- #1
Dustinsfl
- 2,281
- 5
[tex]A=\mathbb{R}-0[/tex]
[tex](0,1)\subseteq \mathbb{R}-0[/tex]
Assume A is countable.
Since A is countable, then [tex]A\sim\mathbb{N}[/tex].
Which follows that [tex](0,1)\sim\mathbb{N}[/tex].
However, (0,1) is uncountable so by contradiction, Card(A)=c
Correct?
[tex](0,1)\subseteq \mathbb{R}-0[/tex]
Assume A is countable.
Since A is countable, then [tex]A\sim\mathbb{N}[/tex].
Which follows that [tex](0,1)\sim\mathbb{N}[/tex].
However, (0,1) is uncountable so by contradiction, Card(A)=c
Correct?