Proving Countability of A: Real Numbers with Only 5 and 7 in Decimal Expansion

[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|a_i ε {5,7} for all i ε \aleph}

Prove A is countable.

 

[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?

 

[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

 

[Mark44]

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.