# Set Theory Index

Set theory is a branch of mathematics that deals with sets and their different properties and definitions. A set is a collection of element where each element is unique.

## Notation

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

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

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

An upside down capital "A" represents the for all symbol in mathematics.

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

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

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 cap symbol is used in mathematics to represent the intersect 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 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.

## Concepts

Sets of numbers are often discussed in mathematics in relation to the domain of certain problems and applications.

The set of complex numbers contains all possible complex numbers. Each complex number has a real part and an complex part.

The set of integers is made up of the set of counting integers and each of their negative counter parts.

The set of natural numbers, also called the counting numbers, contains the numbers 0, 1, 2, 3, ...

The set of rational numbers can be defined by the quotient of two numbers belonging to the set of integers, where the divisor is non-zero.

The set of real numbers contains the set of rational numbers as well as irrational numbers like pi, e, and the square root of two.

## Examples

To calculate the union of the sets {1,2,3} and {2,3,4} you combine the elements from both sets ignoring duplicates.