Talk:Absolute Infinite

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I'm not at all happy with this page. I don't know a lot about transfinites but there are things here that worry me. Limit? Not in the normal sense. This needs expansion at least.

You can't just give something a name and hope that it won't introduce inconsistency to do so. Often it does. Going to have a think about this. Andrewa 10:50 16 Jul 2003 (UTC)


This is a proper noun. I have moved the page back to "Absolute Infinite" (with "absolute infinite" redirecting here). -- The Anome 08:55, 18 Sep 2003 (UTC)

In the see also section, what does "The Absolute" refer to?? Jaberwocky6669 02:28, Mar 30, 2005 (UTC)

Allow me to redo my question, what is the "absolute" at the top of the article? Jaberwocky6669 02:30, Mar 30, 2005 (UTC)

Contents

[edit] Did he seriously think this?

Is this serious? Did Cantor actually believe that "that every property of the Absolute Infinite is also held by some smaller object"? I mean, he was clearly an incredibly smart guy, but on the face of it, that's an idiotic opinion.

For example, it implies that there is some smaller object that is also larger than all objects besides itself. -Rwv37 04:25, Jun 27, 2005 (UTC)

Isn't the universe such an object? 24.174.45.155 21:33, 16 July 2006 (UTC)
No. The universe is an object that is larger than all objects besides itself. But that property is *not* shared with some smaller object. -Rwv37 00:41, 22 July 2006 (UTC)
I am using this exchange as justifying this article as "unclear." Cantor's quote "that every property..." is almost certainly a reference to the Reflection Theorem of set theory--but I can't be sure without a citation. See Reflection principle for more information. Cobaltnova 22:14, 10 November 2007 (UTC)

The notion of multiplicity Cantor describes here can't possibly be the same as on multiplicity A multiplicity is called well-ordered if it fulfills the condition that every sub-multiplicity has a first element; such a multiplicity I call for short a sequence. 24.174.45.155 21:33, 16 July 2006 (UTC)

I think he means what we now call a cardinal number. I just piped the wikilink which I hope is ok. 75.62.4.229 (talk) 04:37, 24 November 2007 (UTC)

[edit] Beyond the Absolute Infinite

Is there any mathematical object that is much larger than the Absolute Infinite? —The preceding unsigned comment was added by 89.1.49.6 (talk) 12:04, 17 January 2007 (UTC).


   Maybe any transinfinite number, or maybe the transabsolute   
   infinity.

[edit] ===========

Sounds funny. No, Cantor's transfinities are altogether not yet the absolute infinity. There is only one such ideal notion. In his letter to Dedekind 1899, Cantor excluded absolutely infinite, so called inconsistent sets because he was aware of the paradox by Burali-Forti. While the absolute infinity has indeed been until now the basis for the real numbers to be quite a different quality as compared to the rational ones, Cantors infinite cardinal numbers are based on his crazy fabrication of an "actual" infinity (infinitum creatum sive transfinitum), something imagined between potential and absolute infinity. Cantor's evidence for it is based on the unproven and untenable conclusion that even an infinite set must be either smaller or equally large or larger than an other one. Cantor intended to show what he intuitively felt: There are more real than rational numbers. Actually there is a so called 4th logical alternative: As already Salviati (Galilei) said: Infinite quantities must not be quantitatively compared with each other.

Weyl called Cantor's set theory a Schaukellogik (logically swinging between two contradictory notions of a set). Cantor's definition of a set has been declared invalid without substitute already by Fraenkel in 1923. Ebbinghaus et al. quoted Lessing saying: obvious error, but it led to something very valuable. Blumschein 17:10, 4 June 2007 (UTC)

[edit] Absolute Absolute Infinite, Absolute Absolute Absolute Infinite, etc.

The way that leads from Infinite to Absolute Infinite could lead also from Absolute Infinite to Absolute Absolute Infinite, from Absolute Absolute Infinite to Absolute Absolute Absolute Infinite and beyond. So, where is the limit? 89.1.112.168 07:25, 13 September 2007 (UTC)

[edit] Proper Classes and Philosophical Qualms

I am removing "mysterious" from the description of proper classes. These ideas are mathematically well-defined (see Kunen, Kenneth "Set Theory: An Introduction to Independence Proofs").

[edit] von Neumann universe

I think the corresponding idea in axiomatic set theory is the von Neumann universe also known as the cumulative hierarchy. 75.62.4.229 (talk) 04:39, 24 November 2007 (UTC)