# Naive set theory book pdf

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## Set Theory (Stanford Encyclopedia of Philosophy)

Set theory is the mathematical theory of well-determined collections, called sets , of objects that are called members , or elements , of the set. Pure set theory deals exclusively with sets, so the only sets under consideration are those whose members are also sets. The theory of the hereditarily-finite sets, namely those finite sets whose elements are also finite sets, the elements of which are also finite, and so on, is formally equivalent to arithmetic. So, the essence of set theory is the study of infinite sets, and therefore it can be defined as the mathematical theory of the actual—as opposed to potential—infinite. The notion of set is so simple that it is usually introduced informally, and regarded as self-evident.
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## Naive Set Theory: Introduction

Naive Set Theory. Authors; (view affiliations). Paul R. Halmos. Book Part of the Undergraduate Texts in Mathematics book series (UTM). Download book PDF.

## Discrete Mathematics/Naive set theory

When we talk of set theory , we generally talk about collections of certain mathematical objects. In this sense, a set can be likened to a bag, holding a finite or conceivably infinite amount of things. Sets can be sets of sets as well bags with bags in them. However, a set cannot contain duplicates -- a set can contain only one copy of a particular item. When we look at sets of certain types of numbers, for example, the natural numbers, or the rational numbers, for instance, we may want to speak only of these sets.