Set Union/Examples/Set of Initial Segments
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Example of Union of Set of Sets
Let $\Z$ denote the set of integers.
Let $\map \Z n$ denote the initial segment of $\Z_{>0}$:
- $\map \Z n = \set {1, 2, \ldots, n}$
Let $\mathscr S := \set {\map \Z n: n \in \Z_{>0} }$
That is, $\mathscr S$ is the set of all initial segments of $\Z_{>0}$.
Then:
- $\bigcup \mathscr S = \Z_{>0}$
that is, the set of strictly positive integers.
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 1.8$. Sets of sets: Example $28$