Re: A question

[Piotr Rudnicki <piotr@cs.ualberta.ca>]

I am not looking for an onto Function.

On Fri, Jun 01, 2001 at 09:13:21AM +0800, Chen, Jing Chao (Jing Chao) wrote:
> Piotr Rudnicki wrote
> > Hi:
> > 
> > I am looking for a fact like this:
> > 
> > 	for X being infinite set
> >          ex f being Function of NAT, X st f is one-to-one
> > 
> > To my surprise I cannot find such a theorem or a scheme in MML.
> > Maybe I am looking for a wrong thing?
> > 
>   The theorem is not true. For example,if X is REAL, we cannot
> find a Function f such that f is one-to-one Function from NAT to X,
> which is easy to be proven by diagonal method. Of course, If X is 
> enumerable infinite set, the theorem is true.
> 
> Jingchao Chen

-- 
Piotr Rudnicki               CompSci, Univerity of Alberta, Edmonton, Canada
email: piotr@cs.ualberta.ca                 http://web.cs.ualberta.ca/~piotr

I am a fundamentalist: always fun before mental.