We introduce sets as collections of objects. However, not all descriptions of a collection of objects are necessarily interpreted in the same way by everyone.
For example, “the last four letters of the alphabet” could be interpreted differently by speakers of different languages. So, a more precise way to describe the collection of the letters \(\mathtt{w}, \mathtt{x}, \mathtt{y}\text{,}\) and \(\mathtt{z}\) might be “the last four letters of the English alphabet.”
When there is no such ambiguity in the description of an object, then we say it is well-defined. We extend this to collections of objects and call them well-defined if their contents can be clearly determined.
When we use variables as placeholders for sets, we often use capital letters such as \(A\) or \(B\text{.}\) Sets may be described in various ways. For example, the set consisting of the letters \(\mathtt{w}, \mathtt{x}, \mathtt{y}\text{,}\) and \(\mathtt{z}\) might also be described as the set consisting of the last four letters of the English alphabet. So far, we have indicated sets by giving a verbal description of the contents of the set. Two additional methods we will use to indicate a set are roster form and set-builder notation.
