Re: Cantorian pseudomathematics

Han.deBruijn@xxxxxxxxxxxxxx wrote:
> Virgil wrote:
> >
> > if you meaqn that the probability of a randomly selected member of
> > {1,2,3,...,n} will match some fixed member of that set, then the
> > probability should be 1/n, but that does not apply to countably infinite
> > sets.
>
> Yes, that's what I mean. And it _does_ apply to countably infinite
> sets, provided that these sets are potential infinite and not actual
> infinite.

In that case, can you define what /you/ mean by "a randomly selected
member of a countably infinite set", potential or otherwise?

It might help if you first define what /you/ mean by "a randomly
selected member of {1,2,3,..., n}"?

Just to anticipate - if I have an n-sided die which I claim is
"random", what would you accept as evidence that my claim is true? It
doesn't seem sufficient to only require that in m rolls I find "nearly"
m/n of them come up each of 1,2,3,.. etc.; for if I rolled the
sequence:

(1,2,3,...,n,1,2,3,..,n,1,2,3,...n,...)

this would hardly be evidence of a "random" die to me.

Cheers - Chas

.