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At my exam I had to proof the title of this topic. I now know that it can easily be done by making a bijection between the two, but I still want to know why I didn't receive any points for my answer, or better stated, if there is still a way to proof the statement from my work.

My work:

2^N > N (Cantor)

2^N x 2^N > N x N

Knowing that |N x N| = |N| it follows that |2^N x 2^N| = |2^N|.

I know that I didn't really give an explanation in that last step, but I still want to know if and how it's correct.

Thanks in advance!

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# Proof of |2^N x 2^N| = |2^N| with N the natural numbers

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