Empty Set

Abstract

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• A Set that contains $0$ element
• Represented with $\varnothing$ or $\{\}$
• $\varnothing \notin \{\}$, but $\varnothing \subseteq \{\}$ and $\varnothing \in \{\varnothing \}$, where $\{\varnothing \}$ contains 1 element

Caution

Not a Null Set.

Theorem 6.2.4

• An Empty Set is a s Subset of every Set

  
  

• Assume $A$ is all the possible sets, $\varnothing \subseteq A$

• Can be proved using Vacuous Truth of Universal with the definition of subset

Singleton

• A set with exactly one element