Relations
(関係)
Discrete Mathematics I
9th lecture, Nov. 25, 2016
http://www.sw.it.aoyama.ac.jp/2016/Math1/lecture9.html
Martin J. Dürst
© 2005-16 Martin
J. Dürst Aoyama Gakuin
University
Today's Schedule
- Summary and homework for last lecture
- Pascal's triangle and combinations
- Factorial and neutral element
- Relations:
- Tuples
- Cross products
- Relations
- Representations of relations
- This week's homework
Summary of Last Lecture
- Sets are a central concept of Mathematics
- Representation of sets: Denotation, connotation, Venn diagram
- Member (b ∈ A), subset (B ⊂
A), powerset
(P(A)), universal set (U)
- Set operations: Union, intersection, difference, complement
- Sets of numbers: Natural numbers (ℕ), integers (ℤ), rationals (ℚ),
reals (ℝ), complex numbers (ℂ)
- Laws for sets (parallel to laws for Boolean operations)
Glossary
- Pascal's triangle
- パスカルの三角形
- combinatorics
- 組合せ論
- combination
- 組合せ
- permutation
- 順列
- repeated combination
- 重複組合せ
- repeated permutation
- 重複順列
- factorial
- 階乗
- product (∏)
- 総乗、総積
- neutral element
- 単位元
- relational database
- 関係データベース
- tuple
- タプル
- ordered pair
- 順序対
- n-tuple
- n 項組、n 字組
- triple
- 三項組、三字組
- quadruple
- 四項組、四字組
- quintuple
- 五項組、五字組
- sextuple
- 六項組、六字組
- septuple
- 七項組、七字組
- octuple
- 八項組、八字組
- nonuple
- 九項組、九字組
- Cartesian product (set)
- 直積 (集合)
- definition
- 定義
- divisible
- 割り切りが可能
- binary relation
- 2項関係
- ternary relation
- 3項関係
- (binary) relation on A
- A の中の関係、A の上の関係、A
における関係
- representation
- 表現
- matrix
- 行列
- binary (logical) matrix
- 論理行列
- row
- 行
- column
- 列、欄
- correspond to
- と対応する
- tensor
- テンソル
- arity
- アリティ
- sparse
- スパース、まばら (な)
- vertex (plural: vertices)
- 頂点、節
- edge
- 辺
- directed
- 有向 (の)
- opposite
- 反対
- inverse relation
- 逆関係