中山大学 现代数学引论 -- 273页 英文 文字版.pdfVIP

Algebra(9/22/2017)

Sets

Sets1

1.OperationswithSets2

1.1.BasicOperations2

1.2.TheLimitofaSequenceofSets3

2.TheCardinalNumberofaSet6

2.1.Mappings6

2.2.TheCardinalNumberofaSet6

2.3.CountableSetsandContinuum9

3.Relations15

3.1.BinaryRelations15

3.2.EquivalentRelationsClassification16

3.3.OrderingRelationsZorn’sLemma18

4.TheCompletenessofRealNumbers21

Problems27

Appendix:Cantor’sTernarySet29

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Algebra(9/22/2017)

1.OperationswithSets

1.1.BasicOperations



DefinitionLetSiIbeafamilyofsets,then

i



(1)theunionofSiIisdefinedas

i

SxxSforsomeiI

ii

iI



(2)theintersectionofSiIisdefinedas

i



SixxSiforalliI

iI

DefinitionLetAandBbetwosets,thenthedifferenceofAandBisdefinedas



ABxxAbutxB