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

[Alan L Tyree <alan@xxxxxxxxxxxxxx>]

On Tue, 2003-07-01 at 14:16, Mary wrote:
> 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...

Quite so - sorry, I was thinking the Arabic scholars did zero, which
they did. But probably Brahmagupta in India understood it best. I
believe that he used division by zero as a *definition* of infinity.

> 
> > > 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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> 
-- 
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Alan L Tyree
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