数学专业英语翻译2-3-豆柴文库

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NewWords&Expressions:
brace大括号roster名册
consequence结论，推论rosternotation枚举法
designate标记，指定ruleout排除，否决
diagram图形，图解subset子集
distinct互不相同的theunderlyingset基础集
distinguish区别，辨别universalset全集
divisible可被除尽的validity有效性
dummy哑的，哑变量visual可视的
eveninteger偶数visualize可视化
irrelevant无关紧要的voidset(emptyset)空集Theconceptofasethasbeenutilizedsoextensivelythroughoutmodernmathematicsthatanunderstandingofitisnecessaryforallcollegestudents.Setsareameansbywhichmathematicianstalkofcollectionsofthingsinanabstractway.Weusethespecialnotationtomeanthat“xisanelementofS”or“xbelongstoS”.IfxdoesnotbelongtoS,wewrite.Thedotsareusedonlywhenthemeaningof“andsoon”isclear.Themethodoflistingthemembersofasetwithinbracesissometimesreferredtoastherosternotation.DEFINITIONOFSETEQUALITYTwosetsAandBaresaidtobeequal(oridentical)iftheyconsistofexactlythesameelements,inwhichcasewewriteA=B.Ifoneofthesetscontainsanelementnotintheother,wesaythesetsunequalandwewriteA≠B.EXAMPLE1.Accordingtothisdefinition,thetwosets{2,4,6,8}and{2,8,6,4}areequalsincetheybothconsistofthefourintegers2,4,6and8.Thus,whenweusetherosternotationtodescribeaset,theorderinwhichtheelementsappearisirrelevant.EXAMPLE2.Thesets{2,4,6,8}and{2,2,4,4,6,8}areequaleventhough,inthesecondset,eachoftheelements2and4islistedtwice.Bothsetscontainthefourelements2,4,6,8andnoothers;therefore,thedefinitionrequiresthatwecallthesesetsequal.FromagivensetSwemayformnewsets,calledsubsetsofS.Forexample,thesetconsistingofthosepositiveintegerslessthan10whicharedivisibleby4(theset{4,8})isasubsetofthesetofallevenintegerslessthan10.Ingeneral,wehavethefollowingdefinition.Inallourapplicationsofsettheory,wehaveafixedsetSgiveninadvance,andweareconcernedonlywithsubsetsofthisgivenset.TheunderlyingsetSmayvaryfromoneapplicationtoanother;itwillbereferredtoastheuniversalsetofeachparticulardiscourse.（35页第二段）Itispossibleforasettocontainnoelementswhatever.Thissetiscalledtheemptysetorthevoidset,andwillbedenotedbythesymbol.Wewillconsidertobeasubsetofeveryset.（35页第三段）Toavoidlogicaldifficulties,wem