# Operators

Math operators define the basic operations that act on numbers and other such math constructs. Typically, operators take between one and two numbers as input and return a number as output.

## Basic Operators

The basic arithmetic operators are addition, subtraction, multiplication, and division. They are typically introduced in elementary mathematics and describe the basic manipulation of numbers. As the notion of a number becomes more complex, the details of how they work are expanded to include the ability to work on more complex numbers. For example, in algebra the operators are expanded to work on fractions as well as the regular counting numbers.

Addition is a basic operation in mathematics for combining two numbers together. It is a binary operation denoted with the plus symbol with an expression on the left and an expression on the right.

Subtraction | Operator

Subraction is a basic arithmetic operation of taking away one number from another number.

Multiplication | Operator

Multiplication is a basic arithmetic operation performed on two numbers. Multiplying a number by another number is the same as taking n groups of the other number.

Division | Operator

Division is the process of dividing a number into equal parts.

These advanced operatores cover some more complicated patterns that appear in mathematics. For example, the factorial operator represents the patterns found in combinations and permutations. Another example is the exponent and logarithm operators which describe expoenential growth and decay.

The radical operator returns the n-th root of the provided expression. The radical operator is an alternative way of writing a fractional exponent.

Exponentiation | Operator

The exponentiation operator is a binary operator. The base is an expression or number that is being raised to some exponent. The exponent expression is denoted using superscript text.

Logarithm | Operator

Taking the logarithm of an number is the inverse operation of exponentiation. The subscript number is the base of the logarithm and the expression is the operand.

Factorial | Operator

The factorial operator is represented using the exclamation mark. The operator is unary, meaning that it only operates on one expression. The operator is useful when calculating combinations and permutations.

Modulus | Operator

The modulus operator returns the remainder of dividing the first expression by the second expression.

Summation | Operator

The capital letter Sigma Σ represents the summation operation in mathematics, often called sum for short. A sum has three parts: an initial value, an end value, and the expression being summed. The summation starts at the initial value and iterates, adding one to the value for each iteration, stopping when the value reaches the end value.

Product | Operator

The product operator multiplies the expression starting at an initial value, incrementing by one for each sub-expression, and ending at the end value.

## Boolean Logical Operators

The boolean logic operators operate on boolean expressions - values that are either true or false. Typically, the binary boolean operators take in two boolean values and return a boolean value as a result. In computing, numbers and more complex data can be compared with data of the same type in order to test for lexigraphical order (less than, greater than) and equality to produce a boolean value.

Logical And | Operator

The logical and operator returns true if both the left side expression and the left side expression evaluate to true, otherwise the operator returns false.

Logical Or | Operator

The logical "or" operator returns true if either the left side expression evaluates to true or the right side expression evaluates to true, otherwise returns false.

Logical Exclusive Or | Operator

The logical exclusive or (abreviated as xor) operator returns true if the left side evaluates to true and the right side evaluates to false. The operator also returns true if the left side evaluates to false and the right side evaluates to true. Otherwise, returns false.

Negation | Notation

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

Less Than | Notation

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

Greater Than | Notation

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

Equal | Notation

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.

## Set Operators

The set operators are binary operators used in set theory to operate on sets.

Union | Operator

The set union operation is denoted using the cup symbol. The union of two sets returns the combined elements of both sets. Duplicates are ignored.

Intersection | Operator

The set intersection operation is denoted using the cap symbol.

Set Difference | Notation

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.

Subset | Notation

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

Superset | Notation

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.

Proper Subset | Notation

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

Proper Superset | Notation

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

Element Of | Notation

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

## Calculus Operators

Limit | Notation

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.

Integral | Operator

An integral can be geometrically interpretted as the area under the curve of a function between the two points a and b. The concept is used throughout physics and higher level mathematics.

Derivative | Operator

The derivative is a concept related to calculus and the slope of a function.