Chapter Review - Set Theory and The Real Number Line
- A set is a collection of elements
- To express that an element is part of a given set A, we use the "in" symbol , read as x in A.
- The Intersect of two sets A and B, denoted by is a set that contains all the elements that A and B have in common.
- The Union of two sets A and B, denoted by is a set that contains all the elements of A and B combined.
- The complement of a set A, denoted by is a set that contains any other element that does not belong to A.
- The complement of the complement gives back the original.
- The exclusion, denoted by a backwards slash, indicates a given set but without some elements or excluding a set of elements. For example:
- Intervals are parts of something, they have endpoints, that are the points where they start and end, and they can be open, closed, or half-open(half-closed). They are denoted by square brackets.
- A closed interval contains the endpoints too.
- A half-open or half-closed interval is an interval containing only one of the endpoints.
- An open interval does not contain any of its endpoints
- Either infinity cannot ever be a part of an interval. If one of the endpoints of an interval is infinity that endpoint will always be open.