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
∀x for all x Something is true for all (any) value of x (usually with a side condition like ∀x > 0).
What does ∈ X mean? ›
Set membership x ∈ X means x is an element of the set X. (Non-membership is written x ∈ X.)
What are all the symbols for math? ›
Key Takeaways. The 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 (.) and percent (%) symbols.
What does X ∈ Z mean? ›
x ∈ R just means that x is a real number (can be any number, fraction, decimal, whole, positive, negative) x ∈ Z means that x is an integar (a positive or negatie whole number e.g. -2,0, 9, -32 etc) At the end of a question it is really just there to give you a way to check if your answer is correct, if it said x ∈ Z ...
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 in math? ›
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 does ø mean in math? ›
The letter "Ø" is sometimes used in mathematics as a replacement for the symbol "∅" (Unicode character U+2205), referring to the empty set as established by Bourbaki, and sometimes in linguistics as a replacement for same symbol used to represent a zero.
What does this symbol ∑ X mean? ›
The symbol ∑ is the Greek letter Sigma and it represents the sum of a set of numbers or expressions. It is often used in mathematical equations and formulas to indicate that a series of values should be added together.
What does ∩ mean in math? ›
∩ The symbol ∩ means intersection. Given two sets S and T, S ∩ T is used to denote the set {x|x ∈ S and x ∈ T}. For example {1,2,3}∩{3,4,5} = {3}. \ The symbol \ means remove from a set. Given two sets S and T, S\T is used to denote the set {x|x ∈ S and x /∈ T}.
What is the unknown symbol in math? ›
In algebra, the letter 'x' is often used to represent an unknown quantity or variable.
The 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 is the 8 symbol in math? ›
The infinity symbol (∞) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate, after the lemniscate curves of a similar shape studied in algebraic geometry, or "lazy eight", in the terminology of livestock branding.
What does X ∈ Q mean? ›
Q represents rational numbers.So X belongs to Q means x is a number which belongs to the set of rational numbers. Thanks 8. Answer rating5.0.
What does x ∈ ∅ mean? ›
The empty set is the (unique) set ∅ for which the statement x∈∅ x ∈ ∅ is always false. You could denote it {} , or you could define it ∅={x|x≠x} ∅ = { x | x ≠ x } , or any other way, as long as it has no members.
What does X ∈ I mean in math? ›
Or if I is the interval [1,2], then x∈I means x is some real number in that interval, i.e., x satisfies 1≤x≤2.
What does for all X mean in math? ›
Variables in mathematics, such as x, y, a, b, c, etc., are quantified with phrases such as "for all x", "for any z", "for every z", "there is at least one a", etc. "For any", "for all", "for every" all mean the same thing: something is true for EVERY object under discussion, WITHOUT EXCEPTION.
What is the set of all X? ›
The set of all x-values is called the domain, and the set of all y-values is called the range.
What is the symbol for the sum of all X values? ›
The symbol Σ (sigma) is generally used to denote a sum of multiple terms.
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