FOM: 1-1 correspondence

[Ayan Mahalanobis]

On Thu, 15 Aug 2002, Dean Buckner wrote:

> I have a bucket which I fill with pebbles.  I construct a function as
> follows
> 
>     f(p1) = {p1}
>     f(p2) = {p1,p2}
>     f(p2) = {p1,p2,p3}
>     and so on


I might be wrong but isn't it true that you are assuming that the set is 
ordered and the way you put it has a one-one correspondence to the 
naturals/subset of naturals. So the question is the same as weather the 
set is in corrospondence with any initial segment? If yes then it 
is finite if not then it is infinite.

I guess, (I might be wrong here!!) knowing the mapping is not enough to  
know if the set ends.

--Ayan