RE: A question

["Chen, Jing Chao (Jing Chao)" <jchen33@lucent.com>]

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