Re: Cantorian pseudomathematics

Shmuel (Seymour J.) Metz wrote:

> In <1137243049.154706.257960@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, on
> 01/14/2006 at 04:50 AM, Han.deBruijn@xxxxxxxxxxxxxx said:
>
> >Who the hell has decided that "there is no uniform distribution on N"
> >!?
>
> Everybody who understands what N is.

That is: everybody who _accepts_ what N is, according to mainstream
mathematics ideology. If want to you call that "understanding", fine.

> >Your logic and mine are mutually incompatible if you can't agree
> >upon the fact that an initial segment (1..n) of N is just N as n ->
> >oo
>
> You have neither fact not logic until you define what you mean by
> limit and probe that it has the requisite properties.

Ah, the usual trick that I haven't defined anything. Well, let me just
say that I might expect some intelligence from my readers. I have
defined already much more than some of my opponents are willing
to absorbe.

> >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.

> In <1137243963.979984.146720@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, on
> 01/14/2006 at 05:06 AM, Han.deBruijn@xxxxxxxxxxxxxx said:
>
> >The fact that I am challenging common notions in mathematics doesn't
> >mean that I'm quite ignorant about how to employ them according to
> >the "official" rules.
>
> No. But that fact that you are unable to cherently express your
> challenge does demonstrate your ignorance.

Again, the usual trick. I'm not impressed by this kind of "argument".

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

Han de Bruijn

.

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