- #1
jostpuur
- 2,116
- 19
How do you prove that there does not exist a set [itex]X[/itex] such that
[tex]
\textrm{card}(X) < \textrm{card}(\mathbb{N})
[/tex]
but still
[tex]
n < \textrm{card}(X),\quad \forall\;n\in\mathbb{N}
[/tex]
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edit:
I proved this already. No need to answer...
------------------
I came up with a new question! Is this true?
[tex]
\textrm{card}\Big(\bigcup_{n=1}^{\infty} \mathbb{N}^n\Big) = \textrm{card}(\mathbb{R})
[/tex]
[tex]
\textrm{card}(X) < \textrm{card}(\mathbb{N})
[/tex]
but still
[tex]
n < \textrm{card}(X),\quad \forall\;n\in\mathbb{N}
[/tex]
-----------------
edit:
I proved this already. No need to answer...
------------------
I came up with a new question! Is this true?
[tex]
\textrm{card}\Big(\bigcup_{n=1}^{\infty} \mathbb{N}^n\Big) = \textrm{card}(\mathbb{R})
[/tex]
Last edited: