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The English could be improved a bit by a native speaker. 217.94.206.120 20:33, 30 March 2007 (UTC)Regards, WM
Probably there are English translations of some books quoted. 217.94.206.120 20:57, 30 March 2007 (UTC) Regards, WM
The whole page consists of pseudo-philosophical gibberish, and it should be deleted altogether. It is clearly conceived as a propaganda pamphlet by people who are completely devoid of any understanding of mathematics, but nonetheless for some reason have a serious issue with it. Let me stress: in mathematics, there is no such thing or object whatsoever as "actual infinity." For Wikipedia to say otherwise is an embarrassment and a disservice to the interested public. Kluto ( talk) 09:55, 22 February 2013 (UTC)
IN-finite means NOT-finite. It is clear that the size of the set of naturals is greater than any "natural number", are finists implying there's something between infinite and finite? How they derived A2 from A is in my opinion erroneous.
Do constructivist share this view? Standard Oil ( talk) 13:57, 27 April 2009 (UTC)
My math is sharper than my philosophy, so perhaps I'm misunderstanding the intent of this section. But let me plainly ask: are these philosophers' heads lodged in their rectums, or is their discussion actually more profound than gibberish spouted based on misunderstandings of set theory? -- Dzhim ( talk) 06:05, 28 May 2009 (UTC)
Is this a real argument? It sounds suspiciously like something someone made up on the spot. I cannot think of a sense in which the axiom A implies the axiom A2. After all, for any natural number n, the sequence eventually gets larger than n, at the n+1th element. I'm tempted to delete this unless someone can provide citation that this argument actually is used by finitists. Or, at least, to replace A with A2, instead of leaving the strangest implication that A implies A2. As it is, I'm replacing the term "series" with "sequence", because "series" is used for sums. 124.120.128.36 ( talk) 07:32, 4 June 2009 (UTC)
Is the Hilbert [6] not referenced properly? I'd like to read the original source but can't find it a reference to what the source actually is here.
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)
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) (Carsten Schultz, TU Berlin)
The references make no sense. For example, in 'A. Fraenkel [4, p. 6]' and 'D. Hilbert [6, p. 169]', what do the 4 and the 6 refer to? Someone needs to take this in hand. 86.132.223.248 ( talk) 19:58, 12 February 2017 (UTC)
pi anyone? 188.29.165.163 ( talk) 12:48, 14 January 2015 (UTC)
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)
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)
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)
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)
The examples given seem to contradict each other. What could the distinction between "adding one to each number before it" and the natural numbers be? The cited source isn't useful relevant to the article either, it only discusses infinity, as opposed to "Actual infinity". I believe that line should be deleted, but do not want to be overly hasty. Tototavros ( talk) 00:20, 4 February 2020 (UTC)
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):
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)
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
John Maynard Friedman has added "Concept in the philosophy of mathematics" as the short description for the article. Prior to the 19th century, yes, discussion of actual infinity was confined to philosophers, and Cantor's defense of the notion necessarily involved philosophical argumentation. As noted in the section § Current mathematical practice, however, "Actual infinity is now commonly accepted," so that discussion has turned to the mathematics of actual infinity. While intuitionism and other finitistic approaches have not quite disappeared, a modern presentation to a general audience has no need defend statements like " [the set of integers] is a subset of the set of all rational numbers ", found in the Integer article; the terms of the statement are, today, nearly uncontroversial mathematical concepts. This no longer lies in the domain of philosophy. A better short description, perhaps, would be "Concept in mathematics". That would still be misleading, though, as much of the article is devoted to pre-19th-century thought. Ideas? Peter Brown ( talk) 20:35, 4 November 2021 (UTC)
What actually is this "axiom of Euclidean finiteness" that states that actualities, singly and in aggregates, are necessarily finite? William M. Connolley ( talk) 14:25, 17 May 2023 (UTC)
![]() | This article was nominated for deletion on 31 August 2013 (UTC). The result of the discussion was keep. |
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||||||||||
|
The English could be improved a bit by a native speaker. 217.94.206.120 20:33, 30 March 2007 (UTC)Regards, WM
Probably there are English translations of some books quoted. 217.94.206.120 20:57, 30 March 2007 (UTC) Regards, WM
The whole page consists of pseudo-philosophical gibberish, and it should be deleted altogether. It is clearly conceived as a propaganda pamphlet by people who are completely devoid of any understanding of mathematics, but nonetheless for some reason have a serious issue with it. Let me stress: in mathematics, there is no such thing or object whatsoever as "actual infinity." For Wikipedia to say otherwise is an embarrassment and a disservice to the interested public. Kluto ( talk) 09:55, 22 February 2013 (UTC)
IN-finite means NOT-finite. It is clear that the size of the set of naturals is greater than any "natural number", are finists implying there's something between infinite and finite? How they derived A2 from A is in my opinion erroneous.
Do constructivist share this view? Standard Oil ( talk) 13:57, 27 April 2009 (UTC)
My math is sharper than my philosophy, so perhaps I'm misunderstanding the intent of this section. But let me plainly ask: are these philosophers' heads lodged in their rectums, or is their discussion actually more profound than gibberish spouted based on misunderstandings of set theory? -- Dzhim ( talk) 06:05, 28 May 2009 (UTC)
Is this a real argument? It sounds suspiciously like something someone made up on the spot. I cannot think of a sense in which the axiom A implies the axiom A2. After all, for any natural number n, the sequence eventually gets larger than n, at the n+1th element. I'm tempted to delete this unless someone can provide citation that this argument actually is used by finitists. Or, at least, to replace A with A2, instead of leaving the strangest implication that A implies A2. As it is, I'm replacing the term "series" with "sequence", because "series" is used for sums. 124.120.128.36 ( talk) 07:32, 4 June 2009 (UTC)
Is the Hilbert [6] not referenced properly? I'd like to read the original source but can't find it a reference to what the source actually is here.
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)
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) (Carsten Schultz, TU Berlin)
The references make no sense. For example, in 'A. Fraenkel [4, p. 6]' and 'D. Hilbert [6, p. 169]', what do the 4 and the 6 refer to? Someone needs to take this in hand. 86.132.223.248 ( talk) 19:58, 12 February 2017 (UTC)
pi anyone? 188.29.165.163 ( talk) 12:48, 14 January 2015 (UTC)
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)
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)
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)
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)
The examples given seem to contradict each other. What could the distinction between "adding one to each number before it" and the natural numbers be? The cited source isn't useful relevant to the article either, it only discusses infinity, as opposed to "Actual infinity". I believe that line should be deleted, but do not want to be overly hasty. Tototavros ( talk) 00:20, 4 February 2020 (UTC)
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):
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)
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
John Maynard Friedman has added "Concept in the philosophy of mathematics" as the short description for the article. Prior to the 19th century, yes, discussion of actual infinity was confined to philosophers, and Cantor's defense of the notion necessarily involved philosophical argumentation. As noted in the section § Current mathematical practice, however, "Actual infinity is now commonly accepted," so that discussion has turned to the mathematics of actual infinity. While intuitionism and other finitistic approaches have not quite disappeared, a modern presentation to a general audience has no need defend statements like " [the set of integers] is a subset of the set of all rational numbers ", found in the Integer article; the terms of the statement are, today, nearly uncontroversial mathematical concepts. This no longer lies in the domain of philosophy. A better short description, perhaps, would be "Concept in mathematics". That would still be misleading, though, as much of the article is devoted to pre-19th-century thought. Ideas? Peter Brown ( talk) 20:35, 4 November 2021 (UTC)
What actually is this "axiom of Euclidean finiteness" that states that actualities, singly and in aggregates, are necessarily finite? William M. Connolley ( talk) 14:25, 17 May 2023 (UTC)