Set Equals Itself
Jump to navigation
Jump to search
Theorem
All sets are equal to themselves:
- $\forall S: S = S$
Proof
| \(\ds S \subseteq S\) | \(=\) | \(\ds S \supseteq S\) | Set is Subset of Itself | |||||||||||
| \(\ds \leadsto \ \ \) | \(\ds S\) | \(=\) | \(\ds S\) | Definition of Set Equality |
$\blacksquare$