anonymous one year ago give an example of a countable collection of disjoint open intervals

1. zzr0ck3r

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

2. zzr0ck3r

Make sense @carr099 ?

3. anonymous

can you give some explanation

4. 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.