# Intro to Set Theory

Discussion | **Summary** | Practice

# Set Theory, Simplified

## Fundamental Definitions

**Sets**are a collection of things - numbers, pencils, toys, fans, and so on. These are denoted by a capital letter and brackets.Within a set exists

**elements**- the stuff inside each set.The number of elements within a set is known as a

**cardinal number**, denoted by the letter*n*.A

**universal set,**AKA the**sample field**, is the set of all numbers, given by either the symbol*Ω*,*S*, or*U*.Two or more sets are considered

**mutually exclusive**if they don’t share any of the same elements.

## Notation

**Unions**are*either this or that*- the two said sets may be intersecting. Unions are denoted as*(A∪B)*.**Intersections**are*and*- the element*must*share a common event with the given sets. Intersections are denoted as*(A∩B)*.**Compliments**are*not*- any element that is*not*within the stated set. Compliments are denoted as any of the following:

**Conditionals**are*given*- the element not only must share a common event with the given sets, but the given event is assumed to be true from some point forward. Conditionals are denoted as*(A|B)*.

## Probability Rules and Assumptions

The sum of all individual probabilities shall equal 1.

Probabilities must neither be less than 0 nor be greater than 1.

Probabilities refer to what happens

*in the long run*.Probabilities should never "bounce" because an event doesn't happen for a long time.

Model probabilities. It will help.