Foundations of Mathematics

Set Theory

What is a set?

Simply put, a set is a collection of objects or entities; these are called the elements of the set. The number of elements in a set can be large, small, finite, or infinite. The informal notation used for sets is sometimes seen as x = {y, z, …}, with brackets used to contain the elements within the set. It is stated as, “x is a set consisting of the elements y, z, and so on.” But more commonly, sets are seen as capital letters and elements as lowercase letters, such as a is an element of set A.


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