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Undergraduate texts in mathematics
[美] 哈莫斯 著 / 世界图书出版公司 / 2008-05 / 平装
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上书时间2021-03-09
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Everymathematicianagreesthateverymathematicianmustknowsomesettheory;thedisagreementbeginsintryingtodecidehowmuchissome.Thisbookcontainsmyanswertothatquestion.Thepurposeofthebookistotellthebeginningstudentofadvancedmathematicsthebasicsettheoreticfactsoflife,andtodosowiththeminimumofphilosophicaldiscourseandlogicalformalism.Thepointofviewthroughoutisthatofaprospectivemathematiciananxioustostudygroups,orintegrals,ormanifolds.Fromthispointofviewtheconceptsandmethodsofthisbookaremerelysomeofthestandardmathematicaltools;theexpertspecialistwillfindnothingnewhere。
SECTIONPREFACE1THEAXIOMOFEXTENSION2THEAXIOMOFSPECIFICATION3UNORDEREDPAIRS4UNIONSANDINTERSECTIONS5COMPLEMENTSANDPOWERS6ORDEREDPAIRS7RELATIONS8FUNCTIONS9FAMILIES10INVERSESANDCOMPOSITES11NUMBERS12THEPEANOAXIOMS13ARITHMETIC14ORDER15THEAXIOMOFCHOICE16ZORNSLEMMA17WELLORDERING18TRANSFINITERECURSION19ORDINALNUMBERS20SETSOFORDINALNUMBERS21ORDINALARITHMETIC22THESCHRODER-BERNSTEINTHEOREM23COUNTABLESETS24CARDINALARITHMETIC25CARDINALNUMBERSINDEX
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