# Math Symbols Reference Chart

Below you'll find a list of all mathematical symbols together with their meaning and examples.

## Basic Math Symbols

Symbol | Name | Description | Example / Definition |
---|---|---|---|

equals sign | equality between two expressions | ||

not equal sign | inequality between two expressions | ||

approximately equal | very similar to but not exactly equal due to | ||

strict inequality | less than | ||

strict inequality | greater than | ||

inequality | greater than or equal to | ||

inequality | less than or equal to | ||

parentheses | calculations in parentheses are performed first | ||

brackets | calculations in brackets are performed first | ||

plus | addition | ||

minus | subtraction | ||

plus - minus | both plus and minus operations in one equation | ||

minus - plus | both plus and minus operations in one equation | ||

times | multiplication | ||

asterisk | multiplication | ||

obelus | division | ||

slash | division | ||

vinculum | fraction bar | ||

modulo | remainder operator | ||

interpunct / dot product | multiplication | ||

power | exponent | ||

caret | exponent | ||

radical | square root | ||

cube root | number which produces a given number when cubed | ||

fourth root | a number, which when multiplied four times by itself the original number will be obtained | ||

n-th root (radical) | nth root of a number x, where n is a positive integer, is any of the n real or complex numbers r whose nth power is x | ||

percent | by a specified amount in or for every hundred | ||

per-mille | by a specified amount in every thousand | ||

per-million | by a specified amount in every million | ||

per-billion | by a specified amount in every billion | ||

per-trillion | by a specified amount in every trillion |

## Geometry Math Symbols

Symbol | Name | Description | Example / Definition |
---|---|---|---|

angle | geometrical figure formed when two rays meet at a common point called vertex | ||

measured angle | an angle with a known size | ||

spherical angle | angle formed by three great circles on a sphere | ||

right angle | if two straight lines intersect each other at 90˚ they form a right angle | ||

degree | represents degrees of an arc | ||

degree | represents degrees of an arc | ||

prime | arcminute | ||

double prime | arcsecond | ||

line | infinite line | ||

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

ray | line that starts at point A | ||

arc | arc from point A to point B | ||

perpendicular | perpendicular lines | ||

parallel | parallell lines | ||

congruent to | equivalence of geometric size and shape | ||

similarity | same shape but not same size | ||

triangle | closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices | ||

distance | distance between points x and y | ||

pi constant | ratio between the circumference and diameter of a circle | ||

radians | one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius | ||

radians | one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius | ||

gradians / gons | unit of angular measure in which the angle of an entire circle is 400 gradians | ||

gradians / gons | unit of angular measure in which the angle of an entire circle is 400 gradians |

## Algebra Math Symbols

Symbol | Name | Description | Example / Definition |
---|---|---|---|

x variable | An unknown or variable value | ||

Equivalence | Identical to | ||

Equal by definition | Equal by definition | ||

Equal by definition | Equal by definition | ||

Approximately equal | Approximation | ||

Approximately equal | Asymptotic equivalence | ||

Proportional to | Proportional to | ||

Lemniscate | Infinity | ||

Much less-than | Much less-than | ||

Much greater-than | Much greater-than | ||

parentheses | calculations in parentheses are performed first | ||

brackets | calculations in brackets are performed first | ||

braces | Defines a set | ||

delta | difference | ||

discriminant | parameter of an object or system calculated as an aid to its classification or solution | ||

sigma | summation of the numbers indicated | ||

sigma | double summation of the numbers indicated | ||

floor brackets | rounds the number down to the lower integer | ||

ceiling brackets | rounds the number up to the higher integer | ||

factorial | product of all integer values up to the provided number | ||

absolute value | the distance from zero that a number is on the number line, without considering direction | ||

function of x | calculate the value of the function substituting x with the provided value | ||

functional composition | The result of function f is passed to function g | ||

open interval | interval that doesn't include its endpoints | ||

closed interval | interval that includes its endpoints | ||

capital pi | product of all the numbers indicated | ||

Euler's number | The irrational number represented by the letter e | ||

Euler's constant / Euler-Mascheroni constant | The limiting difference between the harmonic series and the natural logarithm. Approximately 0.5772156649. | ||

golden ratio | Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Approximately 1.618033988749894 | ||

pi constant | The ratio of a circle's circumference to its diameter. Approximately 3.14159. |

## Linear Algebra Math Symbols

Symbol | Name | Description | Example / Definition |
---|---|---|---|

dot | scalar product | ||

multiplication / times | multiplication of vectors | ||

tensor product | multiplication of vectors | ||

inner product | how much of one vector is pointing in the direction of another one | ||

parentheses | matrix of values | ||

brackets | matrix of values | ||

determinant | scalar value or number calculated using a square matrix | ||

determinant | scalar value or number calculated using a square matrix | ||

double vertical bars | norm | ||

transpose | transposed matrix A | ||

Hermitian matrix | conjugate transposition of matrix A | ||

Hermitian matrix | conjugate transposition of matrix A | ||

inverse matrix | |||

matrix rank | rank of the matrix | ||

dimension | dimension of the matrix |

## Statistics & Probability Math Symbols

Symbol | Name | Description | Example / Definition |
---|---|---|---|

probability function | the probability of event A | ||

probability of intersection of events | the probability of events A and B | ||

probability of union of events | the probability of events A or B | ||

conditional probability | the probability of event a given event B | ||

probability density function | |||

cumulative distribution function | |||

population mean (mu) | mean of population values | ||

expectation value | expected value of a random variable X | ||

considitional expectation | expected value of a random variable X given value Y | ||

variance | variance of a random value X | ||

variance | variance of a population of values | ||

standard deviation | the amount of variation of a set of values | ||

standard deviation | the amount of variation of a set of values | ||

median | the middle value in an ordered set of numbers | ||

covariance | covariance of variables X and Y | ||

correlation | correlation of variables X and Y | ||

pearson correlation | pearson correlation of variables X and Y | ||

summation | sum of all values in the denoted series | ||

double summation | double summation | ||

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

mid-range | |||

sample median | the value separating the higher half from the lower half of a data sample | ||

first quartile | 25% of the population is below the first quartile | ||

second quartile | 50% of the population is below the second quartile | ||

third quartile | 75% of the population is below the third quartile | ||

sample mean | arithmetic mean / average | ||

sample variance | estimates the variance in a sample | ||

sample standard deviation | estimates the standard deviation in a sample | ||

standard score | |||

distribution of X | distribution of X | ||

normal distribution | guassian distribution | ||

uniform distribution | equal probability in the range [a,b] | ||

exponential distribution | exponential distribution | ||

chi-square definition | chi-square definition | ||

F-distribution | F-distribution | ||

binomial distribution | binomial distribution | ||

Poisson distribution | Poisson distribution | ||

geometric distribution | geometric distribution | ||

hypergeometric distribution | hypergeometric distribution | ||

bernoulli distributions | discrete probability distribution where every experiment conducted asks a question that can be answered only in yes or no. |

## Combinatorics Math Symbols

Symbol | Name | Description | Example / Definition |
---|---|---|---|

factorial | product of all integer values up to the provided number | ||

permutation | an arrangement of its members into a sequence or linear order | ||

combination | selection of items from a set that has distinct members, such that the order of selection does not matter |

## Set Theory Math Symbols

Symbol | Name | Description | Example / Definition |
---|---|---|---|

set | collection of elements | ||

intersection | elements that belong to both sets A and B | ||

union | elements that belong to sets A or B | ||

subset | set A is a subset of, or equal to set B | ||

strict subset | set A is a subset of, but not equal to set B | ||

not a subset | set A is a not a subset of set B | ||

strict superset | set A is a superset of, or equal to set B | ||

superset | set A is a superset of, but not equal to set B | ||

not superset | set A is not a superset of set B | ||

power set | all subsets of S | ||

power set | all subsets of S | ||

equality | A and B have the same members | ||

complement | the set of objects that do not belong to set A | ||

relative complement | the set of objects that belong to set A but not to set B | ||

relative complement | the set of objects that belong to set A but not to set B | ||

symmetric difference | the set of objects that belong to set A or set B but not their intersection | ||

symmetric difference | the set of objects that belong to set A or set B but not their intersection | ||

set membership | an element x belongs to set A | ||

no set membership | an element x does not belong to set A | ||

ordered pair | a collection of 2 ordered elements | ||

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

cardinality | the number of elements in set A | ||

cardinality | the number of elements in set A | ||

vertical bar | such that | ||

aleph-null | infinite cardinality of the set of natural numbers | ||

aleph-one | cardinality of countable ordinal set of numbers | ||

empty set | empty set | ||

universal set | set of all possible values | ||

all natural numbers including zero | |||

all natural numbers excluding zero | |||

set of all integers | |||

set of all rational numbers | |||

set of all real numbers | |||

set of all complex numbers |

## Logic Math Symbols

Symbol | Name | Description | Example / Definition |
---|---|---|---|

and | conjunction operator | ||

circumflex / caret | conjunction operator | ||

and | conjunction operator | ||

plus | or operator | ||

inverse circumflex / caret | or operator | ||

vertical line | or operator | ||

prime | negation | ||

bar | negation | ||

not | negation | ||

not | negation | ||

circled plus | xor / exclusive or | ||

tilde | negation | ||

implies | logically implies | ||

equivalent | if and only if | ||

equivalent | if and only if | ||

for all | for any; for each | ||

there exists | there exists | ||

therefore | logical consequence | ||

because | signals reasoning | ||

Domain of discourse | Domain of predicate |

## Calculus Math Symbols

Symbol | Name | Description | Example / Definition |
---|---|---|---|

limit | limit value of a function | ||

epsilon | a very small, near zero value | ||

Euler's constant | e ≈ 2.7182818284 | ||

derivative | derivative using Lagrange's notation | ||

second derivative | derivative of a derivative using Lagrange's notation | ||

nth derivative | derivative applied n-times using Lagrange's notation | ||

derivative | derivative using Leibniz's notation | ||

second derivative | second derivative using Leibniz's notation | ||

nth derivative | nth derivative using Leibniz's notation | ||

time derivative | time derivative using Newton's notation | ||

second time derivative | second time derivative using Newton's notation | ||

nth time derivative | nth time derivative using Newton's notation | ||

derivative | derivative using Euler's notation | ||

second derivative | second derivative using Euler's notation | ||

partial derivative | derivative of a function of two or more variables with respect to one variable | ||

integral | opposite operation to derivation | ||

double integral | the integral of a function of two variables | ||

triple integral | the integral of a function of three variables | ||

line integral / closed integral | integral where the function to be integrated is evaluated along a curve | ||

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

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

closed interval | |||

open interval | |||

imaginary unit | |||

complex conjugate | |||

complex conjugate | |||

real part of a complex number | |||

imaginary part of a complex number | |||

absolute value / magnitude of a complex number | |||

argument of a complex number | the angle of the radius in the complex plane | ||

nabla / del | gradient operator / divergence operator | ||

vector | a quantity that has both magnitude and direction | ||

unit vector | vector which has a magnitude of one | ||

convolution | operation on two functions that produces a third function that expresses how the shape of one is modified by the other | ||

Laplace transform | converts differential equations into purely algebraic equations | ||

Fourier transform | function derived from a given function and representing it by a series of sinusoidal functions | ||

delta function | tool for the normalization of state vectors | ||

lemniscate | infinity symbol |