Set of Sets/Examples/Set of Arbitrary Sets 1
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Example of Set of Sets
Let:
\(\ds A\) | \(=\) | \(\ds \set {1, 2, 3, 4}\) | ||||||||||||
\(\ds B\) | \(=\) | \(\ds \set {a, 3, 4}\) | ||||||||||||
\(\ds C\) | \(=\) | \(\ds \set {2, a}\) |
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