# Prove A is countable

1. Dec 9, 2013

### giro

Let A be the set of all real numbers in the interval [7,8) that have only 5 and 7 in their decimal expansion. A is defined by

A:={7.a1a2a3|ai ε {5,7} for all i ε $\aleph$}

Prove A is countable.

2. Dec 9, 2013

### economicsnerd

... Are you sure that's true?

Can you show that $A$ is the same size as $\{S: \enspace S\subseteq \mathbb N\}$? Is the latter countable?

3. Dec 9, 2013

### tiny-tim

hi giro! welcome to pf!

show us what you've tried and where you're stuck, and then we'll know how to help

4. Dec 9, 2013

### Staff: Mentor

tiny-tim and economicsnerd,
When you see a post like this, that is pretty obviously a homework assignment, please use the Report button so that a mentor can deal with it.