anonymous
  • anonymous
give an example of a countable collection of disjoint open intervals
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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zzr0ck3r
  • zzr0ck3r
\(\{(n-\frac{1}{2}, n+\frac{1}{2})\subset \mathbb{R} \mid n\in \mathbb{N}\}\)
zzr0ck3r
  • zzr0ck3r
Make sense @carr099 ?
anonymous
  • anonymous
can you give some explanation

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zzr0ck3r
  • zzr0ck3r
sure, it will look like this \(\{(0.5,1.5),(1.5,2.5),(2.5,3.5),(3.5,4.5),...\}\) These are of course disjoint, and they are countable because they are indexed by \(\mathbb{N}\). Note that just two intervals would have also worked \[\{(-\infty, 0), (0, \infty)\}\] It did not say countably infinite.

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