
‰ | per-mille | 1 ‰ = 1/1000 = 0.1% | 10 ‰ × 50 |
ppm | per-million | 1 ppm = 1/1000000 | 10 ppm × 50 = 10/1000000 × 50 = 0.0005 |
ppb | per – billion | 1 ppb = 10-9 | 10 ppb × 50 = 10 × 10-9 × 50 = 5 × 10-7 |
ppt | per – trillion | 1 ppt = 10-12 | 10 ppt × 50 = 10 × 10-12 × 50 = 5 × 10-10 |
Algebra Symbols
Algebra is a mathematical component of symbols and rules to deceive those symbols. In algebra, those symbols represent non-fixed values, called variables. How sentences describe the relationship between certain words, in algebra, mathematics describes the relationship between variables.
Symbol | Name | Description | Example |
x, y | Variables | unknown value | 3x = 9 ⇒ x = 3 |
1, 2, 3…. | Numeral constants | numbers | x + 5 = 10, here 5 and 10 are constant |
≠ | In equation | is not equal to | 3 ≠ 5 |
≈ | Approximately equal | is approximately equal to | √2≈1.41 |
≡ | Definition | equal by definition | (a+b)2 ≡ a2+ 2ab + b2 |
:= | Definition | equal by definition | (a-b)2 := a2-2ab + b2 |
≜ | Definition | equal by definition | a2-b2≜ (a-b).(a+b) |
< | Strict Inequality | is less than | 17 < 45 |
> | Strict Inequality | is greater than | 19 > 6 |
<< | Strict Inequality | is much less than | 1 << 999999999 |
>> | Strict Inequality | is much greater than | 999999999 >> 1 |
≤ | Inequality | is less than or equal to | 3 ≤ 5 and 3 ≤ 3 |
≥ | Inequality | is greater than or equal to | 4 ≥ 1 and 4 ≥ 4 |
[ ] | Brackets | Square brackets | [ 1 + 2 ] – [2 +4] + 4 × 5 = 3 – 6 + 4 × 5 = 3 – 6 + 20 = 23 – 6 = 17 |
( ) | Brackets | parentheses (round brackets) | (15 / 5) × 2 + (2 + 8) = 3 × 2 + 10 = 6 + 10 = 16 |
∝ | Proportion | proportional to | x ∝ y⟹ x = ky, where k is constant. |
f(x) | Function | f(x) = x, is used to maps values of x to f(x) | f(x) = 2x + 5 |
! | Factorial | factorial | 6! = 1 × 2 × 3 × 4 × 5 × 6 = 720 |
⇒ | Material implication | implies | x = 2 ⇒x2 = 4, but x2= 4 ⇒ x = 2 is false, because x could also be -2. |
⇔ | Material equivalence | if and only if | x = y + 4 ⇔ x-4 = y |
|….| | Absolute value | absolute value of | |5| = 5 and |-5| = 5 |
Geometry Symbols Used in Maths
There are geometry symbols which are used in mathematics. Here we’re mentioning each and every geometry symbols which are necessary for students to know.
Symbol | Name | Meaning | Example |
∠ | Angle | It is used to mention an angle formed by two rays | ∠PQR = 30° |
∟ | Right angle | It determines the angle formed is right angle i.e. 90° | ∟XYZ = 90° |
. | Point | It describes a location in space. | (a,b,c) it is represented as a coordinate in space by a point. |
→ | Ray | It shows the line has a fixed starting point but no end point. | \overrightarrow{\rm AB} is a ray. |
_ | Line Segment | It shows the line has a fixed starting point and a fixed end point. | \overline{\rm AB} is a line segment. |
↔ | Line | It shows the line neither has a starting point nor an end point. | \overleftrightarrow{\rm AB} is a line. |
\frown | Arc | It determines the degree of an arc from a point A to point B. | \frown\over{\rm AB} = 45° |
∥ | Parallel | It shows that lines are parallel to each other. | AB ∥ CD |
∦ | Not parallel | It shows the lines are not parallel. | AB ∦ CD |
⟂ | Perpendicular | It shows that two lines are perpendicular i.e. they intersect each other at 90° | AB ⟂ CD |
\not\perp | Not perpendicular | It shows lines are not perpendicular to each other. | AB\not\perp CD |
≅ | Congruent | It shows congruency between two shapes, i.e. two shapes are equivalent in shape and size. | △ABC ≅ △XYZ |
~ | Similarity | It shows two shapes are similar to each other i.e. two shapes are similar in shape but not in size. | △ABC ~ △XYZ |
△ | Triangle | It is used to determine a triangular shape. | △ABC, represents ABC is a triangle. |
° | Degree | It is a unit that is used to determine the measurement of an angle. | a = 30° |
rad or c | Radians | 360° = 2πc | |
grad or g | Gradians | 360° = 400g | |
|x-y| | Distance | It is used to determine distance between two points. | | x-y | = 5 |
π | pi constant | It is a predefined constant with value 22/7 or 3.1415926… | 2π= 2 × 22/7 = 44/7 |
Set Theory Symbols
Some of the most common symbols in Set Theory are listed in the following table:
Symbol | Name | Meaning | Example |
{ } | Set | It is used to determine the elements in a set. | {1, 2, a, b} |
| | Such that | It is used to determine the condition of the set. | { a | a > 5} |
: | { x : x > 0} | ||
∈ | belongs to | It determines that an element belongs to a set. | A = {1, 5, 7, c, a} 7 ∈ A |
∉ | not belongs to | It indicates that an element does not belong to a set. | A = {1, 5, 7, c, a} 0 ∉ A |
= | Equality Relation | It determines that two sets are exactly same. | A = {1, 2, 3} B = {1, 2, 3} then A = B |
⊆ | Subset | It represents all of the elements of set A are present in set B or set A is equals to set B | A = {1, 3, a} B = {a, b, 1, 2, 3, 4, 5} A ⊆ B |
⊂ | Proper Subset | It represents all of the elements of set A are present in set B and set A is not equal to set B. | A = {1, 2, a} B = {a, b, c, 2, 4, 5, 1} A ⊂ B |
⊄ | Not a Subset | It determines A is not a subset of set B. | A = {1, 2, 3} B = {a, b, c} A ⊄ B |
⊇ | Superset | It represents all of the elements of set B are present in set A or set A is equals to set B | A = {1, 2, a, b, c} B = {1, a} A ⊇ B |
⊃ | Proper Superset | It determines A is a superset of B but set A is not equal to set B | A = {1, 2, 3, a, b} B = {1, 2, a} A ⊃ B |
Ø | Empty Set | It determines that there is no element in a set. | { } = Ø |
U | Universal Set | It is set that contains elements of all other relevant sets. | A = {a, b, c} B = {1, 2, 3}, then U = {1, 2, 3, a, b, c} |
|A| or n{A} | Cardinality of a Set | It represents the number of items in a set. | A= {1, 3, 4, 5, 2}, then |A|=5. |
P(X) | Power Set | It is the set that contains all possible subsets of a set A, including the set itself and the null set. | If A = {a, b} P(A) = {{ }, {a}, {b}, {a, b}} |
∪ | Union of Sets | It is a set that contains all the elements of the provided sets. | A = {a, b, c} B = {p, q} A ∪ B = {a, b, c, p, q} |
∩ | Intersection of Sets | It shows the common elements of both sets. | A = { a, b} B= {1, 2, a} A ∩ B = {a} |
XC OR X’ | Complement of a set | Complement of a set includes all other elements that does not belongs to that set. | A = {1, 2, 3, 4, 5} B = {1, 2, 3} then X′ = A – B X′ = {4, 5} |
− | Set Difference | It shows the difference of elements between two sets. | A = {1, 2, 3, 4, a, b, c} B = {1, 2, a, b} A – B = {3, 4, c} |
× | Cartesian Product of Sets | It is the product of the ordered components of the sets. | A = {1, 2} and B = {a} A × B ={(1, a), (2, a)} |
Calculus and Analysis Symbols
In calculus, we have come across different math symbols. All mathematical symbols with names and meanings are provided here. Go through the all mathematical symbols used in calculus.
Symbol | Symbol Name in Maths | Math Symbols Meaning | Example |
ε | epsilon | represents a very small number, near-zero | ε → 0 |
e | e Constant/Euler’s Number | e = 2.718281828… | e = lim (1+1/x)x , x→∞ |
limx→a | limit | limit value of a function | limx→2(2x + 2) = 2×2 + 2 = 6 |
y‘ | derivative | derivative – Lagrange’s notation | (4x2)’ = 8x |
y” | Second derivative | derivative of derivative | (4x2)” = 8 |
y(n) | nth derivative | n times derivation | nth derivative of xn xn {yn(xn)} = n (n-1)(n-2)….(2)(1) = n! |
dy/dx | derivative | derivative – Leibniz’s notation | d(6x4)/dx = 24x3 |
dy/dx | derivative | derivative – Leibniz’s notation | d2(6x4)/dx2 = 72x2 |
dny/dxn | nth derivative | n times derivation | nth derivative of xn xn {dn(xn)/dxn} = n (n-1)(n-2)….(2)(1) = n! |
Dx | Single derivative of time | Derivative-Euler’s Notation | d(6x4)/dx = 24x3 |
D2x | second derivative | Second Derivative-Euler’s Notation | d(6×4)/dx = 24×3 |
Dnx | derivative | nth derivative-Euler’s Notation | nth derivative of xn {Dn(xn)} = n (n-1)(n-2)….(2)(1) = n! |
∂/∂x | partial derivative | Differentiating a function with respect to one variable considering the other variables as constant | ∂(x5 + yz)/∂x = 5x4 |
∫ | integral | opposite to derivation | ∫xn dx = xn + 1/n + 1 + C |
∬ | double integral | integration of the function of 2 variables | ∬(x + y) dx.dy |
∭ | triple integral | integration of the function of 3 variables | ∫∫∫(x + y + z) dx.dy.dz |
∮ | closed contour / line integral | Line integral over closed curve | ∮C 2p dp |
∯ | closed surface integral | Double integral over a closed surface | ∭V (⛛.F)dV = ∯S (F.n̂) dS |
∰ | closed volume integral | Volume integral over a closed three-dimensional domain | ∰ (x2 + y2 + z2) dx dy dz |
[a,b] | closed interval | [a,b] = {x | a ≤ x ≤ b} | cos x ∈ [ – 1, 1] |
(a,b) | open interval | (a,b) = {x | a < x < b} | f is continuous within (-1, 1) |
z* | complex conjugate | z = a+bi → z*=a-bi | If z = a + bi then z* = a – bi |
i | imaginary unit | i ≡ √-1 | z = a + bi |
∇ | nabla/del | gradient / divergence operator | ∇f (x,y,z) |
x * y | convolution | Modification in a function due to the other function. | y(t) = x(t) * h(t) |
∞ | lemniscate | infinity symbol | x ≥ 0; x ∈ (0, ∞) |
Combinatorics Symbols Used in Maths
Combinatorics symbols used in maths to study combination of finite discrete structures. Various important combinatorics symbols used in maths are added in table as follows:
Symbol | Symbol Name | Meaning or Definition | Example |
n! | Factorial | n! = 1×2×3×…×n | 4! = 1×2×3×4 = 24 |
nPk | Permutation | nPk = n!/(n – k)! | 4P2 = 4!/(4 – 2)! = 12 |
nCk | Combination | nCk = n!/(n – k)!.k! | 4C2 = 4!/2!(4 – 2)! = 6 |
Numeral Symbols in Maths
There are various types of numbers used in mathematics by mathematician of various region and some of the most prominent number symbols such as Europeean Numbers and Roman Numbers in maths are,
Name | European | Roman |
zero | 0 | n/a |
one | 1 | I |
two | 2 | II |
three | 3 | III |
four | 4 | IV |
five | 5 | V |
six | 6 | VI |
seven | 7 | VII |
eight | 8 | VIII |
nine | 9 | IX |
ten | 10 | X |
eleven | 11 | XI |
twelve | 12 | XII |
thirteen | 13 | XIII |
fourteen | 14 | XIV |
fifteen | 15 | XV |
sixteen | 16 | XVI |
seventeen | 17 | XVII |
eighteen | 18 | XVIII |
nineteen | 19 | XIX |
twenty | 20 | XX |
thirty | 30 | XXX |
forty | 40 | XL |
fifty | 50 | L |
sixty | 60 | LX |
seventy | 70 | LXX |
eighty | 80 | LXXX |
ninety | 90 | XC |
one hundred | 100 | C |
Two hundred | 200 | CC |
Three hundred | 300 | CCC |
Five hundred | 500 | D |
One Thousand | 1,000 | M |
Symbols used in Maths
List of complete alphabets is provided in the following table:
Greek Symbol | Greek Letter Name | English Equivalent | |
Lower Case | Upper Case | ||
Α | α | Alpha | a |
Β | β | Beta | b |
Δ | δ | Delta | d |
Γ | γ | Gamma | g |
Ζ | ζ | Zeta | z |
Ε | ε | Epsilon | e |
Θ | θ | Theta | th |
Η | η | Eta | h |
Κ | κ | Kappa | k |
Ι | ι | Iota | i |
Μ | μ | Mu | m |
Λ | λ | Lambda | l |
Ξ | ξ | Xi | x |
Ν | ν | Nu | n |
Ο | ο | Omicron | o |
Π | π | Pi | p |
Σ | σ | Sigma | s |
Ρ | ρ | Rho | r |
Υ | υ | Upsilon | u |
Τ | τ | Tau | t |
Χ | χ | Chi | ch |
Φ | φ | Phi | ph |
Ψ | ψ | Psi | ps |
Ω | ω | Omega | o |
Logic Symbols Used in Maths
Some of the common logic symbols are listed in the following table:
Symbol | Name | Meaning | Example |
¬ | Negation (NOT) | It is not the case that | ¬P (Not P) |
∧ | Conjunction (AND) | Both are true | P ∧ Q (P and Q) |
∨ | Disjunction (OR) | At least one is true | P ∨ Q (P or Q) |
→ | Implication (IF…THEN) | If the first is true, then the second is true | P → Q (If P then Q) |
↔ | Bi-implication (IF AND ONLY IF) | Both are true or both are false | P ↔ Q (P if and only if Q) |
∀ | Universal quantifier (for all) | Everything in the specified set | ∀x P(x) (For all x, P(x)) |
∃ | Existential quantifier (there exists) | There is at least one in the specified set | ∃x P(x) (There exists an x such that P(x)) |
Discrete Mathematics Symbols
Some symbols related to Discrete Mathematics are:
Symbol | Name | Meaning | Example |
ℕ | Set of natural numbers | Positive integers (including zero) | 0, 1, 2, 3, … |
ℤ | Set of integers | Whole numbers (positive, negative, and zero) | -3, -2, -1, 0, 1, 2, 3, … |
ℚ | Set of rational numbers | Numbers expressible as a fraction | 1/2, 3/4, 5, -2, 0.75, … |
ℝ | Set of real numbers | All rational and irrational numbers | π, e, √2, 3/2, … |
ℂ | Set of complex numbers | Numbers with real and imaginary parts | 3 + 4i, -2 – 5i, … |
n! | Factorial of n | Product of all positive integers up to n | 5! = 5 × 4 × 3 × 2 × 1 |
nCk or C(n, k) | Binomial coefficient | Number of ways to choose k elements from n items | 5C3 = 10 |
G, H, … | Names for graphs | Variables representing graphs | Graph G, Graph H, … |
V(G) | Set of vertices of graph G | All the vertices (nodes) in graph G | If G is a triangle, V(G) = {A, B, C} |
E(G) | Set of edges of graph G | All the edges in graph G | If G is a triangle, E(G) = {AB, BC, CA} |
|V(G)| | Number of vertices in graph G | Total count of vertices in graph G | If G is a triangle, |V(G)| = 3 |
|E(G)| | Number of edges in graph G | Total count of edges in graph G | If G is a triangle, |E(G)| = 3 |
∑ | Summation | Sum over a range of values | ∑_{i=1}^{n} i = 1 + 2 + … + n |
∏ | Product notation | Product over a range of values | ∏_{i=1}^{n} i = 1 × 2 × … × n |
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