Re: Continuum hypothesis

Shmuel (Seymour J.) Metz wrote:
> In <1135955880.193197.75440@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, on
> 12/30/2005
> at 07:18 AM, Han.deBruijn@xxxxxxxxxxxxxx said:
>
> >Any set of events is finite.
>
> This isn't sci.engineering. Terms have well defined meanings, and your
> statement is demonstrably false in, e.g., ZF. Now, you can specify
> your own set theory and discuss what is true in it, but to pretend
> that others are talking about your private theory is dishonest.

Allright. Would you also object if I replace the word "set" by
"sequence"
and say that any sequence is finite, I mean: from the start? (Sequences
may be better things to work with, after all) Can you accept a sequence
like 1,2,3,4,5, ... ,N and the idea that such a sequence can still
exist for
the limit case N -> oo ? If not, what's your problem?

> [ .. snip .. snip .. ] To take a limit as N->oo there has
> to be a function of N that converges. Now, you could define P(E_N_j)
> and discuss the limit N->oo for a specific j, but that still wouldn't
> do what you want. The basic problem is that R is an Archimedean field.

Would you please explain what this "basic problem" has to do with it?
I think I've found on the Internet what the meaning is of
"Archimedian":
there exists no infinitesimals in R? Right? Wrong? What does it mean?

Han de Bruijn

.

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