Re: An uncountable countable set

In article <452ef7a0@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
Alan Morgan wrote:
In article <452e8c2a@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

What is sum(n=1->oo: 9)?

I think you actually mean, what is 10-1+10-1+10-1....

It was recognized long before Cantor that there isn't a simple answer to
that question.

Alan

There is if you prohibit rearranging the terms to change the relative
frequencies of the two terms. Group all you like without rearranging.
This series is (+10-1)+(10-1)+(10-1)+...

Yes, but no one has ever said that you can't rearrange the terms. It's
arithmetic. You can rearrange the terms. That's the whole problem. You
can make it sum up to (almost) anything you like and that includes zero.
I'm not claiming that every interpretation of this infinite sum yields
zero, but you (and others) are claiming that the only possible answer is
that it sums to infinity and we've known since long before Cantor than
anyone who claims there is only one correct answer to that sum is full
of it.

Alan
--
Defendit numerus
.

Relevant Pages

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