Re: Cantorian pseudomathematics

Han.deBruijn@xxxxxxxxxxxxxx wrote:
> Shmuel (Seymour J.) Metz wrote:
>
> > In <1137243049.154706.257960@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, on
> > 01/14/2006 at 04:50 AM, Han.deBruijn@xxxxxxxxxxxxxx said:
> >

<snip>

> > >Oh, and for the sake of "clarity", the limit of a segment (1..n) for
> > >n -> oo "means": if you have a finite segment (1..m), then replace
> > >it by a larger finite segment (1..n) where n > m. Recursively.
> >
> > There is no clarity where there is no definition. Trplacing a finite
> > set with a finite set recursively gives you a finite set.
>
> And so on and so forth. That is what some people call infinity.
>

Assuming that you also mean that that's what you call "infinity",
define the function P on an interval [1,n] as P([1,n]) = 0 if n is even
and 1 if n is odd. In your definition of "in the limit" what is the
limit of P([1,n]) as n->oo?

If you accept that P may not be definable in the limit, is it so odd
that "selecting a random member" may also not be definable "in the
limit" - even though it makes sense for every finite interval?

<snip>

> > >It's a common misunderstanding in 'sci.math' that those who try to
> > >present alternative approaches are always ignorant about mathematics
> > >"as it should be done".
> >
> > Au contraire, it is a common observation of fact that those claiming
> > to present alternative approaches often fail to either understand the
> > conventional approaches or to express a coherent alternative. It is a
> > common observation that those making such claims often fail to either
> > understand conventional definitions of standard nomenclature or to
> > coherently present their private definitions. It is a common
> > observation that those claiming that their original methods are being
> > capriciously rejected fail to realize just how common it is for the
> > Mathematical community to welcome new methods with open arms.
>
> If "common observation" is interpreted as "common observation by
> the community of mainstream mathematicians", then you are right,
> quite obviously.

If "mainstream mathematicians" are those who require an axiomatic
approach involving precise definitions, clear premises and logical
deductions, then yes, he is quite obviously right.

> I suggest you read the original poster by David Petry,
> which describes exactly the kind of behaviour you are exposing here.
>

David seems to have his own, separate axe to grind.

Cheers - Chas

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