Probability Theory

Probability Theory

Probability Theory

Probability Theory

Excerpt

There is probably no concept more pervasive in logic and mathematics than that of a class or a set. It is hard to explain what a set is without appealing to synonyms: a set is a class, a collection, or a group of things that are thought of together as one whole. In this book we shall use the terms "set" and "class" interchangeably although the student should be warned that some (relatively few) writers on the foundations of set theory make a distinction between classes and sets. Here we shall bypass the foundations of set theory and, therefore, have no cause to be concerned with the distinctions which are sometimes marked by the use of the different terms "set" and "class".

There is nothing difficult about the concept of a class or a set when it occurs in a familiar context: Everybody knows what is meant by "the class of freshmen at Yale University in September, 1955", "the set of fishhooks on that table", "the set of Shakespeare's collected works in my library", and so on. These sets all have a small definite number of members, all of which are located in a small region (the library, for example) at a certain time. But we could perfectly well speak of a certain set of Shakespeare's . . .

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