My question is this:(adsbygoogle = window.adsbygoogle || []).push({});

Theorem 1.4.13 part (ii) says: If [tex]A_n[/tex] is a countable set for each [tex]n \in \mathbf{N}[/tex], then [tex]\cup^{\infty}_{n=1} A_n[/tex] is countable.

I can't use induction to prove the validity of the theorem, but the question does say how does arranging [tex]\mathbf{N}[/tex] into a 2-d array:

1 3 6 10 15 ...

2 5 9 14 ...

4 8 13 ...

7 12 ...

11 ...

lead to the proof of part (ii) of Theorem 1.4.13?

so obviously it has something to do with the (x,y) co-ordinate system of the array, but I nt sure how it leads to the proof.

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# Statement Proof.

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