List of all mathematical symbols and signs - meaning and examples.
| Symbol | Symbolname | Meaning / Definition | example |
|---|
| = | equal sign | equality | 5 = 2+3
5 equals 2+3 |
| ≠ | different sign | inequality | 5 ≠ 4
5 is not equal to 4 |
| ≈ | about the same | approximation | sin(0,01) ≈ 0,01,
x≈jmeansxis about the samej |
| > | strict inequality | bigger then | 5 > 4
5 is greater than 4 |
| < | strict inequality | Less than | 4 < 5
4 is less than 5 |
| ≥ | inequality | Better than or equal | 5 ≥ 4,
x≥jmeansxis greater than or equal toj |
| ≤ | inequality | less than or equal to | 4 ≤ 5,
x ≤ ymeansxis less than or equal toj |
| ( ) | brackets | first evaluate the expression in it | 2 × (3+5) = 16 |
| [] | square brackets | first evaluate the expression in it | [(1+2)×(1+5)] = 18 |
| + | plus sign | additive | 1 + 1 = 2 |
| − | minus sign | Subtraction | 2 − 1 = 1 |
| ± | More less | Plus and minus operations | 3 ± 5 = 8 or -2 |
| ± | less more | Operations less and less | 3 ∓ 5 = -2 or 8 |
| * | asterisk | multiplication | 2 * 3 = 6 |
| × | sign times | multiplication | 2 × 3 = 6 |
| ⋅ | multiplication point | multiplication | 2 ⋅ 3 = 6 |
| ÷ | Division sign / Obelus | classification | 6 ÷ 2 = 3 |
| / | split rod | classification | 6/2 = 3 |
| — | horizontal line | division / fraction |  |
| Mod | Module | calculation of the remainder | 7 ways 2 = 1 |
| . | Period | decimal point, decimal separator | 2,56 = 2+56/100 |
| a b | Energy | Exponent | 23 = 8 |
| a^b | Circumflex accent | Exponent | 2 ^ 3 = 8 |
| √a | Quadratwurzel | √a ⋅√a = identical | √9= ±3 |
| 3√a | root cubic | 3√a ⋅3√a ⋅3√a = identical | 3√8= 2 |
| 4√a | fourth root | 4√a ⋅4√a ⋅4√a ⋅4√a = a | 4√16= ±2 |
| n√a | n-te Wurzel (Radical) | | Pron=3,n√8= 2 |
| % | percent | 1% = 1/100 | 10 % × 30 = 3 |
| ‰ | per thousand | 1‰ = 1/1000 = 0,1% | 10‰ × 30 = 0,3 |
| ppm | pro Million | 1ppm = 1/1000000 | 10 ppm × 30 = 0,0003 |
| ppb | per billion | 1 ppb = 1/1000000000 | 10 ppb × 30 = 3 × 10-7 |
| ppt | pro Billion | 1ppt = 10-12 | 10 ppt × 30 = 3 × 10-10 |
| Symbol | Symbolname | Meaning / Definition | example |
|---|
| x | x-Variable | find unknown value | if 2x= 4, thenx= 2 |
| ≡ | equivalence | identical with | |
| ≜ | by definition gleich | by definition gleich | |
| := | by definition gleich | by definition gleich | |
| ~ | about the same | weak approximation | 11 ~ 10 |
| ≈ | about the same | approximation | sin(0,01) ≈ 0,01 |
| ∝ | proportional to | proportional to | j∝xWhenj=kx, kConstantly |
| ∞ | Lemniskata | infinity symbol | |
| ≪ | much less than | much less than | 1 ≪ 1000000 |
| ≫ | much bigger than | much bigger than | 1000000 ≫ 1 |
| ( ) | brackets | first evaluate the expression in it | 2 * (3 + 5) = 16 |
| [] | square brackets | first evaluate the expression in it | [(1+2)*(1+5)] = 18 |
| {} | braces | define | |
| ⌊x⌋ | floor stand | rounds the number to the lower integer | ⌊4,3⌋ = 4 |
| ⌈x⌉ | ceiling mounts | rounds the number up | ⌈4,3⌉ = 5 |
| x! | exclamation mark | Faculty | 4! = 1*2*3*4 = 24 |
| |x| | vertical bars | absolute value | | -5 | = 5 |
| f(x) | function of x | maps x-values 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 area | (a ,b) = {x|a <x<b} | x∈ (2,6) |
| [a ,b] | closed area | [a ,b] = {x|a ≤x≤b} | x∈ [2,6] |
| ∆ | Delta | change / difference | ∆t=t1-t0 |
| ∆ | discriminatory | D=b2- 4ac | |
| ∑ | Sigma | Summation - sum of all values in the series range | ∑xEU= x1+x2+...+xn |
| ∑∑ | Sigma | double sum | |
| ∏ | Capital Pi | Product - Product of all values in the series range | ∏xEU=x1∙x2∙...∙xn |
| e | and constant/ Euler number | e= 2,718281828... | e= border (1+1/x)x,x→∞ |
| c | Constante de Euler-Mascheroni | γ = 0.5772156649... | |
| Phi | Golden cut | Golden section constant | |
| Pi | Pi-Constant | Pi= 3,141592654... is the ratio of the circumference to the diameter of a circle | c=Pi⋅d= 2⋅Pi⋅r |
| Symbol | Symbolname | Meaning / Definition | example |
|---|
| P(A) | probability function | Probability of event A | P(A) = 0,5 |
| P(A⋂B) | Probability of events overlapping | Probability of events A and B | P(A⋂B) = 0,5 |
| P(A⋃B) | Probability of union events | Probability of events A or B | P(A⋃B) = 0,5 |
| P(A|B) | conditional probability function | Probability that event A occurs when event B occurs | 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) | |
| m | average population | average of the population values | m= 10 |
| E(x) | expected value | Expected value of the random variable X | E(x) = 10 |
| E(X | Y) | conditional expectation | Expected value of the random variable X at Y | E(X | Y=2) = 5 |
| Eras(x) | variance | Variance of the random variable X | Eras(x) = 4 |
| p2 | variance | Variance of population values | p2= 4 |
| Standard(x) | standard deviation | Standard deviation of the random variable X | Standard(x) = 2 |
| px | standard deviation | Standard deviation value of the random variable X | px = 2 |
| Median | Mean of the random variable x | |
| That(x,Y) | Kovarianz | Covariance of the random variables X and Y | That(X, Y) = 4 |
| reap(x,Y) | correlation | Correlation of random variables X and Y | reap(X, Y) = 0,6 |
| rx,Y | correlation | Correlation of random variables X and Y | rx,Y= 0,6 |
| ∑ | Soma | Summation - sum of all values in the series range | |
| ∑∑ | double sum | double sum | |
| Mo | Away | Value that occurs most frequently in the population | |
| SR | middle range | SR= (xmaximal+xMinimum)/2 | |
| Md | medium sample | half of the population is below this value | |
| Q1 | lowest/first quartile | 25% of the population is below this value | |
| Q2 | Median/second quartile | 50% of the population are below this value = median of the samples | |
| Q3 | top/third quartile | 75% of the population is below this value | |
| x | sample mean | Mean / arithmetic mean | x= (2+5+9) / 3 = 5.333 |
| s 2 | sample variance | Population sample variance estimator | s 2= 4 |
| s | sample standard deviation | Estimates of the standard deviation of population samples | s= 2 |
| zx | Standard-Score | zx= (x-x)/sx | |
| x~ | distributionfrom X | Distribution of the random variable X | x~N(0,3) |
| N(m,p2) | normal distribution | Gaussian distribution | x~N(0,3) |
| she(a ,b) | even distribution | same probability in interval a,b | x~she(0,3) |
| exp(EU) | exponential distribution | f(x)= λe-λx,x≥0 | |
| Spiel(c, EU) | gamma distribution | f(x)= λcxc-1e-λx/C(c),x≥0 | |
| h2(k) | Chi-Square Distribution | f(x)= xk/2-1e-x/2/ (2k/2C(k/2) ) | |
| F(k1, k2) | F distribution | | |
| Garbage can(n,p) | binomial distribution | f(k)=nCkpk(1-p)n-k | |
| Poisson(EU) | poison distribution | f(k)= λke-EU/k! | |
| geom(p) | geometric distribution | f(k)= p(1-p)k | |
| HG(N,k,n) | hypergeometric distribution | | |
| Berna(p) | Bernoulli distribution | | |
| Symbol | Symbolname | Meaning / Definition | example |
|---|
| {} | define | a collection of items | A = {3,7,9,14},
B = {9,14,28} |
| A ∩ B | overlap | Objects belonging to set A and set B | A ∩ B = {9,14} |
| A ∪ B | Unit | Objects belonging to either set A or set B | A ∪ B = {3,7,9,14,28} |
| A ⊆ B | subset | A is a subset of B. Set A is contained 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 subdivide | Set A is not a subset of set B | {9,66} ⊄ {9,14,28} |
| A ⊇ B | Super recovery | A is a superset of B. Set A contains 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 outstanding | Set A is not a superset of set B | {9,14,28} ⊅ {9,66} |
| 2A | strength set | all subsets of A | |
| strength 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 | complete | all objects that do not belong to set A | |
| A\B | relative complement | Objects owned by A and not B | A = {3,9,14},
B = {1,2,3},
AB = {9,14} |
| AB | relative complement | Objects owned by A and not B | A = {3,9,14},
B = {1,2,3},
AB = {9,14} |
| A ∆ B | symmetrical 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 ⊖ B | symmetrical 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,
heard | set association | A={3,9,14}, 3 ∈ A |
| x∉A | not part of | no clear association | A={3,9,14}, 1 ∉ A |
| (a ,b) | orderly pair | Collection of 2 elements | |
| A×B | Cartesian product | Set of all ordered pairs of A and B | A×B = {(a ,b)|a ∈A ,b∈B} |
| |A| | cardinality | the number of elements in set A | A={3,9,14}, |A|=3 |
| #A | cardinality | the number of elements in set A | A={3,9,14}, #A=3 |
| | | Outside vertical | with it | A={x|3<x<14} |
| Aleph-Null | infinite cardinality of the set of natural numbers | |
| alef-um | Cardinality of the set of countable ordinal numbers | |
| Ö | empty set | Ø = { } | C = {Ø} |
| Universal Set | Set of all possible values | |
| 0 | natural numbers / set of integers (with zero) | 0= {0,1,2,3,4,...} | 0 ∈0 |
| 1 | natural numbers / sets of integers (no zero) | 1= {1,2,3,4,5,...} | 6 ∈1 |
| set of integers | = {...-3,-2,-1,0,1,2,3,...} | -6 ∈ |
| set of rational numbers | = {x|x=a /b,a ,b∈} | 2/6 ∈ |
| Many real numbers | = {x| -∞ <x<∞} | 6,343434∈ |
| set of complex numbers | = {z|z=a+Bi, -∞<a <∞, -∞<b<∞} | 6+2EU∈ |
| Symbol | Symbolname | Meaning / Definition | example |
|---|
| Border | limit of a function | |
| e | Epsilon | represents a very small number close to zero | e→ 0 |
| e | and constant/ Euler number | e= 2,718281828... | e= border (1+1/x)x,x→∞ |
| j' | derived | Derivation - Lagrangian notation | (3x3)' = 9x2 |
| j'' | second derivative | Derived from Derivatives | (3x3)'' = 18x |
| j(n) | nth derivative | n-fold derivative | (3x3)(3)= 18 |
| derived | Derivation - Leibniz notation | d(3x3)/dx= 9x2 |
| second derivative | Derived from Derivatives | d2(3x3)/dx2= 18x |
| nth derivative | n-fold derivative | |
| derivation of time | Derivative with respect to time - Newton notation | |
| second derivative of time | Derived from Derivatives | |
| Dxj | derived | Derivation - Euler notation | |
| Dx2j | second derivative | Derived from Derivatives | |
| partial derivative | | ∂(x2+j2)/∂x= 2x |
| ∫ | Integral- | opposite of derivation | ∫f(x)dx |
| ∫∫ | Doppelintegral | Integration of the function of 2 variables | ∫∫f(x,y)dxdy |
| ∫∫∫ | integral tripla | Integration of the function of 3 variables | ∫∫∫f(x,y,z)dxdydz |
| ∮ | closed contour/line integral | | |
| ∯ | closed surface integral | | |
| ∰ | closed volume integral | | |
| [a ,b] | closed area | [a ,b] = {x|a ≤x≤b} | |
| (a ,b) | open area | (a ,b) = {x|a <x<b} | |
| EU | imaginary unit | EU≡ √-1 | z= 3 + 2EU |
| z* | complex conjugated | z=a +Bi→z*=a -Bi | z*= 3 - 2EU |
| z | complex conjugated | z=a +Bi→z=a -Bi | z= 3 - 2EU |
| Period (z) | Real part of a complex number | z=a +Bi→ Re(z)=a | Re(3 - 2EU) = 3 |
| I am(z) | imaginary part of a complex number | z=a +Bi→ I am (z)=b | i am 32 years oldEU) = -2 |
| |z| | Absolute value/magnitude of a complex number | |z| = |a +Bi| = □(a 2+b2) | |3 - 2EU| = 13 |
| Arg(z) | Argument of a complex number | The angle of the ray in the complex plane | arg(3 + 2EU) = 33,7° |
| ∇ | nabla / del | Gradient/divergence operator | ∇f(x,j,z) |
| Vector | | |
| unit vector | | |
| x*j | folding | j(t) =x(t) *h(t) | |
| Laplace-Transformation | F(s) ={f(t)} | |
| Fourier-Transformation | x(oh) ={f(t)} | |
| d | Delta Function | | |
| ∞ | Lemniskata | infinity symbol | |
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