List of all mathematical symbols and signs - meaning and examples.
| Symbol | Symbol Name | Meaning / definition | Example |
|---|
| = | equals sign | equality | 5 = 2+3
5 is equal to 2+3 |
| ≠ | not equal sign | inequality | 5 ≠ 4
5 is not equal to 4 |
| ≈ | approximately equal | approximation | sin(0.01) ≈ 0.01,
x≈ y means x is approximately equal to y |
| > | strict inequality | greater than | 5 > 4
5 is greater than 4 |
| < | strict inequality | less than | 4 < 5
4 is less than 5 |
| ≥ | inequality | greater than or equal to | 5 ≥ 4,
x ≥ ymeans x is greater than or equal to y |
| ≤ | inequality | less than or equal to | 4 ≤ 5,
x ≤ y means xis less than or equal to y |
| ( ) | parentheses | calculate expression inside first | 2 × (3+5) = 16 |
| [ ] | brackets | calculate expression inside first | [(1+2)×(1+5)] = 18 |
| + | plus sign | addition | 1 + 1 = 2 |
| − | minus sign | subtraction | 2 − 1 = 1 |
| ± | plus - minus | both plus and minus operations | 3 ± 5 = 8 or -2 |
| ± | minus - plus | both minus and plus operations | 3 ∓ 5 = -2 or 8 |
| * | asterisk | multiplication | 2 * 3 = 6 |
| × | times sign | multiplication | 2 × 3 = 6 |
| ⋅ | multiplication dot | multiplication | 2 ⋅ 3 = 6 |
| ÷ | division sign / obelus | division | 6 ÷ 2 = 3 |
| / | division slash | division | 6 / 2 = 3 |
| — | horizontal line | division / fraction |  |
| mod | modulo | remainder calculation | 7 mod 2 = 1 |
| . | period | decimal point, decimal separator | 2.56 = 2+56/100 |
| ab | power | exponent | 23 = 8 |
| a^b | caret | exponent | 2 ^ 3 = 8 |
| √a | square root | √a⋅ √a = a | √9 = ±3 |
| 3√a | cube root | 3√a⋅ 3√a ⋅ 3√a = a | 3√8 = 2 |
| 4√a | fourth root | 4√a⋅ 4√a ⋅ 4√a ⋅ 4√a =a | 4√16 = ±2 |
| n√a | n-th root (radical) | | for n=3, n√8 = 2 |
| % | percent | 1% = 1/100 | 10% × 30 = 3 |
| ‰ | per-mille | 1‰ = 1/1000 = 0.1% | 10‰ × 30 = 0.3 |
| ppm | per-million | 1ppm = 1/1000000 | 10ppm × 30 = 0.0003 |
| ppb | per-billion | 1ppb = 1/1000000000 | 10ppb × 30 = 3×10-7 |
| ppt | per-trillion | 1ppt = 10-12 | 10ppt × 30 = 3×10-10 |
| Symbol | Symbol Name | Meaning / definition | Example |
|---|
| x | x variable | unknown value to find | when 2x = 4, then x = 2 |
| ≡ | equivalence | identical to | |
| ≜ | equal by definition | equal by definition | |
| := | equal by definition | equal by definition | |
| ~ | approximately equal | weak approximation | 11 ~ 10 |
| ≈ | approximately equal | approximation | sin(0.01) ≈ 0.01 |
| ∝ | proportional to | proportional to | y ∝ x when y = kx, k constant |
| ∞ | lemniscate | infinity symbol | |
| ≪ | much less than | much less than | 1 ≪ 1000000 |
| ≫ | much greater than | much greater than | 1000000 ≫ 1 |
| ( ) | parentheses | calculate expression inside first | 2 * (3+5) = 16 |
| [ ] | brackets | calculate expression inside first | [(1+2)*(1+5)] = 18 |
| { } | braces | set | |
| ⌊x⌋ | floor brackets | rounds number to lower integer | ⌊4.3⌋ = 4 |
| ⌈x⌉ | ceiling brackets | rounds number to upper integer | ⌈4.3⌉ = 5 |
| x! | exclamation mark | factorial | 4! = 1*2*3*4 = 24 |
| | x | | vertical bars | absolute value | | -5 | = 5 |
| f (x) | function of x | maps values of x to f(x) | f (x) = 3x+5 |
| (f ∘ g) | function composition | (f ∘ g) (x) = f (g(x)) | f (x)=3x,g(x)=x-1⇒(f ∘ g)(x)=3(x-1) |
| (a,b) | open interval | (a,b) = {x | a < x < b} | x∈ (2,6) |
| [a,b] | closed interval | [a,b] = {x | a ≤ x ≤ b} | x ∈ [2,6] |
| ∆ | delta | change / difference | ∆t = t1 - t0 |
| ∆ | discriminant | Δ = b2 - 4ac | |
| ∑ | sigma | summation - sum of all values in range of series | ∑ xi= x1+x2+...+xn |
| ∑∑ | sigma | double summation | |
| ∏ | capital pi | product - product of all values in range of series | ∏ xi=x1∙x2∙...∙xn |
| e | e constant/ Euler's number | e = 2.718281828... | 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 | c = π⋅d = 2⋅π⋅r |
| Symbol | Symbol Name | Meaning / definition | Example |
|---|
| · | dot | scalar product | a · b |
| × | cross | vector product | a × b |
| A⊗B | tensor product | tensor product of A and B | A ⊗ B |
| inner product | | |
| [ ] | brackets | matrix of numbers | |
| ( ) | parentheses | matrix of numbers | |
| | A | | determinant | determinant of matrix A | |
| det(A) | determinant | determinant of matrix A | |
| || x || | double vertical bars | norm | |
| AT | transpose | matrix transpose | (AT)ij = (A)ji |
| A† | Hermitian matrix | matrix conjugate transpose | (A†)ij = (A)ji |
| A* | Hermitian matrix | matrix conjugate transpose | (A*)ij =(A)ji |
| A-1 | inverse matrix | A A-1 = I | |
| rank(A) | matrix rank | rank of matrix A | rank(A) = 3 |
| dim(U) | dimension | dimension of matrix A | dim(U) = 3 |
| Symbol | Symbol Name | Meaning / definition | 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 |
| var(X) | variance | variance of random variable X | var(X) = 4 |
| σ2 | variance | variance of population values | σ2 = 4 |
| std(X) | standard deviation | standard deviation of random variable X | std(X) = 2 |
| σX | standard deviation | standard deviation value of random variable X | σX = 2 |
| median | middle value of random variable x | |
| cov(X,Y) | covariance | covariance of random variables X and Y | cov(X,Y) = 4 |
| corr(X,Y) | correlation | correlation of random variables X and Y | corr(X,Y) = 0.6 |
| ρX,Y | correlation | correlation of random variables X and Y | ρX,Y= 0.6 |
| ∑ | summation | summation - sum of all values in range of series | |
| ∑∑ | double summation | double summation | |
| Mo | mode | value that occurs most frequently in population | |
| MR | mid-range | MR = (xmax+xmin)/2 | |
| Md | sample median | half the population is below this value | |
| Q1 | lower / first quartile | 25% of population are below this value | |
| Q2 | median / second quartile | 50% of population are below this value = median of samples | |
| Q3 | upper / third quartile | 75% of population are below this value | |
| x | sample mean | average / arithmetic mean | x = (2+5+9) / 3 = 5.333 |
| s 2 | sample variance | population samples variance estimator | s 2 = 4 |
| s | sample standard deviation | population samples standard deviation estimator | s = 2 |
| zx | standard score | zx = (x-x)/ sx | |
| X ~ | distribution of X | distribution of random variable X | X ~ N(0,3) |
| N(μ,σ2) | normal distribution | gaussian distribution | X ~ N(0,3) |
| U(a,b) | uniform distribution | equal probability in range a,b | X ~ U(0,3) |
| exp(λ) | exponential distribution | f (x) = λe-λx , x≥0 | |
| gamma(c, λ) | gamma distribution | f (x) = λ c xc-1e-λx/ Γ(c), x≥0 | |
| χ 2(k) | chi-square distribution | f (x) = xk/2-1e-x/2/ ( 2k/2 Γ(k/2) ) | |
| F (k1, k2) | F distribution | | |
| Bin(n,p) | binomial distribution | f (k) = nCk pk(1-p)n-k | |
| Poisson(λ) | Poisson distribution | f (k) = λke-λ / k! | |
| Geom(p) | geometric distribution | f (k) = p(1-p) k | |
| HG(N,K,n) | hyper-geometric distribution | | |
| Bern(p) | Bernoulli distribution | | |
| Symbol | Symbol Name | Meaning / definition | Example |
|---|
| { } | set | a collection of elements | A = {3,7,9,14},
B = {9,14,28} |
| A ∩ B | intersection | objects that belong to set A and set B | A ∩ B = {9,14} |
| A ∪ B | union | objects that belong to set A or set B | A ∪ B = {3,7,9,14,28} |
| A ⊆ B | subset | A is a subset of B. set A is included in set B. | {9,14,28} ⊆ {9,14,28} |
| A ⊂ B | proper subset / strict subset | A is a subset of B, but A is not equal to B. | {9,14} ⊂ {9,14,28} |
| A ⊄ B | not subset | set A is not a subset of set B | {9,66} ⊄ {9,14,28} |
| A ⊇ B | superset | A is a superset of B. set A includes set B | {9,14,28} ⊇ {9,14,28} |
| A ⊃ B | proper superset / strict superset | A is a superset of B, but B is not equal to A. | {9,14,28} ⊃ {9,14} |
| A ⊅ B | not superset | set A is not a superset of set B | {9,14,28} ⊅ {9,66} |
| 2A | power set | all subsets of A | |
| power set | all subsets of A | |
| A = B | equality | both sets have the same members | A={3,9,14},
B={3,9,14},
A=B |
| Ac | complement | all the objects that do not belong to set A | |
| A \ B | relative complement | objects that belong to A and not to B | A = {3,9,14},
B = {1,2,3},
A-B = {9,14} |
| A - B | relative complement | objects that belong to A and not to B | A = {3,9,14},
B = {1,2,3},
A-B = {9,14} |
| A ∆ B | symmetric difference | objects that belong to A or B but not totheir intersection | A = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14} |
| A ⊖ B | symmetric difference | objects that belong to A or B but not to their intersection | A = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14} |
| a∈A | element of,
belongs to | set membership | A={3,9,14}, 3 ∈ A |
| x∉A | not element of | no set membership | A={3,9,14}, 1 ∉ A |
| (a,b) | ordered pair | collection of 2 elements | |
| A×B | cartesian product | set of all ordered pairs from A and B | A×B = {(a,b)|a∈A , b∈B} |
| |A| | cardinality | the number of elements of set A | A={3,9,14}, |A|=3 |
| #A | cardinality | the number of elements of set A | A={3,9,14}, #A=3 |
| | | vertical bar | such that | A={x|3<x<14} |
| aleph-null | infinite cardinality of natural numbers set | |
| aleph-one | cardinality of countable ordinal numbers set | |
| Ø | empty set | Ø = { } | C = {Ø} |
| universal set | set of all possible values | |
| 0 | natural numbers / whole numbers set (with zero) | 0 = {0,1,2,3,4,...} | 0 ∈ 0 |
| 1 | natural numbers / whole numbers set (without zero) | 1 = {1,2,3,4,5,...} | 6 ∈ 1 |
| integer numbers set | = {...-3,-2,-1,0,1,2,3,...} | -6 ∈ |
| rational numbers set | = {x | x=a/b,a,b∈} | 2/6 ∈ |
| real numbers set | = {x | -∞ < x <∞} | 6.343434∈ |
| complex numbers set | = {z | z=a+bi, -∞<a<∞, -∞<b<∞} | 6+2i ∈ |
| Symbol | Symbol Name | Meaning / definition | Example |
|---|
| ⋅ | and | and | x ⋅ y |
| ^ | caret / circumflex | and | x ^ y |
| & | ampersand | and | x & y |
| + | plus | or | x + y |
| ∨ | reversed caret | or | x ∨ y |
| | | vertical line | or | x | y |
| x' | single quote | not - negation | x' |
| x | bar | not - negation | x |
| ¬ | not | not - negation | ¬ x |
| ! | exclamation mark | not - negation | ! x |
| ⊕ | circled plus / oplus | exclusive or - xor | x ⊕ y |
| ~ | tilde | negation | ~ x |
| ⇒ | implies | | |
| ⇔ | equivalent | if and only if (iff) | |
| ↔ | equivalent | if and only if (iff) | |
| ∀ | for all | | |
| ∃ | there exists | | |
| ∄ | there does not exists | | |
| ∴ | therefore | | |
| ∵ | because / since | | |
| Symbol | Symbol Name | Meaning / definition | Example |
|---|
| 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... | e = lim (1+1/x)x , x→∞ |
| y ' | derivative | derivative - Lagrange's notation | (3x3)' = 9x2 |
| y '' | second derivative | derivative of derivative | (3x3)'' = 18x |
| y(n) | nth derivative | n times derivation | (3x3)(3) = 18 |
| derivative | derivative - Leibniz's notation | d(3x3)/dx = 9x2 |
| second derivative | derivative of derivative | d2(3x3)/dx2 = 18x |
| nth derivative | n times derivation | |
| time derivative | derivative by time - Newton's notation | |
| time second derivative | derivative of derivative | |
| Dx y | derivative | derivative - Euler's notation | |
| Dx2y | second derivative | derivative of derivative | |
| partial derivative | | ∂(x2+y2)/∂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 | | |
| ∯ | closed surface integral | | |
| ∰ | closed volume integral | | |
| [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 = 3 + 2i |
| z* | complex conjugate | z = a+bi → z*=a-bi | z* = 3 - 2i |
| z | complex conjugate | z = a+bi → z =a-bi | z = 3 - 2i |
| Re(z) | real part of a complex number | z = a+bi → Re(z)=a | Re(3 - 2i) = 3 |
| Im(z) | imaginary part of a complex number | z = a+bi → Im(z)=b | Im(3 - 2i) = -2 |
| | z | | absolute value/magnitude of a complex number | |z| = |a+bi| = √(a2+b2) | |3 - 2i| = √13 |
| arg(z) | argument of a complex number | The angle of the radius in the complex plane | arg(3 + 2i) = 33.7° |
| ∇ | nabla / del | gradient / divergence operator | ∇f (x,y,z) |
| vector | | |
| unit 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 | |
| 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 |
| 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 |
| Number | Roman numeral |
|---|
| 0 | not defined |
| 1 | I |
| 2 | II |
| 3 | III |
| 4 | IV |
| 5 | V |
| 6 | VI |
| 7 | VII |
| 8 | VIII |
| 9 | IX |
| 10 | X |
| 11 | XI |
| 12 | XII |
| 13 | XIII |
| 14 | XIV |
| 15 | XV |
| 16 | XVI |
| 17 | XVII |
| 18 | XVIII |
| 19 | XIX |
| 20 | XX |
| 30 | XXX |
| 40 | XL |
| 50 | L |
| 60 | LX |
| 70 | LXX |
| 80 | LXXX |
| 90 | XC |
| 100 | C |
| 200 | CC |
| 300 | CCC |
| 400 | CD |
| 500 | D |
| 600 | DC |
| 700 | DCC |
| 800 | DCCC |
| 900 | CM |
| 1000 | M |
| 5000 | V |
| 10000 | X |
| 50000 | L |
| 100000 | C |
| 500000 | D |
| 1000000 | M |
FAQs
Basic Mathematical Symbols With Name, Meaning and Examples
| Symbol | Symbol Name in Maths | Math Symbols Meaning |
|---|
| ± | plus – minus | both plus and minus operations |
| × | times sign | multiplication |
| * | asterisk | multiplication |
| ÷ | division sign / obelus | division |
27 more rowsThe 11 basic symbols essential for writing mathematical equations are the plus (+), minus (-), equals (=), does not equal (≠), multiplication (×), division (÷), greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), fraction (/), decimal (.)
What does ∈ X mean? ›
Set membership x ∈ X means x is an element of the set X. (Non-membership is written x 6∈ X.) Set inclusion X ⊆ Y means every element of X is an element of Y ; X is a subset of Y .
What is ⨂ in math? ›
⨂ is the Kronecker product of two matrices.
What are X symbols? ›
In the Cartesian coordinate system, x is used to refer to the horizontal axis. It is also sometimes used as a typographic approximation for the multiplication sign, ×. In mathematical typesetting, x meaning an algebraic variable is normally in italic type ( ), partly to avoid confusion with the multiplication symbol.
What is X plus X equal? ›
Answer and Explanation:
X plus x would equal 2x. No matter what number you use in place of the variable x, in this problem you are adding two of that variable together. Adding a number to itself is the same as multiplying the number by 2.
What is (+) (+)? ›
Addition/Subtraction Formulas:
(+) + (+) = +
What are all the symbols in algebra? ›
Algebra Symbols With Names
| Symbol | Symbol Name | Meaning/definition |
|---|
| ⟨ x , y ⟩ < | inner product | |
| A⊗B | tensor product | tensor product of A and B |
| [ ] | brackets | matrix of numbers |
| ( ) | parentheses | matrix of numbers |
10 more rowsThe use of ± for an approximation is most commonly encountered in presenting the numerical value of a quantity, together with its tolerance or its statistical margin of error. For example, 5.7 ± 0.2 may be anywhere in the range from 5.5 to 5.9 inclusive.
What does ∑ X mean in math? ›
❖ ΣX = “the sum of X values” or “sum of scores” ❖ Example. X: 10, 6, 7, 4. oΣX = 10+6+7+4 = 27, N = 4.
The intersection of sets can be denoted using the symbol '∩'. As defined above, the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.
What does epsilon X mean? ›
Εε Epsilon. ε: “Error term” in regression/statistics; more generally used to denote an arbitrarily small, positive number. ∈ (Variant Epsilon) This version of epsilon is used in set theory to mean “belongs to” or “is in the set of”: x ∈ X; similarly used to indicate the range of a parameter: x ∈ [0, 1].
What does ∏ mean in math? ›
Presenting the symbols
The second symbol is the product symbol. It's a capital Greek letter called pi. It's written like this: ∏ and can be called as "product notation".
What does ⊕ mean in math? ›
⊕︀ (logic) exclusive or. (logic) intensional disjunction, as in some relevant logics. (mathematics) direct sum. (mathematics) An operator indicating special-defined operation that is similar to addition.
What is the ⊙ symbol in math? ›
⊙ Hadamard Product
This circle-dot symbol can mean a few different things, depending on context. Typically in machine learning literature, it refers to the Hadamard product (component-wise multiplication for matrices).
What is X represents in math? ›
In algebra, the letter 'x' is often used to represent an unknown quantity or variable.
What is the X mean symbol in math? ›
Usage. The x bar (x̄) symbol is used in statistics to represent the sample mean, or average, of a set of values. It's calculated by adding up all the numbers in the sample and then dividing by the number of values in that sample. Read more…
What is the squiggly X in math? ›
Tilde. The symbol "~" is pronounced "tilde" (till-day or till-dee), or informally "twiddle" or "squiggle". The tilde may be placed on top of a variable, for example "˜x" with several possible meanings. Before a number the tilde is used to mean "approximately". "~42" means "approximately 42".
What does || X || mean in math? ›
be an n-vector in ℂn. Then, a vector norm, denoted by the symbol ||x||, is a real-valued continuous function of the components x1, x2,…, xn of x, satisfying the following properties: 1. ||x|| > 0 for every nonzero x. ||x|| = 0 if and only if x is the zero vector.
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