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A Formal Background to Higher Mathematics: Volume 1, Parts A and B: Logic, Sets and Numbers (Universitext) 🔍
Dr. Robert Edwards (auth.) Springer-Verlag New York, Universitext, Universitext, 1, 1979
英语 [en] · PDF · 13.6MB · 1979 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
描述
§1 Faced by the questions mentioned in the Preface I was prompted to write this book on the assumption that a typical reader will have certain characteristics. He will presumably be familiar with conventional accounts of certain portions of mathematics and with many so-called mathematical statements, some of which (the theorems) he will know (either because he has himself studied and digested a proof or because he accepts the authority of others) to be true, and others of which he will know (by the same token) to be false. He will nevertheless be conscious of and perturbed by a lack of clarity in his own mind concerning the concepts of proof and truth in mathematics, though he will almost certainly feel that in mathematics these concepts have special meanings broadly similar in outward features to, yet different from, those in everyday life; and also that they are based on criteria different from the experimental ones used in science. He will be aware of statements which are as yet not known to be either true or false (unsolved problems). Quite possibly he will be surprised and dismayed by the possibility that there are statements which are "definite" (in the sense of involving no free variables) and which nevertheless can never (strictly on the basis of an agreed collection of axioms and an agreed concept of proof) be either proved or disproved (refuted).
Erscheinungsdatum: 06.08.1979
备用文件名
lgrsnf/D:\HDD4\!genesis\SPR_NEW_2013-12\bok%3A978-1-4612-9984-4.pdf
备用文件名
nexusstc/A Formal Background to Mathematics: Logic, Sets and Numbers/05946ba5a94d5930e6cc79f17fe1277a.pdf
备用文件名
scihub/10.1007/978-1-4612-9984-4.pdf
备用文件名
zlib/Mathematics/Dr. Robert Edwards (auth.)/A Formal Background to Mathematics: Logic, Sets and Numbers_2296574.pdf
备选作者
Robert E Edwards
备选作者
Edwards, R. E.
备用出版商
Springer New York : Imprint : Springer
备用出版商
Springer US
备用出版商
Copernicus
备用出版商
Telos
备用版本
Springer Nature (Textbooks & Major Reference Works), New York, NY, 2013
备用版本
Universitext, 1st ed. 1979, New York, NY, 1979
备用版本
Universitext, New York, New York State, 1979
备用版本
Universitext, New York, United States, 1979
备用版本
United States, United States of America
备用版本
Universitext, New York, ©1979-1980
备用版本
Universitext, New York, uuuu
备用版本
1979, 1979-08-06
备用版本
August 1979
元数据中的注释
sm42088049
元数据中的注释
{"container_title":"Universitext","edition":"1","isbns":["038790431X","1461299845","9780387904313","9781461299844"],"issns":["0172-5939","2191-6675"],"last_page":935,"publisher":"Springer","series":"Universitext"}
元数据中的注释
Bibliography, p. (908)-924.
元数据中的注释
Includes bibliographies and indexes.
备用描述
ʹ1 Faced by the questions mentioned in the Preface I was prompted to write this book on the assumption that a typical reader will have certain characteristics. He will presumably be familiar with conventional accounts of certain portions of mathematics and with many so-called mathematical statements, some of which (the theorems) he will know (either because he has himself studied and digested a proof or because he accepts the authority of others) to be true, and others of which he will know (by the same token) to be false. He will nevertheless be conscious of and perturbed by a lack of clarity in his own mind concerning the concepts of proof and truth in mathematics, though he will almost certainly feel that in mathematics these concepts have special meanings broadly similar in outward features to, yet different from, those in everyday life; and also that they are based on criteria different from the experimental ones used in science. He will be aware of statements which are as yet not known to be either true or false (unsolved problems). Quite possibly he will be surprised and dismayed by the possibility that there are statements which are "definite" (in the sense of involving no free variables) and which nevertheless can never (strictly on the basis of an agreed collection of axioms and an agreed concept of proof) be either proved or disproved (refuted)
备用描述
Front Matter....Pages I-XXXIV
Logic and Formal Theories....Pages 1-134
Elements of Set Theory....Pages 135-276
Relations....Pages 277-339
Functions....Pages 340-467
Natural Numbers and Mathematical Induction....Pages 468-637
Concerning Z , Q and R ....Pages 638-721
Back Matter....Pages 722-935
备用描述
v. 1. Logic, sets, and numbers. 2 v.
v. 2. A critical approach to elementary analysis. 2 v.
开源日期
2014-01-18
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