Infinite sequence Xn countability

  • Thread starter Wildcat
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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).



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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.
 

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