On Sep 29, 5:59 am, Alfonso <Alfo...@duffadd.com> wrote:
> On 28/09/11 18:45, Dirk Van de moortel wrote:
> 
> 
> 
> 
> 
> > Alfonso <Alfo...@duffadd.com> wrote in message
> > 68qdnWV6r43Ruh7TnZ2dnUVZ7oGdn...@bt.com
> 
> > [snip]
> 
> > > I did not do so. What I said was that only "nothingness" can be
> > > infinite as an infinite amount of nothing is still nothing.
> 
> > Actually, an integral can be seen as "infinite amount" of
> > "nothingness":
> 
> >     Integral { f(x) dx } = Limit { Dx->0 ; Sum{ f(x) Dx } }
> 
> > with some suitable qualifications for the expressions of the
> > Integral, Limit and Sum. This can be interpreted as an "infinite sum"
> > of "nothingnesses", since each summed quantity f(x) Dx satisfies the
> > condition
> 
> >     Limit { Dx->0 ; f(x) Dx } = 0
> 
> > > I said that the amount of matter in the universe must be finite
> > > because no matter how much there is it is still 0% of an infinite
> > > amount. My argument was not based upon personal whim but on
> > > mathematic impossibility.
> 
> > Alas, mathematics strongly disagrees with you as well. Did you ever
> > had calculus in highschool?
> 
> I did it at university and have used it during my career. One can find
> the limit, the finite limit of a series of terms which converge. One can
> integrate between limits one of which is infinity. That is hardly the
> same thing.
> 
> I repeat - the amount of matter in the universe must be finite because
> no matter how much there is it is still 0% of an infinite amount. That
> has nothing to do with calculus or with converging series.

You are entirely correct. By definition, a countable infinity is
a contradiction in terms. Since matter is a countable reality,
it can never be actually infinite and, however great, is, as you
say, always "still 0% of an infinite amount".

A mathematical infinity itself also doesn't really exist. In
the definition of integration, the reduction of dx to zero, in
summing f(x)dx over an interval along x, is really shorthand
for  'making dx to be so small that making it smaller would
make no significant difference'. If dx actually became zero,
the entire summation of f(x)dx would be zero. Also, there
can be no such thing as a summation of an 'infinite
number' of elements.

Alen

Is this a 'fumble', Dirk!?? :)