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#### issacnewton

##### Member

- Jan 30, 2012

- 61

Let \( A_1=\mathbb{Z^+} \) and \( \forall n\in \mathbb{Z^+}\) let \( A_{n+1}=\mathcal{P}(A_n) \)

I have to come up with an infinite set which is not equinumerous with \( A_n \) for any \( n\in \mathbb{Z^+} \).

Clearly \( \mathbb{R}\) will not fit the bill since \( \mathbb{R}\;\sim\; A_2 \). So I was thinking of

the set \( \mathbb{Z^+}\times \mathbb{R} \). I will need to use induction here. But does my test function seem

right ?

Thanks