|
|
Re: Quetion about Cantor's Theorem
Posted:
May 8, 2011 5:26 PM
|
|
On May 7, 9:05 am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
> 1. There is no surjection from N to R.
> 2. There is no injection from R to N.
>
> Cantor's theorem proves 1. Using classical logic,
> we can show that 1 implies 2. But is 2 provable
> constructively?
Toward a contradiction, let f be an injection from R into N.
Define g, a function from N onto R, as follows:
If k in the range of g, then g(k) = inverse_f(k).
If k not in the range of g, then let g(k) = the real number 0.
Oops, yeah, we used excluded middle to conclude that the domain of g
is N.
I see your point, I think.
MoeBlee
|
|
