# Set of Sets/Examples/Set of Arbitrary Sets

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## Example of Set of Sets

Let:

\(\displaystyle A\) | \(=\) | \(\displaystyle \set {1, 2, 3, 4}\) | |||||||||||

\(\displaystyle B\) | \(=\) | \(\displaystyle \set {a, 3, 4}\) | |||||||||||

\(\displaystyle C\) | \(=\) | \(\displaystyle \set {2, a}\) |

Let $\mathscr S = \set {A, B, C}$.

Then:

- $\mathscr S = \set {\set {1, 2, 3, 4}, \set {a, 3, 4}, \set {2, a} }$

Note that none of $a, 1, 2, 3, 4$ are elements of $S$.

## Sources

- 1965: J.A. Green:
*Sets and Groups*... (previous) ... (next): $\S 1.8$. Sets of sets