# Notation

This is a collection of pages that document how math is written.

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

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

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.

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

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

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.

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 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.

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

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.

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.

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

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

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

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

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.

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

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

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.

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.

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

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

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

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

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

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.

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

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 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.

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.

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

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

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.

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

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.

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

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

A proper subset is denoted by the symbol ⊂

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 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.

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

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

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.

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.

Congruent angles are denoted with tick marks across the angle.

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

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

A line is written as two letter with a line overtop, where the letters represent the end points of the line.

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 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.

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°.

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

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

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

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.