- #1
tomkoolen
- 40
- 1
Hello,
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!
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!