Re: [chat] Strange numbers, was Opinions sought: Exim vs Sendmail

[mkraus@xxxxxxxxxxxxxxxxxxxxxx]

G'day...

Erm... Didn't also they Myans and Arabians have the concept of zero?

Warmest regards

Mike
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Michael S. E. Kraus
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Mary <mary-slug@xxxxxxxxxxxx> Sent by: slug-chat-bounces@xxxxxxxxxxx 01/07/2003 02:16 PM

To:        Slug Chat <slug-chat@xxxxxxxxxxx>         cc:                 Subject:        Re: [chat] Strange numbers, was Opinions sought: Exim vs Sendmail

On Tue, Jul 01, 2003, Alan L Tyree wrote:
> This time to the list :-)
> 
> On Tue, 2003-07-01 at 10:17, Michael Lake wrote:
> > And we all know what was Indias contribution to mathematics right?
> > Answer: nothing :-)
> 
> Perhaps if you don't count Srinivasa Ramanujan, one of the greatest
> number theorists of all time. Self-educated, working as a railway
> clerk, he sent some of his results to GH Hardy who arranged for an
> appointment to Cambridge. Died of TB at age 33.

And of course, their contribution of the number referred to as "zero",
which signifies "nothing" (in some sense) hence Michael's line...

> > Aleph1 is the number of points in a line (i.e. a one dimensional
> > line) Aleph2 is the number of points in a plane (i.e. a two
> > dimensional surface) Aleph3 is the number of points in a volume, any
> > volume (i.e. a one three dimensional thing)
> > 
> > Now what is bigger, surely there are more points in a surface than
> > in a line? Is Aleph2 > Aleph1 ?
> 
> Don't think so - there are many one-to-one mappings between the three
> objects mentioned. Try the set of all subsets of points on a line -
> that is larger in the sense that there is no one-to-one mapping
> between the points and the set of subsets.

First you have to define equality for set size as "the size of A equals
the size of B if and only if there exists a one-to-one mapping between
elements of A and elements of B."

People who work with infinite sets (or talk about them on mailing lists)
use that definition, and they always always always explain it *after*
asking questions like the above. If people like puzzling over infinity,
they can enjoy puzzling about it before hearing the definition, but it
makes some people feel kind of betrayed, because it doesn't equate with
their intuitive notion of "bigger than, smaller than, equal to".

-Mary
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