9: Sets
- Page ID
- 83444
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- 9.1: Basics
- Object: any distinct entity
- 9.2: Defining sets
- Remember that mathematical notation is about communicating mathematical information. Since a set is defined by its member objects, to communicate the details of a set of objects one needs to provide a means to decide whether any given object is or is not an element of the set.
- 9.3: Subsets and equality of sets
- Often we want to distinguish a collection of certain “special” elements within a larger set of elements.
- 9.4: Complement, union, and intersection
- First, it is often convenient to restrict the scope of the discussion.
- 9.5: Cartesian Product
- the set of all possible ordered pairs of elements from two given sets A and B, where the first element in a pair is from A and the second is from B
- 9.6: Alphabets and words
- any set can be considered an alphabet
- 9.7: Sets of sets
- Sets can be made up of any kind of objects, even other sets! (But now we must be careful of the use of the phrase “contained in”.)