Most people have seen or are aware of welding. It is the process of joining two metal parts. However, owing to its extensive use, providing information about the type and…
Exhaustive List of Mathematical Symbols and Their Meaning
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!
It signifies addition of values.
It symbolizes subtraction of values.
It signifies multiplication of values.
It denotes division of values.
It signifies two sides are equal.
It denotes two sides are unequal.
It shows one value is greater than the other.
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.
It signifies finding the remainder of division of two numbers.
Plus – minus/Minus – plus
It denotes, the value can be both plus and minus.
It implies calculation of the equation inside it should be carried out first.
It indicates calculation of the equation inside it should be carried out first.
It signifies the number of times the number is used in multiplication.
It symbolizes the value that can be multiplied by itself to give the original number.
It gives the value that can be multiplied by itself three times to give the original number.
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.
It signifies ratio expressed as a fraction of 100.
It symbolizes number of parts per thousand.
It indicates number of parts per million.
It signifies number of parts per billion.
It symbolizes number of parts per trillion.
It indicates the figure formed by two rays.
It signifies the angle whose value is known.
It indicates the angle that bisects the angle formed by two straight lines.
It symbolizes the angle between two intersecting arcs of a sphere.
It gives the angular measurement equal to 1/60 of one degree.
It indicates the measurement of plane angle representing one full rotation.
It signifies the angular measurement equal to 1/60 of one arcminute.
It shows the straight line with negligible width and thickness.
It signifies the part of line with definite start and endpoints.
It indicates the line with start point but no endpoint.
It signifies the part of circumference of circle or a curve.
It symbolizes lines that are at right angles to each other.
It symbolizes the objects with similar geometric shape and size.
It indicates the lines that are equidistant from each other.
It signifies objects with similar shape but not similar size.
It indicates polygon with three vertices and three line segments as edges.
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).
It gives the ratio between circumference and diameter of a circle.
It signifies the unit of angle measurement.
It indicates variables having same or identical value.
It signifies an unknown value.
It symbolizes equality by definition.
It indicates variables that are equal by definition.
It signifies changes in variables that are always related to each other, using a constant.
It symbolizes variables that are approximately equal to each other.
It signifies variables that are weakly similar to each other.
It signifies the product of all integers less than or equal to n.
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.
It indicates rounding the variable value to higher integer.
It refers rounding the variable value to lower integer.
It defines one variable in relation to the other.
It gives a non-negative value of x, ignoring its sign.
It gives product of all values in the specified range.
It gives the interval with specified end points.
It combines functions such that output from function becomes input for the other function.
It symbolizes interval has no limits, i.e., without any end points.
It refers to change or difference in values.
It gives the nature of roots for a quadratic equation.
It refers to summation of all values in the specified range.
It signifies summation of values in two ranges.
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.
It indicates rectangular array of numbers arranged in rows and columns.
It gives the value associated with a square matrix.
It assigns positive length (size) to each non-zero vector in space.
It symbolizes the matrix whose multiplication with the original matrix is an identical matrix.
It refers to the matrix formed by replacing rows of the given matrix with columns and vice versa.
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.
It gives the number of rows and columns of the matrix, written as rows x columns.
It indicates the number of non-zero rows (or columns) in the reduced matrix.
Probability & Statistics Symbols
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.
It denotes the probability of occurrence of events A and B.
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.
It denotes the expected value of random variable X.
It denotes the arithmetic mean of the population while considering each member of the population.
It expresses the spread of numbers of a given set.
It denotes the expected value of random variable X when the variable Y is given.
It denotes the variation from the existing average value.
It indicates the number of standard deviations a variable is from the mean.
It measures how much two random variables, X and Y, change together.
It denotes the middle value of random variable X.
It denotes the statistical relationship between two random variables, X and Y.
It signifies the most frequently occurring value in the given set.
It signifies the arithmetic mean between the maximum and minimum value of the set.
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.
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.
It indicates the variance of the data set in the chosen sample size.
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.
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.
It signifies probability distribution which describes time between continuously occurring events at a constant average rate.
It denotes the continuous two-parameter distribution from which chi-square and exponential distributions are derived.
It signifies the distribution of sum of squares of k independent standard normal random variable.
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).
It denotes the discrete probability distribution of the number of successes in n number of experiments, where each success is yielded by probability p.
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.
It indicates the possible arrangement of things without any particular order.
It signifies the possible arrangement of things in a particular order.
It indicates objects that belong to both sets, A and B.
It signifies the collection of distant elements.
It refers to objects that belong to either set A or set B.
It signifies few elements in the subset A are similar to the elements in set.
It signifies that A is not a subset of the set B.
It indicates that subset A has fewer elements than the set B.
It symbolizes that set A has more or equal elements than set B.
It indicates that set A has more elements than set B.
It represents objects that do not belong to set A.
It signifies that sets A and B have same elements.
It indicates objects that belong to both sets A and B but not to their intersection.
It refers to objects that belong to set A but not to set B.
It symbolizes that a is an element of set A.
Not element of
It indicates that x is not an element of set A.
It gives the product of two sets.
It represents collection of elements of a set in a particular order.
It indicates infinite cardinality (number of elements of a set) of natural numbers set.
It signifies cardinality (number of elements of a set) of countable ordinal (well ordered) numbers set.
It represents set having all possible values.
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.
It signifies the number of elements in set A.
It signifies logical conjunction where two true operands can only produce a true value.
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.
It denotes material equivalence where true value is returned only when both operands are true or false.
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.
It indicates existential quantification where function of the operand is true only for one value of operand.
It is placed before a logical sequence indicating assumption or reason.
It is placed before a logical sequence indicating conclusion of the required operation.
It signifies universal quantification where function of the operand is true for all values of the operand.
It represents a very small number nearing zero.
It denotes the value that function approaches when input approaches specified value.
It indicates change in the function when the input values change.
It returns a value which is the derivative of the derivative of the given function.
It indicates change in the function with respect to change in time.
It returns a value which is calculated by deriving the given function for n times.
It refers to antiderivative, and is the signed area of a region which is bounded by graph (definite integral).
It denotes the value that is obtained by calculating derivative with respect to one variable, while other variables are constant.
It denotes the integration of a function of three variables.
It denotes the integration of a function of two variables.
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.
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.
It signifies a vector with magnitude 1.
It indicates quantity with magnitude and direction.
It defines the integral of product of two functions when one function is reversed and shifted.
It is defined as the limit of a class of delta sequences.
It signifies the transformation of signals into time and frequency domains, i.e., breaks them into sines and cosines.
It indicates the linear operator of function f which transforms f(t) to F(s), with s being the complex argument.