Mathematics is a universal language and Mathematical symbols play a major role in this. Meaning and value Mathematical symbols are constant.

The symbols of mathematics not only refer to different quantities but also represent the relationship between two quantities. Mathematical symbols are mainly used to conduct mathematical operations under various concepts.

We know that the concept of mathematics is purely dependent on numbers and symbols. The relationship between symbol and value reflects the basic fundamental of mathematics.

## Different types of Mathematical Symbols

- Basic math Symbols
- Numeral Symbols
- Greek Alphabets Symbols
- Geometry Symbols
- Algebra Symbols
- Probability and Statistics Symbols
- Logic Symbols
- Calculus & Analysis Symbols
- Set Theory Symbols

**List of all mathematical symbols with Meaning.**

### Basic math symbols

Basic mathematical symbols are used to express mathematical ideas. With the help of basic symbols, some concepts and ideas of mathematics are clearly explained.

Symbol | Symbol Name | Meaning of Symbol |

≠ | Not Equal Sign | Inequality |

= | Equals Sign | Equality |

≈ | Approximately Equal | Approximation |

< | Strict Inequality | Less Than |

> | Strict Inequality | Greater Than |

≤ | Inequality | Less Than or Equal To |

≥ | Inequality | Greater Than or Equal To |

[ ] | Brackets | Calculate Expression Inside First |

( ) | Parentheses | Calculate Expression Inside First |

− | Minus Sign | Subtraction |

+ | Plus Sign | Addition |

∓ | Minus – Plus | Both Minus and Plus Operations |

± | Plus – Minus | Both Plus and Minus Operations |

× | Times Sign | Multiplication |

* | Asterisk | Multiplication |

÷ | Division Sign / Obelus | Division |

∙ | Multiplication Dot | Multiplication |

– | Horizontal Line | Division or Fraction |

/ | Division Slash | Division |

% | Percent | 1% = 1/100 (The amount in every hundred.) |

. | Period | Decimal Point, Decimal Separator |

mod | Modulo | Remainder Calculation |

a^{b} | Power | Exponent |

a^b | Caret | Exponent |

√a | Square Root | √a ⋅ √a = a |

^{3}√a | Cube Root | ^{3}√a ·^{3}√a · ^{3}√a = a |

^{4}√a | Fourth Root | ^{4}√a ·^{4}√a · ^{4}√a · ^{4}√a = a |

^{n}√a | N-Th Root (Radical) | ^{n}√a · ^{n}√a · · · n times = a |

ppm | Per-Million | 1 ppm = 1/1000000 |

‰ | Per-Mille | 1‰ = 1/1000 = 0.1% |

ppt | Per-Trillion | 1ppt = 10^{-12} |

ppb | Per-Billion | 1 ppb = 1/1000000000 |

### Numeral Symbols

Symbols and collections of mathematical symbols used to represent numbers based on different types of the ancient system.

Name | Western Arabic | Roman | Eastern Arabic | Hebrew |
---|---|---|---|---|

zero | 0 | ٠ | ||

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 |

### Greek Alphabets Symbols

Greek alphabets are generally used to represent the variables, constants, functions and other mathematical objects. Some Greek Alphabets mathematical symbols are mentioned below:

Upper Case Letter | Lower Case Letter | Greek Letter Name | English Equivalent | Letter Name Pronounce |
---|---|---|---|---|

Α | α | Alpha | a | al-fa |

Β | β | Beta | b | be-ta |

Γ | γ | Gamma | g | ga-ma |

Δ | δ | Delta | d | del-ta |

Ε | ε | Epsilon | e | ep-si-lon |

Ζ | ζ | Zeta | z | ze-ta |

Η | η | Eta | h | eh-ta |

Θ | θ | Theta | th | te-ta |

Ι | ι | Iota | i | io-ta |

Κ | κ | Kappa | k | ka-pa |

Λ | λ | Lambda | l | lam-da |

Μ | μ | Mu | m | m-yoo |

Ν | ν | Nu | n | noo |

Ξ | ξ | Xi | x | x-ee |

Ο | ο | Omicron | o | o-mee-c-ron |

Π | π | Pi | p | pa-yee |

Ρ | ρ | Rho | r | row |

Σ | σ | Sigma | s | sig-ma |

Τ | τ | Tau | t | ta-oo |

Υ | υ | Upsilon | u | oo-psi-lon |

Φ | φ | Phi | ph | f-ee |

Χ | χ | Chi | ch | kh-ee |

Ψ | ψ | Psi | ps | p-see |

Ω | ω | Omega | o | o-me-ga |

### Geometry Symbols

In mathematics, geometric symbols are used to configure geometric objects – the most basic straight lines, circles, and end points.

Symbol | Symbol Name | Meaning of Symbol |
---|---|---|

∠ | angle | the figure formed by two rays meeting at a common end |

spherical angle | an angle formed by the intersection of two great circles of a sphere. | |

∟ | right angle | a right angle is = 90° |

° | degree | one full rotation is = 360° |

deg | degree | one full rotation is = 360deg |

′ | prime | arcminute, (1′=1/60) |

″ | double prime | arcsecond, 1″ = 1/3600=1/60′) |

line | infinite line | |

AB | line segment | line from point A to point B |

ray | line that start from point A | |

arc | arc from point A to point B (= 60°) | |

⊥ | perpendicular | perpendicular lines (90° angle) |

∥ | parallel | parallel lines |

≅ | congruent to | equivalence of geometric shapes and size |

~ | similarity | same shapes, not same size |

Δ | triangle | triangle shape |

|x–y| | distance | distance between points x and y |

π | pi constant | π = 3.141592654…is the ratio between the circumference and diameter of a circle |

rad | radians | radians angle unit (360° = 2π rad) |

^{c} | radians | radians angle unit (360° = 2π ^{c}) |

grad | gradians / gons | grads angle unit (360° = 400 grad) |

^{g} | gradians / gons | grads angle unit (360° = 400 ^{g}) |

### Algebra symbols

Algebra mathematical symbols are the major component of math that is used to unify mathematics concepts.

Algebra symbols are used to represent variables to find the distance, the perimeter of an area, volume, determining the cost of something, renting something, time relationships, pricing options for something you want to buy, and more.

Symbol | Symbol Name | Meaning of Symbol |
---|---|---|

x | x variable | to find the unknown value |

≡ | equivalence | identical to |

≜ | equal by definition | equal by definition |

:= | equal by definition | equal by definition |

~ | approximately equal | weak approximation |

≈ | approximately equal | approximation |

∝ | proportional to | proportional to |

∞ | lemniscate | figure-eight or ∞-shaped curves |

≪ | much less than | much less than |

≫ | much greater than | much greater than |

( ) | parentheses | calculate expression inside first |

[ ] | brackets | calculate expression inside first |

{ } | braces | set |

⌊x⌋ | floor brackets | rounds number to lower integer |

⌈x⌉ | ceiling brackets | rounds number to upper integer |

x! | exclamation mark | factorial |

| x | | vertical bars | absolute value |

f (x) | function of x | maps values of x to f(x) |

(f ∘ g) | function composition | (f ∘ g) (x) = f (g(x)) |

(a,b) | open interval | (a,b) = {x | a < x < b} |

[a,b] | closed interval | [a,b] = {x | a ≤ x ≤ b} |

∆ | delta | change / difference |

∆ | discriminant | Δ = b^{2} – 4ac |

∑ | sigma | summation – sum of all values in range of series |

∑∑ | sigma | double summation |

∏ | capital pi | product – product of all values in range of series |

e | e constant / Euler’s number | e = 2.718281828… or e = lim (1+1/x) , ^{x}x→∞ |

γ | Euler-Mascheroni constant | γ = 0.5772156649… |

φ | golden ratio | golden ratio constant |

π | pi constant | π = 3.141592654…is the ratio between the circumference and diameter of a circle |

### Probability and Statistics Symbols

Probability and statistics correspond to the mathematical study of chance and data, respectively.

Statistics and Probability theory have some commonly used rules, in addition to standard mathematical notation and mathematical symbols.

Symbol | Symbol Name | Meaning of Symbol |
---|---|---|

P(A) | probability function | probability of event A |

P(A ⋃ B) | probability of events union | probability that of events A or B |

P(A ⋂ B) | probability of events intersection | probability that of events A and B |

P(A | B) | conditional probability function | probability of event A given event B occurred |

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 |

E(X) | expectation value | expected value of random variable X |

E(X | Y) | conditional expectation | expected value of random variable X given Y |

var(X) | variance | variance of random variable X |

σ^{2} | variance | variance of population values |

std(X) | standard deviation | standard deviation of random variable X |

σ_{X} | standard deviation | standard deviation value of random variable X |

median | middle value of random variable x | |

cov(X,Y) | covariance | covariance of random variables X and Y |

corr(X,Y) | correlation | correlation of random variables X and Y |

ρ_{X,Y} | correlation | correlation of random variables X and Y |

∑ | summation | summation – sum of all values in range of series |

∑∑ | double summation | double summation |

Mo | mode | value that occurs most frequently in population |

Md | sample median | half the population is below this value |

MR | mid-range | MR = (x+_{max}x)/2_{min} |

Md | sample median | half the population is below this value |

Q_{1} | lower / first quartile | 25% of population are below this value |

Q_{2} | median / second quartile | 50% of population are below this value = median of samples |

Q_{3} | upper / third quartile | 75% of population are below this value |

x | sample mean | average / arithmetic mean |

s | sample standard deviation | population samples standard deviation estimator |

s^{2} | sample variance | population samples variance estimator |

z_{x} | standard score | z = (_{x}x–x) / s_{x} |

X ~ | distribution of X | distribution of random variable X |

N(μ,σ^{2}) | normal distribution | Gaussian distribution |

U(a,b) | uniform distribution | equal probability in range a,b |

exp(λ) | exponential distribution | f (x) = λe^{–λx} , x≥0 |

gamma(c, λ) | gamma distribution | f (x) = λ c x^{c-1}e^{–λx} / Γ(c), x≥0 |

χ^{ 2}(k) | chi-square distribution | f (x) = x^{k}^{/2-1}e^{–x/2} / ( 2^{k/2 }Γ(k/2) ) |

F (k_{1}, k_{2}) | F distribution | |

Bin(n,p) | binomial distribution | f (k) = (1_{n}C_{k} p^{k}-p)^{n-k} |

Poisson(λ) | Poisson distribution | f (k) = λ^{k}e^{–λ} / k! |

Geom(p) | geometric distribution | f (k) = p(1-p)^{ k} |

HG(N,K,n) | hyper-geometric distribution | |

Bern(p) | Bernoulli distribution |

### Logic Symbols

Logic symbols is commonly used to express logical representation. Some Logic mathematical symbols are mentioned below:

Symbol | Symbol Name | Meaning of Symbol |
---|---|---|

⋅ | and | and |

^ | caret / circumflex | and |

& | ampersand | and |

+ | plus | or |

∨ | reversed caret | or |

| | vertical line | or |

x‘ | single quote | not – negation |

x | bar | not – negation |

¬ | not | not – negation |

! | exclamation mark | not – negation |

⊕ | circled plus / oplus | exclusive or – xor |

~ | tilde | negation (equivalent to) |

⇒ | implies | if is true, then is also true |

⇔ | equivalent | if and only if (iff) |

↔ | equivalent | if and only if (iff) |

∀ | for all | |

∃ | there exists | |

∄ | there does not exists | |

∴ | therefore | |

∵ | because / since |

### Calculus & Analysis Symbols

In mathematics, calculus represents courses of elementary and analysis which are mainly dedicated to the study of function limits.

Symbol | Symbol Name | Meaning of Symbol |
---|---|---|

limit | limit value of a function | |

ε | epsilon | represents a very small number, near zero: ε →0 |

e | e constant / Euler’s number | e = 2.718281828…ore = lim (1+1/x) , ^{x}x→∞ |

y ‘ | derivative | derivative – Lagrange’s notation |

y ” | second derivative | derivative of derivative |

y^{(n)} | nth derivative | n times derivation |

derivative | derivative – Leibniz’s notation | |

second derivative | derivative of derivative | |

nth derivative | n times derivation | |

time derivative | derivative by time – Newton’s notation | |

time second derivative | derivative of derivative | |

D_{x }y | derivative | derivative – Euler’s notation |

D_{x}^{2}y | second derivative | derivative of derivative |

partial derivative | Example: ∂(x^{2}+y^{2})/∂x = 2x | |

∫ | integral | opposite to derivation: ∫ f(x)dx |

∫∫ | double integral | integration of function of 2 variables: ∫∫ f(x,y)dxdy |

∫∫∫ | triple integral | integration of function of 3 variables: ∫∫∫ f(x,y,z)dxdydz |

∮ | closed contour / line integral | contour integral |

∯ | closed surface integral | generalization of multiple integrals to integration over surfaces |

∰ | closed volume integral | integral over a 3-dimensional domain |

[a,b] | closed interval | [a,b] = {x | a ≤ x ≤ b} |

(a,b) | open interval | (a,b) = {x | a < x < b} |

i | imaginary unit | i ≡ √-1 |

z* | complex conjugate | z = a+bi → z*=a–bi |

z | complex conjugate | z = a+bi → z = a–bi |

Re(z) | real part of a complex number | z = a+bi → Re(z)=a |

Im(z) | imaginary part of a complex number | z = a+bi → Im(z)=b |

| z | | absolute value/magnitude of a complex number | |z| = |a+bi| = √(a^{2}+b^{2}) |

arg(z) | argument of a complex number | The angle of the radius in the complex plane |

∇ | nabla / del | gradient / divergence operator |

vector | ||

unit vector | Direction Vector | |

x * y | convolution | y(t) = x(t) * h(t) |

Laplace transform | F(s) = {f (t)} | |

Fourier transform | X(ω) = {f (t)} | |

δ | delta function | |

∞ | lemniscate | infinity symbol |

### Set Theory Symbols

Set theory mathematical symbols are used to define the properties of well-defined collections such as objects or numbers or functions.

Symbol | Symbol Name | Meaning of Symbol |

{ } | set | a collection of elements |

A ∪ B | union | Elements that belong to set A or set B |

A ∩ B | intersection | Elements that belong to both the sets, A and B |

A ⊆ B | subset | subset has few or all elements equal to the set |

A ⊄ B | not subset | left set is not a subset of right set |

A ⊂ B | proper subset / strict subset | subset has fewer elements than the set |

A ⊃ B | proper superset / strict superset | set A has more elements than set B |

A ⊇ B | superset | set A has more elements or equal to the set B |

Ø | empty set | Ø = { } |

P (C) | power set | all subsets of C |

A ⊅ B | not superset | set X is not a superset of set Y |

A = B | equality | both sets have the same members |

A \ B or A-B | relative complement | objects that belong to A and not to B |

A^{c} | complement | all the objects that do not belong to set A |

A ∆ B | symmetric difference | objects that belong to A or B but not to their intersection |

a∈B | element of | set membership |

(a,b) | ordered pair | collection of 2 elements |

x∉A | not element of | no set membership |

|B|, #B | cardinality | the number of elements of set B |

A×B | cartesian product | set of all ordered pairs from A and B |

N_{1} | natural numbers / whole numbers set (without zero) | N_{1} = {1, 2, 3, 4, 5,…} |

N_{0} | natural numbers / whole numbers set (with zero) | N_{0} = {0, 1, 2, 3, 4,…} |

Q | rational numbers set | Q= {x | x=a/b, a, b∈Z} |

Z | integer numbers set | Z= {…-3, -2, -1, 0, 1, 2, 3,…} |

C | complex numbers set | C= {z | z=a+bi, -∞<a<∞, -∞<b<∞} |

R | real numbers set | R= {x | -∞ < x <∞} |

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