Notation

A collection of math syntax and notation. The pages demonstrate the usage of symbols, expressions, and operators to represent mathematical concepts. See the order of operations to see how mathematicians disambiguate how expressions are evaluated.

Arithmetic

Addition

In mathematics the plus symbol represents addition between two numbers. Addition is the process of combining two things together.

Subtraction

In mathematics the minus symbol represents the subtraction operator. The expression on the right is subtracted from the expression on the left.

Multiplication

A dot between two numbers denotes multiplication in mathematics. The formal name for the dot symbol is an interpunct.

Division

In mathematics there are multiple different ways to represent division. The obelus is often used in elementary mathematics, then later the horizontal bar is adopted for convenience, and the forward slash is used because of the prevelence of computers and calculators.

Grouping

In mathematics parentheses are used to group expressions to be evaluated together and organize the order of operations. Everything within the parantheses is evaluated, then the rest of the calculation is carried out.

Multiplication Parentheses

Two expressions placed next to eachother and separated by parenthesis are assumed to be multiplied together.

Multiplication Variables

In mathematics when two variables are next to each other the implied operation is multiplication. This makes many equations and formulas more simple.

Fraction

A fraction is represented using a horizontal bar between two expressions. The expression on top is called the numerator and the expression on bottom is called the denominator.

Decimal Point

The decimal point is used to separate the whole part of a number from the decimal part. The whole part is represented using number digits to the left of the decimal point. The decimal part is also represented using digits to the right of the decimal point.

Ratio

The syntax for a ratio is two numbers separated by the colon symbol.

Algebra

Function

In mathematics functions are denoted using the name of the function followed by parentheses which contain the input to the function. If the function has multiple inputs they are separated by a comma.

Slope

Slope is denoted as the change in y over the change in x. The capital greek letter delta (Δ) is used to represent the change in a variable.

Absolute Value

The notation for taking the absolute value is two vertical lines on either side of the expression being evaluated.

Factorial

The exclamation mark is used to represent the factorial of a number in mathematics. A factorial is a unary operator.

Exponent

In mathematics superscript text is used to indicate the exponent of some number.

Logarithm

Logarithms are often abreviated as "log" followed by a subscript number representing the base and the number that the logarithm is being applied to.

Radical

A radical is used to represent fractional exponents. By itself it is used to represent the square root of an expression, but it also is used to represent higher roots as well.

Square Root

The radical symbol by itself is used to denote taking the square root of a number.

Summation

The summation operator is represented by the ∑ (capital sigma) and represents the operation of summing a sequence of expressions together.

Product

The capital Greek letter Pi is used to represent the product operator in mathematics. The operator has three parts: an initial value, an end value, and the expression being evaluated.

Logic

Equal

Two stacked horizontal lines respresents the equals symbol in mathematics. The two expressions on either side are equal, or the same, when the equal sign is placed in between them.

Greater Than

The symbol > represents the logical expression that the left side is greater than the right side.

Greater Than or Equal

The greater than or equal to symbol represents two expressions that

Less Than

The symbol < represents the logic expression that the left side is less than the right side.

Less Than or Equal

The symbol for a less than or equal to is ≤. It combines the less than symbol < and the equals symbol = together.

Not Equal

The symbol for not equal is a equal sign with a diagonal line through it.

Approximately

The symbol for approximately equal is a squiggly equals sign. It is used to show that two numbers are roughly equal, but not exactly equal.

Geometry

Slope

Slope is denoted as the change in y over the change in x. The capital greek letter delta (Δ) is used to represent the change in a variable.

Cartesian Coordinate System

A point in the cartesian coordinate system is denoted by two numbers in parentheses separated by a comma. The first number represents the distance from origin in the x-direction and teh second number represents the distance from the origin in the y-direction.

Polar Coordinate System

A point in the polar coordinate system is denoted by two numbers in parentheses separated by a comma. The first number represents the radius r (distance from the origin) and an angle θ (the greek letter theta) relative to the origin.

Angle

The notation for a symbol is a small symbol written in text, sometimes followed by three letters that correspond to a figure.

Circle

A circle in text is denoted using the circle symbol with a dot in the center followed by a letter that corresponds to the center point of the circle.

Complementary Angles

Complementary angles can visually be denoted as two angles who sum to a perpendicular or square angle.

Congruent Angles

Congruent angles are denoted with tick marks across the angle.

Line

A line is denoted by two letters representing the start and end of the line with a line over top.

Parallel Lines

Parallel lines are denoted by the parallel symbol placed betwen the notation of the two lines. A line is denoted by the start and end letter with a line over top.

Perpendicular Angle

A perpendicular angle is visually denoted by drawing a square at the vertex of the angle. The measured angle is equal to π/2 radians or 90°.

Perpendicular Lines

The symbol for two perpendicular lines is a horizontal line with another line drawn perpendicular to it.

Supplementary Angles

Supplementary angles can visually be denoted as two angles who sum to 180 degrees or PI degrees.

Triangle

A triangle is denoted using the triangle symbol followed by three letters that represent the points of the triangle.

Trigonometry

Angle

The notation for a symbol is a small symbol written in text, sometimes followed by three letters that correspond to a figure.

Line

A line is denoted by two letters representing the start and end of the line with a line over top.

Perpendicular Angle

A perpendicular angle is visually denoted by drawing a square at the vertex of the angle. The measured angle is equal to π/2 radians or 90°.

Perpendicular Lines

The symbol for two perpendicular lines is a horizontal line with another line drawn perpendicular to it.

Triangle

A triangle is denoted using the triangle symbol followed by three letters that represent the points of the triangle.

Probability

Random Variable

In probability a random variable is denoted using capital latin letters usually X, Y, and Z or A, and B respectively.

Probability Distribution

A probability distribution is denoted like a function. Often a capital P is used for the function name, and the capital letter X is used for the argument to the function.

Conditional Probability

Conditional probability is denoted using a vertical bar between the two variables

Joint Distribution

A joint probability distribution is denoted like a function often using P as the function name. The capital letters X and Y are often used to represent the random variables of the distribution and are arguments to the function.

Expected Value

The expected value of a probability distribution is denoted as the function E(X).

Arithmetic Mean

The arithmetic mean of a data set is denoted by a horizontal bar over the variable x.

Combinations

The number of possible ways to choose r combinations from n total items is denoted using two parentheses with the n value above the r value. A subscript p or c is used to denote whether it is a combination or permutation.

Permutations

The number of possible ways to choose r permutations from n total items is denoted using two parentheses with the n value above the r value. A subscript p or c is used to denote whether it is a combination or permutation.

Numbers

Set of Natural Numbers

This page explains the notation for the set of natural numbers

Eulers Number

Euler's Number is represented in mathematics with the letter e and has some unique exponential properties.

Pi

The greek letter pi is a number in mathematics that describes the ratio a circle's circumference divided by its diamater.

Set of Integers

This page explains the notation for the set of integers.

Set of Rational Numbers

This page explains the notation for the set of rational numbers

Tau

The symbol tau is used in mathematics to represent the ratio of the circumeference of the circle divided by its radius.

Set of Real Numbers

This page explains the notation for the set of real numbers

2D Space

Two dimensional space is denoted using the symbol for the set of real numbers followed by a superscript two.

3D Space

Three dimensional space is denoted using the symbol for the set of real numbers followed by a superscript three.

Complex Number

A complex number is represented in two parts. The first is the real number part and the second is the imaginary number part.

Decimal Point

The decimal point is used to separate the whole part of a number from the decimal part. The whole part is represented using number digits to the left of the decimal point. The decimal part is also represented using digits to the right of the decimal point.

Set of Complex Numbers

The set of complex numbers is denoted using the Latin capital letter C most often presented with a double-struck typeface.

Scientific Notation

Scientific notation is a notation that scientists use to keep track of the number of significant digits in a number as well as easily recognize the magnitude of a number.

Imaginary Number

The letter i is used in mathematics to represent the square root of negative one.

Set Theory

Empty Set

An empty set is respresented as a zero with a diagonal line through it, or as an empty pair of curly braces.

Set

The notation for a set is two curly braces containing the elements of the set separated by commas.

Exists

The syntax for "there exists" is a backwards captial E. It is often used in conjuction with a variable with certain properties.

For All

The ∀ (for all) symbol is used in math to describe the meaning of one or more variables in a statement.

Element of

The element of symbol describes membership to a set. When reading an equation the symbol can be read as "in" or "belongs to".

Proper Subset

A proper subset is denoted by the subset symbol which looks like a U rotated ninety degrees to the right.

Proper Superset

A proper superset is denoted by the superset symbol which looks like a U rotated ninety degrees to the left.

Such That

The colon symbol is used in math to denote a condition for a statement. The symbol can be read as "such that" in a math expression.

Superset

The superset operator in set theory is denoted using the superset symbol which looks like a U turned ninety degrees counter clockwise with a horizontal line underneath.

Subset

The subset operator is denoted using a U shapes symbol rotated ninety degrees to the righ with a horizontal line underneath.

Intersection

The cap symbol is used in mathematics to represent the intersect operation for two sets.

Set Difference

The minus symbol is used in set theory to represent the difference operator for two sets. The operation removes all elements found in one set from another and returns the resulting set.

Union

The cup symbol is used in mathematics to represent the union operation for two sets. The union operator returns a set containing the elements from both sets.

Boolean Logic

And

The "and" operator is denoted with the carrot symbol, which looks like a equilateral triangle with no bottom side. The operator evaluates to true if both the left and right expressions are true, otherwise evaluates to false.

Equal

Two stacked horizontal lines respresents the equals symbol in mathematics. The two expressions on either side are equal, or the same, when the equal sign is placed in between them.

Or

The logical or symbol describes when either one thing is true, the other thing is true, or both is true.

Equivalent

The equivalent operator is used to express that two expressions are equivalent, although not necassarily equal.

Implies

The boolean operator for implication is denoted using a double arrow pointing to the right.

Negation

The negation symbol is used to reperesent the unary operator for negation, which inverts the value of the expression it is applied to.

Xor

Xor is the boolean operator that describes the operation of exclusive or.

Linear Algebra

Vector

A variable that represents a vector often has an arrow over the top to indicate that it is a vector.

Magnitude

To vertical bars on either side of a vector represent taking the magnitude or length of that vector

Cross Product

In linear algebra the cross product operator is the times operator that is used in elementary mathematics.

Matrix

In Linear Algebra, a m by n matrix is denoted as a grid of numbers with two brackets on either side. The variable m corresponds to the number of rows, and the variable n corresponds to the number of columns.

Determinant

The syntax for a determinant is to vertical bars on either side of the matrix.

Scalar Product

The syntax for a scalar product is to angle brackets on either side of two vectors separated by a comma.

Calculus

Limit

The syntax for a limit is a the abbreviation "lim" followed an expression. Underneath the letters "lim" is the value the variable approaches within the expression denoted as the variable with an arrow to the value it is approaching.

Antiderivative

The antiderivative of a function is denoted using the capital Latin letter F.

Derivative

The first derivative of a function is denoted by a apostrophe after the function name. Alternatively the partial symbol can be used to represent the derivative with respect to a variable.

Integral

The notation for an integral in mathematics is a slanted vertical line with a start and end value that describe the range of the integral. This is followed by the function being integrated and the variable with respect to which the integral is being evaluated.

Gradient

The nabla symbol is used to represent taking the gradient of a function.

Computing

Division Computing

When entering an equation into a calculator or the computer the forward slash is used to represent division.

Exponent Computing

When computing an expression which contains the exponent operator, the caret symbol is often used in place of what normally would be superscript text.

Multiplication Computing

When entering an expression in a computer multiplication is represented using the asterisk symbol.

Subtraction Computing

In computing subtraction is denoted using the hyphen symbol.

Array

An array is common data structure used throughout programming and computing.