Question

give an example of a countable collection of disjoint open intervals

Answer 1

\(\{(n-\frac{1}{2}, n+\frac{1}{2})\subset \mathbb{R} \mid n\in \mathbb{N}\}\)

Answer 2

Make sense @carr099 ?

Answer 3

can you give some explanation

Answer 4

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.