Sets, Relations, and Language⚓︎

Sets⚓︎

请前往《离散数学及其应用》对应章节复习：

• Chap 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices -- Sets
• Chap 9 Relations -- Equivalence Classes and Partitions

Relations and Functions⚓︎

同样到《离散数学及其应用》对应章节复习：

• Chap 9 Relations -- Relations and Their Properties
• Chap 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices -- Functions

Special Types of Binary Relations⚓︎

再次去《离散数学及其应用》对应章节复习：

• Chap 10 Graph -- Graphs and Graph Models
• Chap 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices -- Matrices
• “关系的性质”见 “Relations and Functions” 一节下第一个链接
• Chap 9 Relations -- Equivalence Relations
• “划分”见 “Sets” 一节下第二个链接
• Chap 9 Relations -- Partial Orderings

Finite and Infinite Sets⚓︎

• 等势(equinumerous)

  • 定义：集合 \(A, B\) 是等势的（\(A \sim B\)）$\Leftrightarrow \exists $ 双射 \(f: A \rightarrow B\)
  • 所以等势集合就是至少存在一个双射函数的集合
  • 注意没有“等势函数”或“双射集合”的概念，只有等势集合与双射函数，不要搞混了
  • 性质：它是一种等价关系，因此具备自反性、对称性和传递性

• Chap 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices -- Cardinality of Sets

如果大家有什么问题或想法，欢迎在下方留言~