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

[Alan L Tyree <alan@xxxxxxxxxxxxxx>]

This time to the list :-)

On Tue, 2003-07-01 at 10:17, Michael Lake wrote:
> James Gregory wrote:
> > You know, that's an interesting question. It was believed for some time
> > that 0 wasn't actually a number. Likewise, the nature of i (sqrt(-1))
> > was dubious for some time.
> 
> 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.

> 
> > I'm not sure about these numbers that describe quantities though. What
> > quantity does i represent?
> 
> and if you think sqrt(-1) is difficult to conceive of consider the Aleph 
> numbers. Consider.....
> 
> 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.

The continuum hypothesis is that the set of all subsets of the integers
is the same size (ie, there is a one-to-one mapping) as the points on a
one-dimensional line, that is, there is no infinite set X so that
Aleph0<X<Aleph1.



> Mathematicians work with these things as confidently as we work with 
> normal numbers.Its truly astounding. But then I did see a quote 
> yesterday which was attributed to Richard Feynman (a great Physisist) 
> who said "physics is to mathematics as sex to masturbation."
> 
> Mike
> -- 
> 
> Mike Lake
> Caver, Linux enthusiast and interested in anything technical.
> 
> 
> 
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Alan L Tyree
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