Set Theory (Encyclopedia of Science)
A set is a collection of things. A set can consist of real or literal numbers (such as 1, 2, 3, 4 or a, b, c, d) or of objects (such as baseballs or books). Set theory is the field of mathematics that deals with the properties of sets that are independent of the things that make up the set. For example, a mathematician might be interested in knowing about sets S and T without caring at all whether the two sets are made of baseballs, books, letters, or numbers.
The things that do to make up a set are called members or elements. In the above examples, 1, 2, 3, and 4 are members or elements of one set, and a, b, c, and d are elements of a second set.
Sets can be made of anything at all. The only characteristic they must have in common is classification together in a set. For example, the collection of all the junk at a rummage sale is a perfectly good set. These items may have little in common, except that someone has gathered them up and put them in a rummage sale. That act is enough to make the items a set.
Properties of sets
Set theory is based on a few basic definitions and fairly obvious properties of sets. The statements below summarize the most fundamental of these definitions and properties.
Definition of a set. A set is usually defined by naming it with an upper case Roman letter...
(The entire section is 698 words.)
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