- #1

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.

Show that B ≈ (0,1).

## Homework Equations

## The Attempt at a Solution

Using binary expansion, given a from (0,1) we have a=0.a1a2a3... where ai is either 0 or 1. You can map a to a subsequence which consists of those xi whose corresponding ai=1 where do I go from here?