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Topic: (infinity) A real story
Replies: 9   Last Post: Oct 17, 2013 6:56 AM

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Posts: 3,628
From: London
Registered: 2/8/08
Re: (infinity) A real story
Posted: Oct 16, 2013 5:12 PM
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"Albrecht" <albstorz@gmx.de> wrote in message
> On Wednesday, October 16, 2013 12:21:34 AM UTC+2, Julio Di Egidio wrote:
>> <mueckenh@rz.fh-augsburg.de> wrote in message
>> news:070c8685-8bde-4ddc-9b71-93058e60463c@googlegroups.com...

>> > Above you see their widely known formulation of the natural numbers.
>> > They
>> > did not think about the problem of inclusion monotony, probably because
>> > they did not imagine the set in the form of my table.

>> > 1
>> > 1, 2
>> > 1, 2, 3
>> > ...

>> The set of natural numbers is the limit of that sequence:
>> 1: 1
>> 2: 1,2
>> 3: 1,2,3
>> ...
>> n: 1,2,3,...,n
>> ...
>> ---
>> w: 1,2,3,...,n,...,___w
>> For geometric reasons, namely for there being a last index, that
>> construction rather demands actual infinities.
>> In that sense, I should concede you have a point, although that is still
>> not
>> that actual infinities in mathematics make no sense, in fact on the
>> contrary.

> The actual infinity of modern math is a wishing well.

You make no sense, you should rather congratulate me for a construction
showing that "necessarily, numbers count themselves".

> First, the elementar principle that a collection with X elements contains
> a X-th element is broken for the sake of the glory of some dead and the
> comfort of some living mathematicians.

Then you have not even bothered to actually read what I have written.

> And second, the arising problems like the Skolem Paradoxon are downplayed
> with some pettyfoggeries. Nobody can prove an antinomy in the system of
> ZFC, to date. Okay. But the existence of different infinities remains an
> angle of view. It is not a "necessity of thinking". There are not more
> reals than naturals in a factual sense.

Okay? Angles of view? Factual sense?? The facts of which world, please?

> In the majority, the defenders of Cantors actual infinity are "religious
> warriors" without any credentials, are clueless about the whole issue and
> are unable of logical reasoning.

Yeah, sure, in the meantime you can't even read.


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