Set Union/Examples/Set of Initial Segments

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 $28$
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