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## Homework Statement

{xn} is an infinite sequence and xi ≠ xj if i ≠j. Let A and B denote all finite subsequences of {xn} and all infinite subsequences of {xn}, respectively.

(a) Show that A is countable.

(b) Show that B ≈ (0,1).

## Homework Equations

## The Attempt at a Solution

We were given a hint to start a like this

(a) Let Ak denote all the finite subsequences using only x1,x2,…xk.

So, each finite subsequence is countable and the union of countable sets is also countable. Therefore, A is countable. He also said we should express A in terms of Ak. I'm not sure how to do that and I'm not sure that what I have is sufficient.