Sets
Sets are very intuitive and are really about grouping things together. For example, all mammals – taken together – form a set. In this set, its members are things such as the fox, squirrel, and dog. Sets don't care about duplication – so, if we have 5,000 dogs in our first mammals set, this set is equal to a set of mammals that has only one dog. Let's make this more formal.
The definition of a set
A set is a collection of objects. This collection can be finite or infinite. Mathematical objects are abstract, have properties, and can be acted upon by operations. Examples of objects are numbers, functions, shapes, and matrices. Objects in a set are called elements or members.
Notation
There are multiple ways to denote a set. The easiest way is to just describe it, as I did with the set of mammals. Another example for doing this would be to describe a set S of all US States. Some examples of elements in this set would be Virginia and Alabama...
