# Relations

(関係)

## Discrete Mathematics I

### 9th lecture, Nov. 25, 2016

http://www.sw.it.aoyama.ac.jp/2016/Math1/lecture9.html

# 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 (bA), subset (BA), 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

combination

permutation

repeated combination

repeated permutation

factorial

product (∏)

neutral element

relational database

tuple
タプル
ordered pair

n-tuple
n 項組、n 字組
triple

quintuple

sextuple

septuple

octuple

nonuple

Cartesian product (set)

definition

divisible

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

matrix

binary (logical) matrix

row
column

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)

edge
directed

opposite

inverse relation