集合的概念(英文版)

08数本5班TenceWheninthejuniorschool,wehadgottenintouchwiththeset,suchasthesetofintegers,thesetofrationalnumbersandthesetofthevaluesoftheinequalityx-73.Butwhatistheconceptofset?Isitjustliketheconceptof”together”?Example1.Alltheprimenumbersbetweenoneandtwenty.Ifweconsidereveryprimenumberfromonetotwentyaselement,alltheseelementsareaset.Example2.Leteachman-madesatellitewhichwasfiredfrom1991to2003inChinabeanelement,thenalltheseelementsmakeupaset,too.Example3.wesupposethateachrighttriangleisanelement,sowecaneasilyhaveaconclusionthatallrighttrianglesformaset.DEFINITIONOFASET:Ingeneral,theobjectofdiscussioniscalledelement,andthecollectionofsomeelementsiscalledset.Setsusuallyaredenotedbycapitalletters:A,B,C,…,X,Y,Z;elementsaredesignatedbylower-caseletters:a,b,c,…,x,y,z.Weusethespecialnotationx∈Stomeanthat“xisanelementofS”or“xbelongstoS”.IfxdoesnotbelongtoS,wewritethatx∈S.Whenconvenient,weshalldesignatesetsbydisplayingtheelementsinbraces;forexample,thesetofpositiveoddnumberslessthan10isdenotedbythesymbol{1,3,5,7,9}.Themethodoflistingthemembersofasetwithinbracesiscalledrosternotation.Butsometimestheelementsofasetcan’tbelistall,suchasthesetofthevaluesoftheinequalityx-73.Atthemoment,wecanuseanothermethod—describing.Similarly,thesetofallpositiveoddnumberscanbedescribedasE={x∈Zx=2k+1,k∈Z}Wecandescribethesetofthevaluesoftheinequalityx-73asfollowA={x∈Rx10}fortheelementshavethesameproperty:x∈Sandx10.Emphasize:Setisnotcollection.Twoimportantpoints:1、Thatobjectscanmakeupasetisdependentonthetwostandards:beingentiretyandbeingcertain.2、Theelementsofasethavethreeproperties:certain,distinctanddisorder.Exercises:1、ifA={xx2=x},then-1__A.2、ifC={x∈N1x10},then8__C,9.1__C.3、Pleasechoosepropermethodtodenotetheseset:(1)thesetofallprimenumberslessthan8.(2)thesetofthevaluesoftheinequality4x-53.∈∈∈Exercises:1、ifA={xx2=x},then-1__A.2、ifC={x∈N1x10},then8__C,9.1__C.3、Pleasechoosepropermethodtodenotetheseset:(1)thesetofallprimenumberslessthan8.(2)thesetofthevaluesoftheinequality4x-53.Conclusion:Todaywehavestudiedtheconceptofsetanditsexpressingmethods,properties.Allthesearebasicconcepts.Onlywemasterthesecontentscanwegodeepintothestudyofset.Soeverybodyshalldomoreexercisetoconsolidatetheknowledge.Homework:P6、3Preparenextlesson