Talk:Actual infinity

message: The English could be improved a bit by a native speaker. 217.94.206.120 20:33, 30 March 2007 (UTC)
thread_title: Improvements

message: I like the bolding which can help an overwhelmed newcomer/novice to the page navigate the material.  This bolding could improve all (many) articles on Wikipedia because it would give more levels of detail to peruse through (Large font titles first, bolded important sentences within titled sections, and then the text).  Of course, I know the whole article is really supposed to be an "introduction" anyway.  —Preceding unsigned comment added by 71.164.236.198 (talk) 21:29, 18 June 2009 (UTC)
thread_title:  Bolding Good (for all articles on Wikipedia) 

message: I object to two of the references.  Both of them are in German and of little use to the reader.
The first is Mückenheim's book.  Wolfgang Mückenheim (WM) has also edited this page and probably inserted the reference to his essentially self-published book.  Anyone with a basic understanding of mathematics can examine what he has uploaded to the arxiv to see that his reasoning is not to be trusted.  This reference had been removed before.
The website by Sponsel lists links without differentiating between scholarly sources and mere cranks.  Also, he would not be qualified to make such a distinction.
130.149.15.196 (talk) 10:46, 3 March 2010 (UTC)
replies: text: If in your estimation that these sources were not used to write the article, and given they are not used for quotation purposes etc, then I suggest you go ahead and remove them. Bill Wvbailey (talk) 19:02, 3 March 2010 (UTC)
replies: text: Now that's a tough one:  Did Mückenheim use his own book when writing large parts of this article? 87.160.141.93 (talk) 10:10, 4 March 2010 (UTC)
thread_title:  References 

message: pi anyone? 188.29.165.163 (talk) 12:48, 14 January 2015 (UTC)
thread_title:  I'm hungry 

message: The final two sections look like someone's scrapbook on infinity.  I don't think that the reader is served by such a long list of quotes without any context or explanation. Phiwum (talk) 13:27, 14 March 2016 (UTC)
thread_title:  Long list of quotations with no context 

message: While the Valspeak translation is entertaining, it may be better to give it in its context: "Je suis tellement pour l'infini actuel [we currently stop here], qu'au lieu d'admettre que la nature l'abhorre, comme l'on dit vulgairement, je tiens qu'elle l'affecte partout, pour mieux marquer les perfections de son auteur." Double sharp (talk) 13:20, 23 May 2016 (UTC)
thread_title:  The Leibniz quote 

message: This article weirdly starts with "Pre-Socratic" then jumps to "Aristotle". If Socrates isn't interesting, why doesn't it start with "Pre-Aristolean"? William M. Connolley (talk) 20:25, 20 December 2017 (UTC)
replies: text: Can't be a serious question: Compare search results for "Pre-Socratic" and "Pre-Aristolean". Pre-Socratic philosophy is a well established term for a period in the history of western philosophy. One wonders, what the knowledge of WP editors might be...--2.247.255.159 (talk) 04:13, 21 December 2017 (UTC)
thread_title:  Pre-Socratic? 

message: The first sentence: "Actual infinity is the idea that numbers, or some other type of mathematical object, can form an actual, completed totality; namely, a set", makes no sense as any kind of definition of actual infinity. Paul August ☎ 18:28, 27 December 2017 (UTC)
replies: text: Re-reading it (don't look at me, I didn't write it) I think the first sentence just isn't needed or helpful; so I tried removing it William M. Connolley (talk) 00:22, 28 December 2017 (UTC)
replies: text: Yes, much better. Paul August ☎ 00:49, 28 December 2017 (UTC)
thread_title: The first sentence makes no sense

message: The article, as currently written, does not seem to offer any sharp description of actual infinity, or defend why anyone might ever believe in it. It seems mostly a compendium of quotes to reject it. I would describe the success of actual infinity in mathematics in this way (my take may be non-standard, but seems to be what actually happens):
:Actual infinity is now commonly accepted, because mathematicians have learned how to construct algebraic statements using it. For example, one may write down a symbol, \omega, with the verbal description that "\omega stands for completed (countable) infinity". This symbol may be added as an ur-element to any set. One may also provide axioms that define addition, multiplication and inequality; specifically, ordinal arithmetic, such that expressions like n<\omega can be interpreted as "any natural number is less than completed infinity", or even statements such as \omega < \omega+1 are possible and consistent. The theory is so well developed, that even rather complex algebraic expressions, such as \omega^2, \omega^\omega and even 2^\omega can all be given a precise verbal description, and can be used in a wide variety of theorems and claims which appear to be consistent and meaningful. This detailed richness, the ability to define ordinal numbers in a consistent, meaningful way, renders much of the debate moot: whatever personal opinion one may hold about infinity or constructability, the existence of a rich theory for working with actual infinities using the tools of algebra is clearly in hand.
I'm gonna be bold and slot this in somewhere, and perhaps someone can improve upon this. 67.198.37.16 (talk) 23:45, 5 June 2021 (UTC)
replies: text: I disagree that the formal theory of ordinal numbers is relevant to any philosophical question about how infinity works or whether it exists. The theory does not require any "actual infinities" to exist. 47.35.146.128 (talk) 14:49, 1 July 2022 (UTC)
thread_title:  Missing defense of actual infinity! 

message: Cantor was the inventor of transfinite, the first mathematician to distinguish two types of actual infintie and to clearly demonstrate the Absolute can't be described by numbers and Maths.
This is a basic result for Mathematical science. In philosophy, the same result was given by Aristotle some centuries before. Zeno of Elea had just demonstrated that an actual infinite can't move by itself nor by other moving bodies. Aristotle conceived the Supreme Being as the immobile mover. Aristotle demonstrated that an actual infinite can't exist in the space and time of physics, where any quantity can be solely defined as continous, to say, infinitely divisible, whereas the actual infnite shall be unique and not divisible. 
This statement didn't exclude the existence of an actual infinite above the world of number. The existence of God, conceived as an actual and trascendent infinite, was at least made known by the works of St. Thomas Aquinas.
78.14.138.162 (talk) 11 June 2021
:Many problems with this.
:*The transfinite was not invented by Cantor.  Space had infinitely many points well before Cantor was born.
:*The Absolute is not a mathematical concept, so its properties are not a basic mathematical result.
:*Zeno, who died around 15 years before Aristotle was born, had not "just" demonstrated anything when Aristotle presented his views. 
:*Whether space or time is infinite in extent is unknown. Aristotle did not "demonstrate" that they are not infinite.
:*Continuity is not the same as infinite divisibility.
:*Atheism is a viable theory. Thomas Aquinas did not "make known" God's existence.
:Peter Brown (talk) 16:59, 12 June 2021 (UTC)
thread_title:  Cantor