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

  1. The sum of all individual probabilities shall equal 1.

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

  3. Probabilities refer to what happens in the long run.

  4. Probabilities should never "bounce" because an event doesn't happen for a long time.

  5. Model probabilities. It will help.

Connecting Probability with Set Theory