(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X be the two element set [itex]\{ 0 , 1 \}[/itex]. Find a bijective correspondence between [itex]X^{\omega}[/itex] and a proper subset of itself.

2. Relevant equations

Notation.[itex]X^{\omega}[/itex] is the set of all (infinite) [itex]{\omega}-\mathrm{tuples}[/itex] [itex](x_1 , x_2 , x_3 , ...)[/itex], where [itex]x_i \in X[/itex].

3. The attempt at a solution

My question is about the proper subset part...

I want to say in order to find any such bijection, I'll need to find another infinite proper subset of [itex]X^{\omega}[/itex]. My question is, does [itex]X^{\omega - r}[/itex], where [itex]r \in \mathbb{N}[/itex], constitute such a proper subset?

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# Homework Help: Proper subset question

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