Set of Sets/Examples/Set of Arbitrary Sets 1

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