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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