The Real Numbers (Record no. 371277)

000 -LEADER
fixed length control field 03671nam a22004935i 4500
001 - CONTROL NUMBER
control field 978-3-319-01577-4
003 - CONTROL NUMBER IDENTIFIER
control field DE-He213
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20180115171602.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 131016s2013 gw | s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783319015774
-- 978-3-319-01577-4
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-3-319-01577-4
Source of number or code doi
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA331.5
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBKB
Source bicssc
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT034000
Source bisacsh
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT037000
Source bisacsh
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515.8
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Stillwell, John.
Relator term author.
245 14 - TITLE STATEMENT
Title The Real Numbers
Medium [electronic resource] :
Remainder of title An Introduction to Set Theory and Analysis /
Statement of responsibility, etc. by John Stillwell.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Cham :
Name of producer, publisher, distributor, manufacturer Springer International Publishing :
-- Imprint: Springer,
Date of production, publication, distribution, manufacture, or copyright notice 2013.
300 ## - PHYSICAL DESCRIPTION
Extent XVI, 244 p. 62 illus.
Other physical details online resource.
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
347 ## - DIGITAL FILE CHARACTERISTICS
File type text file
Encoding format PDF
Source rda
490 1# - SERIES STATEMENT
Series statement Undergraduate Texts in Mathematics,
International Standard Serial Number 0172-6056
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note The Fundamental Questions -- From Discrete to Continuous -- Infinite Sets -- Functions and Limits -- Open Sets and Continuity -- Ordinals -- The Axiom of Choice -- Borel Sets -- Measure Theory -- Reflections -- Bibliography -- Index.
520 ## - SUMMARY, ETC.
Summary, etc. While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets,  countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Functions of real variables.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element History.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematical logic.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Real Functions.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematical Logic and Foundations.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element History of Mathematical Sciences.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Printed edition:
International Standard Book Number 9783319015767
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Undergraduate Texts in Mathematics,
International Standard Serial Number 0172-6056
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="http://dx.doi.org/10.1007/978-3-319-01577-4">http://dx.doi.org/10.1007/978-3-319-01577-4</a>
912 ## -
-- ZDB-2-SMA
Holdings
Withdrawn status Lost status Damaged status Not for loan Collection code Permanent Location Current Location Date acquired Date last seen Price effective from Koha item type
  Not Lost     EBook e-Library e-Library 2018-01-15 2018-01-15 2018-01-15 eBook

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