Talk:Infinitesimal

I added the following statements to the second paragraph:

"An infinitesimal object by itself is often useless and not very well defined; in order to give it a meaning it usually has to be compared to another infinitesimal object in the same context (as in a derivative) or added together with an extremely large (an infinite) amount of other infinitesimal objects (as in an integral)."

I know that there maybe exists other ways to give infinitesimal numbers a meaning, but I didn't really know how to continue the lasts sentence. "Or in any other way give it a meaning" does just not sound right. Feel free to extend this statement to complete it. —Kri (talk) 22:42, 17 June 2012 (UTC)

Do you have a source for your "uselessness" claim? Tkuvho (talk) 16:35, 25 December 2012 (UTC)

No, I don't. I was about to comment on this myself and ask what the person who wrote the original comment meant by "useless" (exactly like you also did), only to notice that it was myself who had written it, twelve years ago. :P I think the way I think about numbers has changed a bit over time; I guess that studying abstract mathematics tends to have that effect.

I think that what I meant when I wrote that in order to give an infinitesimal number a meaning it usually has to be compared to another infinitesimal object in the same context, was that it (for example) is impossible to say whether a single infinitesimal number is large or small without putting it into a context and comparing it with another (non-zero) infinitesimal number, just like it is impossible to say whether a physical quantity is large or small without comparing it with another quantity with the same dimensions. To say whether something that is unitless is large or small without being given any further context is in principle possible since you always can compare it with unity, but if it is dimensionful, you can't do that, and an infinitesimal number can be considered a dimensionful quantity where ε is the unit (unless you want to say that all infinitesimal numbers always are small, but that's not especially helpful). —Kri (talk) 09:46, 9 April 2024 (UTC)

I think most of the information in the lead section, while useful, might do better in the 'history' section; it's very long and there's information in there that doesn't show up elsewhere in the article. Perciv (talk) 18:01, 9 April 2020 (UTC)

"His Archimedean property defines a number x as infinite if it satisfies the conditions |x|>1, |x|>1+1, |x|>1+1+1, ..., and infinitesimal if x≠0 and a similar set of conditions holds for x and the reciprocals of the positive integers." Which similar set of conditions? It could be interpreted as |x|> 1, |x|> 1/(1+1), |x|> 1(1+1+1),..., or as |x|< 1, |x| < 1/(1+1), |x| < 1/(1+1+1),.... L1ucas (talk) 00:26, 31 August 2021 (UTC)

In spite of a comment from 2012 about a "statutory" 4 paragraphs, I think the lede gets too far into details. The lede should be a summary. The third paragraph, for example, seems to be "detailed content" and not summary content. Maybe also the fourth paragraph. Why is (or was) there a desire to make the lede as long as possible? Thanks. David10244 (talk) 13:42, 30 December 2022 (UTC)

According to the picture, it looks like the infinitesimals are a set of numbers that include zero, but the lead of the article mentions explicitly that an infinitesimal number "is not 0." So, is zero included in the infinitesimals or not? If it is not included, I think this should be indicated in some way in the image, because right now I would say that it is at best misleading. —Kri (talk) 10:41, 9 April 2024 (UTC)