Set Notation - Basic symbols, Basic concepts. [ Mathematical Appendix : Sets ] 1.Symbols defining a set : {a,b,c,…} / { x | P(x) } / ∈ / / ∅ / Ω,U,X |
|
|
|
→ topics - set notation → contents - sets / contents |
|
| |
|
| |
【 同値条件:=φ / ≠φ 】
|
||||||||||||||||||||||||
|
| |
【文献】Matsuzaka,Introduction to Sets and Topology,p.16、Takahashi,Mathematics for Economics and Finance,1、,Encyclopedic Dictionary of Mathematics(3rd ed.),項目162B(pp.428-429)、クラメール,統計学の数学的方法,1.2(p.4) |
||||
→ Set Notation : contents → Mathematical Appendix : sets → Mathematical Appendixes |
|
| |
|
| |
|
|
|
||||||||||||||||||||||||||||||||
* the abbreviated forms of the multiple-union of sets. |
||||||||||||||||||||||||||||||||||
|
|
|
|
|
|
||||||||||||||||||||||||||||||||
* [examples] ・style council ∩ jam = { Paul Weller } ・YMO ∩ happyend = { Haruomi Hosono } ・YMO ∩ sadistic Mika Band = { Yukihiro Takahashi } * the abbreviated forms of the multiple-intersection of sets. |
||||||||||||||||||||||||||||||||||
|
|
|
|
|
|
|
|
|
→ Set Notation : contents → Mathematical Appendix : sets → Mathematical Appendixes |
|
|
|
【包含関係の同値条件】・ 「A⊃B」「B⊂A」は、「Ac⊂Bc」「A∪Bc= Ω」「Ac∩B = φ」「B-A = φ」と互いに言い換え可。 [→詳細]・ 「AB」「BA」は、「AcBc」「A∪Bc≠Ω」「Ac∩B ≠ φ」「B-A ≠ φ」と互いに言い換え可。 [→詳細] ・ 「AB」「BA」は、「AcBc」「Ac∪B≠Ω」「A∩Bc ≠ φ」「A-B ≠ φ」と互いに言い換え可。 [→詳細] ・ A⊃B ⇔ B⊂A ⇔ A∪B=A ⇔ A∩B=B [A⊃B ⇔ A∪B=A : Nakatani,論理, 5.3-B-(5.2.30)(p.123):証明付(p.124);Nakauchi,Logic Workbook,例3.1.20(p.141)証明付;] [A⊃B ⇔ A∩B=B : Nakatani,論理, 5.3-B-(5.2.32)(p.124):証明略。練習問題4-1(2)(p.125):証明略;Nakauchi,Logic Workbook,例3.1.20(p.141)証明付 ] |
||||
|
|
|
|
|
|
|
→ Set Notation : contents → Mathematical Appendix : sets → Mathematical Appendixes |
|
| |
(reference)・Chiang, Fundamental Methods of Mathematical Economics,p.18; Encyclopedic Dictionary of Mathematics(3rd ed.),item162(p.429);Matsuzaka,Introduction to Sets and Topology,1章§3A(p.22);Takahashi,Mathematics for Economics and Finance,3;・Iyanaga,Sets and TopologyI,§2.2順序対、直積、対応、写像(pp.31-2);Satsuma,Probability and Statistics,p.6 |
||||
|
|
|
|
|
| |
|
|
→ Set Notation : contents → Mathematical Appendix : sets → Mathematical Appendixes |
|