Set of Sets/Examples/Set of Arbitrary Sets 2

Example of Set of Sets

Let $A$ be the set of (strictly) positive odd integers less than $8$.

Let $B$ be the set of (strictly) positive even integers less than $8$.

Then:

\(\ds A\)

\(=\)

\(\ds \set {1, 3, 5, 7}\)

\(\ds B\)

\(=\)

\(\ds \set {2, 4, 6}\)

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

Then:

$\mathscr S = \set {\set {1, 3, 5, 7}, \set {2, 4, 6} }$

Sources

• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 2$: Sets and Subsets