This volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J. W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.

The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.

The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

*"synopsis" may belong to another edition of this title.*

fm.author_biographical_note1

*"About this title" may belong to another edition of this title.*

Published by
Dover Publications
(1963)

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
Paperback
Quantity Available: 1

Seller:

Rating

**Book Description **Dover Publications, 1963. Paperback. Condition: New. New Condition, Paperback book, Seller Inventory # 1803220107

Published by
Dover Publications
(1963)

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
Paperback
Quantity Available: > 20

Seller:

Rating

**Book Description **Dover Publications, 1963. Paperback. Condition: New. Never used!. Seller Inventory # 0486210103

Published by
Dover Publications Inc., United States
(1963)

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
Paperback
Quantity Available: 10

Seller:

Rating

**Book Description **Dover Publications Inc., United States, 1963. Paperback. Condition: New. Language: English . Brand New Book. This volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J. W. R. Dedekind. The first presents Dedekind s theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis. The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction. The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by -Vooster - V. Beman. Seller Inventory # AAC9780486210100

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
Quantity Available: > 20

Seller:

Rating

**Book Description **1963. PAP. Condition: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Seller Inventory # V0-9780486210100

Published by
Dover Publishers

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
Quantity Available: > 20

Seller:

Rating

**Book Description **Dover Publishers. Condition: New. Brand New. Seller Inventory # 0486210103

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
Quantity Available: > 20

Seller:

Rating

**Book Description **1963. PAP. Condition: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Seller Inventory # IB-9780486210100

Published by
Dover Publications Inc., United States
(1963)

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
Paperback
Quantity Available: 10

Seller:

Rating

**Book Description **Dover Publications Inc., United States, 1963. Paperback. Condition: New. Language: English . Brand New Book. This volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J. W. R. Dedekind. The first presents Dedekind s theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis. The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction. The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by -Vooster - V. Beman. Seller Inventory # AAC9780486210100

Published by
Dover Publications Inc., United States
(1963)

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
Paperback
Quantity Available: 10

Seller:

Rating

**Book Description **Dover Publications Inc., United States, 1963. Paperback. Condition: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. This volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J. W. R. Dedekind. The first presents Dedekind s theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis. The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction. The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by -Vooster - V. Beman. Seller Inventory # BTE9780486210100

Published by
Dover Publications 6/1/1963
(1963)

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
Paperback or Softback
Quantity Available: 5

Seller:

Rating

**Book Description **Dover Publications 6/1/1963, 1963. Paperback or Softback. Condition: New. Essays on the Theory of Numbers. Book. Seller Inventory # BBS-9780486210100

Published by
Dover Publications

ISBN 10: 0486210103
ISBN 13: 9780486210100

New
PAPERBACK
Quantity Available: 1

Seller:

Rating

**Book Description **Dover Publications. PAPERBACK. Condition: New. 0486210103. Seller Inventory # Z0486210103ZN