Exhaustive List of Mathematical Symbols and Their Meaning

Mathematical symbols and their meaning
Finding it difficult to recollect the exact meaning of a notation while solving mathematical equations? Don't worry, Buzzle 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, at Buzzle, 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
Plus
It signifies addition of values.
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.

Plus - minus/Minus - plus
It denotes, the value can be both plus and minus.
Modulo
It signifies finding the remainder of division of two numbers.

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

Nth root (radical)
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.

Spherical angle
It symbolizes the angle between two intersecting arcs of a sphere.
Right angle
It indicates the angle that bisects the angle formed by two straight lines.

Degree
It indicates the measurement of plane angle representing one full rotation.
Arcminute
It gives the angular measurement equal to 1/60 of one degree.

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.

Parallel
It indicates the lines that are equidistant from each other.
Congruent
It symbolizes the objects with similar geometric shape and size.

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

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

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Algebra Symbols

X variable
It signifies an unknown value.
Equivalence
It indicates variables having same or identical 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.

Weak approximation
It signifies variables that are weakly similar to each other.
Approximation
It symbolizes variables that are approximately equal to each other.

Lemniscate/Infinity symbol
It indicates a variable without any limit.
Factorial
It signifies the product of all integers less than or equal to n.

Much less than
It symbolizes one variable is much less than the other.
Much greater than
It indicates one variable is much greater than the other.

Floor brackets
It refers rounding the variable value to lower integer.
Ceiling brackets
It indicates rounding the variable value to higher integer.

Absolute value
It gives a non-negative value of x, ignoring its sign.
Function of
It defines one variable in relation to the other.

Function composition
It combines functions such that output from function becomes input for the other function.
Capital pi
It gives product of all values in the specified range.

Open interval
It symbolizes interval has no limits, i.e., without any end points.
Closed interval
It gives the interval with specified 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.

E constant / Euler's number
Its value is equal to 2.718281828...
Euler-Mascheroni constant
The constant is equal to 0.527721566...

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

Dot Product (Scalar)
It signifies multiplying magnitudes of vectors and cosine of angle between them.
Cross Product (Vector)
It refers to multiplying magnitudes of vectors and sin 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.

Matrix rank
It indicates the number of non-zero rows (or columns) in the reduced matrix.
Dimension
It gives the number of rows and columns of the matrix, written as rows x columns.

Probability & Statistics Symbols

Probability function
It signifies the likeliness of the occurrence of the event A.
Probability density function
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.

Population mean
It denotes the arithmetic mean of the population while considering each member of the population.
Expectation value
It denotes the expected value of random variable X.

Conditional expectation
It denotes the expected value of random variable X when the variable Y is given.
Variance
It expresses the spread of numbers of a given set.

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.

Median
It denotes the middle value of random variable X.
Covariance
It measures how much two random variables, X and Y, change together.

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

Normal (Gaussian) distribution
It indicates the probability of an observation falling between two real numbers.
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.

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.
Poisson distribution
It indicates the probability of a given number occurring in a fixed time interval and/or space, if the events occur with a given average rate.

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

Permutation
It signifies the possible arrangement of things in a particular order.
Combination
It indicates the possible arrangement of things without any particular order.

Set Theory

Set
It signifies the collection of distant elements.
Intersection
It indicates objects that belong to both sets, A and B.

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.

Proper subset
It indicates that subset A has fewer elements than the set B.
Not Subset
It signifies that A is not a subset of 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.

Equality
It signifies that sets A and B have same elements.
Complement
It represents objects that do not belong to set A.

Relative complement
It refers to objects that belong to set A but not to set B.
Symmetric difference
It indicates objects that belong to both sets A and B but not to their intersection.

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.

Ordered pair
It represents collection of elements of a set in a particular order.
Cartesian product
It gives the product of two sets.

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.

Empty set
It refers to set having no elements.
Universal set
It represents set having all possible values.

Natural/whole numbers set
It refers to set of whole/natural numbers with zero.
Integer numbers set
It indicates set of integer numbers.

Real numbers set
It refers to set of real numbers.
Complex numbers set
It represents set of complex 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.

Not - negation
It indicates negation of the given value.
Exclusive or (XOR)
It denotes exclusive disjunction where either of the operands should be true to return a true value.

Implies
It indicates material implication where true value is returned only if either of the operand is true or false.
Equivalent
It denotes material equivalence where true value is returned only when both operands are true or false.

There exists
It indicates existential quantification where function of the operand is true only for one value of operand.
There does not exists
It indicates existential quantification where function of the operand is true only for one value of operand.

Therefore
It is placed before a logical sequence indicating conclusion of the required operation.
Because/since
It is placed before a logical sequence indicating assumption or reason.

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

Calculus Symbols

Limit
It denotes the value that function approaches when input approaches specified value.
Epsilon
It represents a very small number nearing zero.

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.

Nth Derivative
It returns a value which is calculated by deriving the given function for n times.
Time derivative
It indicates change in the function with respect to change in time.

Partial Derivative
It denotes the value that is obtained by calculating derivative with respect to one variable, while other variables are constant.
Integral
It refers to antiderivative, and is the signed area of a region which is bounded by graph (definite integral).

Double integral
It denotes the integration of a function of two variables.
Triple integral
It denotes the integration of a function of three variables.

Closed contour / line integral
It denotes the integral of a function evaluated along a curve, i.e., with respect to arc length.
Imaginary unit
It indicates the square root of -1.

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.

Vector
It indicates quantity with magnitude and direction.
Unit vector
It signifies a vector with magnitude 1.

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.

Laplace transform
It indicates the linear operator of function f which transforms f(t) to F(s), with s being the complex argument
Fourier transform
It signifies the transformation of signals into time and frequency domains, i.e., breaks them into sines and cosines.

Greek Symbols

Alpha
Beta

Gamma
Delta

Epsilon
Zeta

Eta
Theta

Iota
Kappa

Lambda
Mu

Nu
Xi

Omicron
Pi

Rho
Sigma

Tau
Upsilon

Phi
Chi

Psi
Omega