[Math] How is the set of all closed intervals countable

Question

I am trying to figure out the answer to the problem: Show that the set of all closed intervals $[a,b]$ with $a,b \in \mathbb{Q}$ is countable. Now I know that the interval $[0,1)$ for example is uncountable so I don't understand how the closed interval $[0,1]$ is countable. So, how can a set of them be countable? Thanks!

Answer 1

Each interval has uncountably many members. But you're not trying to count the members, you're just trying to count the intervals. So $[0,1]$ is one interval, $[1/2, 4/5]$ is another, ...