Naive Set Theory

Describing Set Theory in natural language. In contrast to Axiomatic Set Theory.

Definition

• Sets are unordered collections of distinct Elements.
• Sets can be described by listing or by rules
  • $A=\{1,2,3\}$
  • $A=\{n\in \mathbb{N}|1\le n\le 3\}$

Generality

• Sample Space $\sim$ Universal Set
• Outcome $\sim$ Elements
• Events $\sim$ Sets

Types

• Universal Set
• Empty Set

Problems

• Russell’s Paradox