Notation

Addition is a fundamental arithmetic operation represented by the plus symbol (+). It combines two or more numbers into a single numerical value.

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

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

In math, we write division using a horizontal bar between the numerator and denominator.

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

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 and the decimal part is represented using digits to the right of the decimal point.

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.

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

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

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

In math, we use the √ symbol to represent the square root and the n-th root of an expression.

A set is written with curly braces containing the elements of the set separated by commas.

An empty set, also called the null set, is represented as a zero with a diagonal line through it or as an empty pair of curly braces.

A function is written as the function's name followed by parentheses containing the input to the function. If the function has multiple inputs they are separated by a comma.

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

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

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

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

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.

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

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.

The summation operator is written with the N-Ary Summation symbol (∑) and represents sum of a sequence of expressions.

The N-ary product symbol (∏) represents the product operator in math. The operator has three parts: an initial value, an end value, and the evaluated expression.

A line is written as two letters with a double-headed arrow overtop, where the letters name two points the line passes through.

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

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

When referring to a circle in a diagram the symbol ⊙ (odot) is used followed by the variable associated with the center point of the circle. For example, ⊙P would mean the circle whose center is located at the point P.

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

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

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°.

Congruent angles are denoted with tick marks across the angle.

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 the origin in the x-direction and the second number represents the distance from the origin in the y-direction.

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.

Euler's number is shorthand for the exponential function. Euler's number is also related to the numeric value 2.718... This site considers the notation primarily as shorthand for the exponential function.

The syntax for a limit is the abbreviation "lim" followed by 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.

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

An antiderivative of a function f(x) is represented by a function F(x) such that the derivative of F(x) is f(x). Essentially, an antiderivative reverses the process of differentiation.

The integral operator is written using the integral symbol ∫ and has four parts: the expression being integrated, the differential, and start value and an end value.

A vector has many notations in math. When written as a variable it often has an arrow over top. When written as a column vector the components are arranged vertically with brackets.

In math, the magnitude of a vector typically appears with two vertical bars on either side.

The syntax for a dot product is a dot between the two vectors.

In linear algebra, the cross product of two vectors is written using the times symbol (×).

In linear algebra, a matrix is denoted as a grid of expressions 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.

The determinant of a matrix is denoted by placing the matrix entries between vertical bars, similar to the absolute value notation for numbers.

The number of combinations of r items chosen from n total items is written as the two values stacked inside parentheses with a subscript c.

The number of permutations of r items chosen from n total items is written as the two values stacked inside parentheses with a subscript p.

A subset is denoted by the symbol ⊂ and is used to indicate that one set is a subset of another set, but not equal to it.

The subset or equal symbol ⊆ is used in math to denote that one set is a subset of another set or is equal to another set.

A superset is denoted by the superset symbol ⊃ and is used to indicate that one set is a superset of another set, but not equal to it.

The superset or equal symbol ⊇ is used in math to denote that one set is a superset of another set or is equal to another set.

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.

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

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