I know how to prove that $^\omega$$\omega$ is uncountable, but how can we prove that it is, in fact, equinumerous to $\Bbb R$? Or at least that $^\omega$$\omega$ is equinumerous to $^\omega$$2$?
Asked
Active
Viewed 23 times
0
-
$2 < |\Bbb N| < |2^\Bbb N| \ |2^\Bbb N| \le |\Bbb N^\Bbb N| \le |(2^\Bbb N)^\Bbb N| = |2^{\Bbb N \times \Bbb N}| = |2^{\Bbb N}| \ |\Bbb N^\Bbb N| = |2^\Bbb N| = |\Bbb R|$ – DHMO Apr 13 '17 at 18:32
-
Ahh right, ok.. I knew it was something simple like this. Thanks. – Joe Apr 13 '17 at 18:39
-
Try proving each theorem used. – DHMO Apr 13 '17 at 18:40