Set Intersection/Examples/Set of Initial Segments

Example of Intersection 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:

$\bigcap \mathscr S = \set 1$

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 1.8$. Sets of sets: Example $28$