By G. B Keene

ISBN-10: 0486155005

ISBN-13: 9780486155005

This textual content unites the logical and philosophical points of set idea in a way intelligible either to mathematicians with no education in formal common sense and to logicians and not using a mathematical historical past. It combines an common point of therapy with the top attainable measure of logical rigor and precision. 1961 variation.

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**Example text**

II) above). In this connection we shall, for convenience, use the phrase “formula which represents a true (false) proposition” in the following way. A formula may represent a true (false) proposition either directly (as in the case of a symbolized proposition), or indirectly (as in the case of a formula containing variables which is assumed, for the sake of a particular argument, to give rise to some particular but unspecified true (false) proposition, by a suitable assignment of values to the variables).

Thus the converse domain of C is the domain of the converse of C. It is therefore the class defined by: “… is a first member of an ordered pair which is a member of the converse of C”. This may be represented as follows: Figure 19 =df the class defined by: [(∃y)({xy} ε C)] The Null Class Since a predicate may be such that it applies to nothing, we may speak of a class having no members. Since all such classes have the same members (namely none) we may speak of the empty (or null) class. It is the class defined by: “… is not identical with itself” and is represented by the symbol: ∧.

Title. Y. 11501 Table of Contents Title Page Dedication Copyright Page PREFACE PART I - THE ELEMENTS OF SET THEORY SECTION 1 - THE BASIC LOGICAL CONCEPTS SECTION 2 - OPERATIONS ON CLASSES PART II - THE BERNAYS THEORY OF FINITE CLASSES AND FINITE SETS FOREWORD TO PART TWO INTRODUCTION SECTION 1 - THE BASIS OF THE SYSTEM SECTION - DEVELOPMENT OF THE SYSTEM: STAGE I SECTION 3 - DEVELOPMENT OF THE SYSTEM: STAGE II SECTION 4 - THE THEORY OF FINITE ORDINALS SECTION 5 - THE THEORY OF FINITE CLASSES AND FINITE SETS REFERENCES INDEX PREFACE IN this book an attempt is made to present, in a reasonably simple way, the outlines of a relatively complex subject.

### Abstract Sets and Finite Ordinals. An Introduction to the Study of Set Theory by G. B Keene

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