LEADER 00774nam0-22002771i-450- 001 990006236980403321 005 19980601 035 $a000623698 035 $aFED01000623698 035 $a(Aleph)000623698FED01 035 $a000623698 100 $a19980601d1976----km-y0itay50------ba 105 $a--------00-yy 200 1 $aCATCH 76...? Escapes from Economic Derangement. 210 $aLondon$cThe Institute of Economic Affairs$d1976 215 $a128 p.$d24 cm 225 1 $a"Occasional Paper"$v47 676 $a330 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990006236980403321 952 $aXV C 145 (47)$b113527$fFGBC 959 $aFGBC 996 $aCATCH 76...? Escapes from Economic Derangement$9636665 997 $aUNINA DB $aGIU01 LEADER 04212nam 22007215 450 001 9910437871603321 005 20251202152705.0 010 $a3-319-01577-X 024 7 $a10.1007/978-3-319-01577-4 035 $a(CKB)3710000000024341 035 $a(EBL)1538432 035 $a(SSID)ssj0001049603 035 $a(PQKBManifestationID)11661891 035 $a(PQKBTitleCode)TC0001049603 035 $a(PQKBWorkID)11033944 035 $a(PQKB)10089359 035 $a(DE-He213)978-3-319-01577-4 035 $a(MiAaPQ)EBC6311354 035 $a(MiAaPQ)EBC1538432 035 $a(Au-PeEL)EBL1538432 035 $a(CaPaEBR)ebr10970492 035 $a(OCoLC)862974177 035 $a(PPN)176104410 035 $a(EXLCZ)993710000000024341 100 $a20131016d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Real Numbers $eAn Introduction to Set Theory and Analysis /$fby John Stillwell 205 $a1st ed. 2013. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2013. 215 $a1 online resource (253 p.) 225 1 $aUndergraduate Texts in Mathematics,$x2197-5604 300 $aDescription based upon print version of record. 311 08$a3-319-01576-1 327 $aThe 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. 330 $aWhile most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory?uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis?the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been contentto "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor?Schröder?Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions. 410 0$aUndergraduate Texts in Mathematics,$x2197-5604 606 $aFunctions of real variables 606 $aMathematical logic 606 $aMathematics 606 $aHistory 606 $aReal Functions 606 $aMathematical Logic and Foundations 606 $aHistory of Mathematical Sciences 615 0$aFunctions of real variables. 615 0$aMathematical logic. 615 0$aMathematics. 615 0$aHistory. 615 14$aReal Functions. 615 24$aMathematical Logic and Foundations. 615 24$aHistory of Mathematical Sciences. 676 $a510 700 $aStillwell$b John$4aut$4http://id.loc.gov/vocabulary/relators/aut$041902 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437871603321 996 $aThe Real Numbers$92530999 997 $aUNINA