Talk:Actual infinity

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The English could be improved a bit by a native speaker. 20:33, 30 March 2007 (UTC)Regards, WM

Probably there are English translations of some books quoted. 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)

Can there be infinitely many finite natural numbers?[edit]

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)

Yes I share your view that these "philosophers" have taken set theory too seriously. A formalist like me would view these infinities as statements in a formal language, so it's meaningless to ask how big an inaccessible cardinal really is (can anyone imagine it?). It even says in the article
Finally, let us return to our original topic, and let us draw the conclusion from all our reflections on the infinite. The overall result is then: The infinite is nowhere realized. Neither is it present in nature nor is it admissible as a foundation of our rational thinking - a remarkable harmony between being and thinking. (D. Hilbert [6, 190])Standard Oil (talk) 14:09, 31 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. (talk) 07:32, 4 June 2009 (UTC)

It's clearly a more philosophical argument than a logical one. After all finitists don't believe in infinity which is a consequence if we adhere to logic only. I recommend removing it so new comers won't get confused (like me 6month ago). Standard Oil (talk) 14:01, 5 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.

Done. (talk) 11:11, 6 June 2009 (UTC)

Bolding Good (for all articles on Wikipedia)[edit]

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 (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. (talk) 10:46, 3 March 2010 (UTC) (Carsten Schultz, TU Berlin)

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)
Now that's a tough one: Did Mückenheim use his own book when writing large parts of this article? (talk) 10:10, 4 March 2010 (UTC) (CS again)

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. (talk) 19:58, 12 February 2017 (UTC)

I'm hungry[edit]

pi anyone? (talk) 12:48, 14 January 2015 (UTC)

Long list of quotations with no context[edit]

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)

The Leibniz quote[edit]

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)