## Exhaustive List of Mathematical Symbols and Their Meaning

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Like it? Share it! Finding it difficult to recollect the exact meaning of a notation while solving mathematical equations? Don’t worry, ScienceStruck is here to help you out. Here’s a list of mathematical symbols and their meaning, for your reference.

### Did You Know?

The first mathematical symbols to be used were ciphers. They were introduced even before the written language was introduced.

Mathematics or math is considered to be the language of science, vital to understanding and explaining science behind natural occurrences and phenomena. It also happens to be one of the most dreaded subjects of most students the world over. Utter the word mathematics and even grown ups are known to shudder at the mere mention of it! We shall not delve into the reasons for this, but the variety of symbols used in equations also happen to add to the dread. Each branch of mathematics has its own special symbols that represent a particular concept. Thus, it is necessary for you to at least have a ready reference list of these conventions so that you don’t mistake one for the other.

We have put forth a consolidated list of all the symbols used in various branches of mathematics. So, the next time you try to solve any math problem, you will at least know what the notations stand for!

## Basic Symbols

### Minus

It symbolizes subtraction of values.

### Multiplication

It signifies multiplication of values.

### Division

It denotes division of values.

### Equals

It signifies two sides are equal.

### Not Equal

It denotes two sides are unequal.

### Greater than

It shows one value is greater than the other.

### Less than

It implies one value is less than the other.

### Greater than or equal to

It symbolizes one value is greater than or equal to the other.

### Less than or equal to

It indicates one value is less than or equal to the other.

### Modulo

It signifies finding the remainder of division of two numbers.

### Plus – minus/Minus – plus

It denotes, the value can be both plus and minus.

### Parentheses

It implies calculation of the equation inside it should be carried out first.

### Brackets

[ ]
It indicates calculation of the equation inside it should be carried out first.

### Exponent

It signifies the number of times the number is used in multiplication.

### Square root

It symbolizes the value that can be multiplied by itself to give the original number.

### Cube root

It gives the value that can be multiplied by itself three times to give the original number.

### Fourth root

It is the value that can be multiplied by itself four times to give the original number.

It shows the value that can be multiplied by itself n times to give the original number.

### Percent

It signifies ratio expressed as a fraction of 100.

### Per-mille

It symbolizes number of parts per thousand.

### Per-million

It indicates number of parts per million.

### Per-billion

It signifies number of parts per billion.

### Per-trillion

It symbolizes number of parts per trillion.

## Geometric Symbols

### Angle

It indicates the figure formed by two rays.

### Measured angle

It signifies the angle whose value is known.

### Right angle

It indicates the angle that bisects the angle formed by two straight lines.

### Spherical angle

It symbolizes the angle between two intersecting arcs of a sphere.

### Arcminute

It gives the angular measurement equal to 1/60 of one degree.

### Degree

It indicates the measurement of plane angle representing one full rotation.

### Arcsecond

It signifies the angular measurement equal to 1/60 of one arcminute.

### Line

It shows the straight line with negligible width and thickness.

### Line segment

It signifies the part of line with definite start and endpoints.

### Ray

It indicates the line with start point but no endpoint.

### Arc

It signifies the part of circumference of circle or a curve.

### Perpendicular

It symbolizes lines that are at right angles to each other.

### Congruent

It symbolizes the objects with similar geometric shape and size.

### Parallel

It indicates the lines that are equidistant from each other.

### Similarity

It signifies objects with similar shape but not similar size.

### Triangle

It indicates polygon with three vertices and three line segments as edges.

### Distance

It symbolizes the distance between the points x and y.

It symbolizes the unit of plane angle measurement and is equal to 1/400 of 1 turn (360 deg).

### Pi

It gives the ratio between circumference and diameter of a circle.

It signifies the unit of angle measurement.

## Algebra Symbols

### Equivalence

It indicates variables having same or identical value.

### X variable

It signifies an unknown value.

### It symbolizes equality by definition.

It indicates variables that are equal by definition.

### Proportional

It signifies changes in variables that are always related to each other, using a constant.

### Approximation

It symbolizes variables that are approximately equal to each other.

### Weak approximation

It signifies variables that are weakly similar to each other.

### Factorial

It signifies the product of all integers less than or equal to n.

### Lemniscate/Infinity symbol

It indicates a variable without any limit.

### Much greater than

It indicates one variable is much greater than the other.

### Much less than

It symbolizes one variable is much less than the other.

### Ceiling brackets

It indicates rounding the variable value to higher integer.

### Floor brackets

It refers rounding the variable value to lower integer.

### Function of

It defines one variable in relation to the other.

### Absolute value

It gives a non-negative value of x, ignoring its sign.

### Capital pi

It gives product of all values in the specified range.

### Closed interval

It gives the interval with specified end points.

### Function composition

It combines functions such that output from function becomes input for the other function.

### Open interval

It symbolizes interval has no limits, i.e., without any end points.

### Delta

It refers to change or difference in values.

### Discriminant

It gives the nature of roots for a quadratic equation.

### Sigma (Summation)

It refers to summation of all values in the specified range.

### Double summation

It signifies summation of values in two ranges.

### Euler-Mascheroni constant

The constant is equal to 0.527721566…

### E constant / Euler’s number

Its value is equal to 2.718281828…

### Golden ratio constant

It indicates ratio of two variables should be equal to the ratio of their sum to the larger of the two variables.

## Linear Algebra Symbols

### Cross Product (Vector)

It refers to multiplying magnitudes of vectors and sin of angle between them.

### Dot Product (Scalar)

It signifies multiplying magnitudes of vectors and cosine of angle between them.

### Brackets

It indicates rectangular array of numbers arranged in rows and columns.

### Determinant

It gives the value associated with a square matrix.

### Norm

It assigns positive length (size) to each non-zero vector in space.

### Inverse matrix

It symbolizes the matrix whose multiplication with the original matrix is an identical matrix.

### Transpose

It refers to the matrix formed by replacing rows of the given matrix with columns and vice versa.

### Hermitian matrix

It signifies matrix with complex entries where the i-th row and j-th column is equal to complex conjugate of j-th row and i-th column.

### Dimension

It gives the number of rows and columns of the matrix, written as rows x columns.

### Matrix rank

It indicates the number of non-zero rows (or columns) in the reduced matrix.

## Probability & Statistics Symbols

### Probability function

It signifies the likeliness of the occurrence of the event A.

### Probability density function

f(x)
Integral of function of a continuous random variable gives the probability that the value of the variable lies in the given interval.

### Intersection

It denotes the probability of occurrence of events A and B.

### Union

It denotes the probability of occurrence of events A or B.

### Conditional probability function

It denotes the probability of occurrence of event A when event B has occurred.

### Cumulative distribution function

It denotes the probability that random variable X takes a values less than or equal to x.

### Expectation value

It denotes the expected value of random variable X.

### Population mean

It denotes the arithmetic mean of the population while considering each member of the population.

### Variance

It expresses the spread of numbers of a given set.

### Conditional expectation

It denotes the expected value of random variable X when the variable Y is given.

### Standard Deviation

It denotes the variation from the existing average value.

### Standard score

It indicates the number of standard deviations a variable is from the mean.

### Covariance

It measures how much two random variables, X and Y, change together.

### Median

It denotes the middle value of random variable X.

### Correlation

It denotes the statistical relationship between two random variables, X and Y.

### Mode

It signifies the most frequently occurring value in the given set.

### Mid-range

It signifies the arithmetic mean between the maximum and minimum value of the set.

### Sample median

It denotes the average of all the values of a given set.

### Lower / first quartile

It denotes the 25th percentile of the given set data.

### Median / second quartile

It denotes the median of the given set.

### Upper / third quartile

It denotes the 75th percentile of the given set data.

### Sample mean

It signifies the average of the given set data, i.e., the sum of the set data divided by number of entries in the set.

### Sample standard deviation

It indicates the standard deviation of the data set in the chosen sample size.

### Sample variance

It indicates the variance of the data set in the chosen sample size.

### Bernoulli distribution

It denotes the theoretical distribution of number of successes in a finite data set with constant probability of successes.

### Distribution of x

It indicates the distribution of random variable X.

### Uniform distribution

It indicates the probability that each value in the given data set has equal interval length in the given range from a to b.

### Normal (Gaussian) distribution

It indicates the probability of an observation falling between two real numbers.

### Exponential distribution

It signifies probability distribution which describes time between continuously occurring events at a constant average rate.

### Gamma distribution

It denotes the continuous two-parameter distribution from which chi-square and exponential distributions are derived.

### Chi-squared distribution

It signifies the distribution of sum of squares of k independent standard normal random variable.

### F distribution

It denotes probability distribution function, which is a ratio of two independent random variables, each of which has a chi-square distribution and is divided by number of degrees of freedom (k).

### Binomial distribution

It denotes the discrete probability distribution of the number of successes in n number of experiments, where each success is yielded by probability p.

### Geometric distribution

It signifies the negative binomial distribution which is used to find out the number of failures before single success.

### Hyper Geometric Distribution

It is used to calculate random selection of a variable without repetition.

## Combinatorics

### Combination

It indicates the possible arrangement of things without any particular order.

### Permutation

It signifies the possible arrangement of things in a particular order.

## Set Theory

### Intersection

It indicates objects that belong to both sets, A and B.

### Set

It signifies the collection of distant elements.

### Union

It refers to objects that belong to either set A or set B.

### Subset

It signifies few elements in the subset A are similar to the elements in set.

### Not Subset

It signifies that A is not a subset of the set B.

### Proper subset

It indicates that subset A has fewer elements than the set B.

### Superset

It symbolizes that set A has more or equal elements than set B.

### Proper Superset

It indicates that set A has more elements than set B.

### Complement

It represents objects that do not belong to set A.

### Equality

It signifies that sets A and B have same elements.

### Symmetric difference

It indicates objects that belong to both sets A and B but not to their intersection.

### Relative complement

It refers to objects that belong to set A but not to set B.

### Element of

It symbolizes that a is an element of set A.

### Not element of

It indicates that x is not an element of set A.

### Cartesian product

It gives the product of two sets.

### Ordered pair

It represents collection of elements of a set in a particular order.

### Aleph-null

It indicates infinite cardinality (number of elements of a set) of natural numbers set.

### Aleph-one

It signifies cardinality (number of elements of a set) of countable ordinal (well ordered) numbers set.

### Universal set

It represents set having all possible values.

### Empty set

It refers to set having no elements.

### Integer numbers set

It indicates set of integer numbers.

### Natural/whole numbers set

It refers to set of whole/natural numbers with zero.

### Complex numbers set

It represents set of complex numbers.

### Real numbers set

It refers to set of real numbers.

### Cardinality

It signifies the number of elements in set A.

## Logic Symbols

### And

It signifies logical conjunction where two true operands can only produce a true value.

### Or

It signifies logical disjunction where two false operands produce a false value.

### Exclusive or (XOR)

It denotes exclusive disjunction where either of the operands should be true to return a true value.

### Not – negation

It indicates negation of the given value.

### Equivalent

It denotes material equivalence where true value is returned only when both operands are true or false.

### Implies

It indicates material implication where true value is returned only if either of the operand is true or false.

### There does not exists

It indicates existential quantification where function of the operand is true only for one value of operand.

### There exists

It indicates existential quantification where function of the operand is true only for one value of operand.

### Because/since

It is placed before a logical sequence indicating assumption or reason.

### Therefore

It is placed before a logical sequence indicating conclusion of the required operation.

### For all

It signifies universal quantification where function of the operand is true for all values of the operand.

## Calculus Symbols

### Epsilon

It represents a very small number nearing zero.

### Limit

It denotes the value that function approaches when input approaches specified value.

### Derivative

It indicates change in the function when the input values change.

### Second derivative

It returns a value which is the derivative of the derivative of the given function.

### Time derivative

It indicates change in the function with respect to change in time.

### Nth Derivative

It returns a value which is calculated by deriving the given function for n times.

### Integral

It refers to antiderivative, and is the signed area of a region which is bounded by graph (definite integral).

### Partial Derivative

It denotes the value that is obtained by calculating derivative with respect to one variable, while other variables are constant.

### Triple integral

It denotes the integration of a function of three variables.

### Double integral

It denotes the integration of a function of two variables.

### Imaginary unit

It indicates the square root of -1.

### Closed contour / line integral

It denotes the integral of a function evaluated along a curve, i.e., with respect to arc length.

### Complex conjugate

It indicates the pair of complex numbers with same real part and imaginary part with equal magnitude but opposite signs.

### Nabla / del

It denotes the gradient and vector derivatives.

### Unit vector

It signifies a vector with magnitude 1.

### Vector

It indicates quantity with magnitude and direction.

### Convolution

It defines the integral of product of two functions when one function is reversed and shifted.

### Delta function

It is defined as the limit of a class of delta sequences.

### Fourier transform

It signifies the transformation of signals into time and frequency domains, i.e., breaks them into sines and cosines.

### Laplace transform

It indicates the linear operator of function f which transforms f(t) to F(s), with s being the complex argument.