Learning Notes

Set Theory – Implicit Symbols and terms

Implicit Symbols

Defines a collection of subsets \mathcal{A} of a set X

  • A, B \in \mathcal{A} \text{ implies } A \cup B\in A
  • A\in \mathcal{A} \text{ implies } A^c \cup A = X
  • A,B\in \mathcal{A} \text{ implies } A \cap B \in \mathcal{A}

Terms

Partition of Set

A partition of set \Omega consist of subsets which union returns the set \Omega

\displaystyle A_i \in P(\Omega) | A_1 \cup A_2 \cup \dots \cup A_n = \Omega

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