User:Tkuvho/1/ ∞

1/∞ is not a symbol. It is an expression containing the symbol ∞. The assertion "is the symbolic representation of the mathematical concept of an infinitesimal" is wrong: 1/∞ is not and has never been an infinitesimal, it is simply zero. Thus this draft is pure original research and is also mathematically wrong. I strongly recommend to reject it. D.Lazard (talk) 15:34, 11 July 2014 (UTC)


 * To D.Lazard: Nowadays 1/∞ "is not an infinitesimal"; but are you sure "it has never been"? What about the book of Wallis mentioned below? Boris Tsirelson (talk) 18:20, 11 July 2014 (UTC)


 * To D.Lazard, Tsirel|Boris Tsirelson:

I have begun my research on this topic in order to address the concerns and see if a first version will at least be sufficient to decide on a reasonable threshold for inclusion. Regarding the comment that "1/∞ is not and has never been an infinitesimal" This statement clearly implies that references in both the Infinitesimal article and John Wallis' article will need to be revised. The comment essentially asserts that John Wallis' work as it is referenced (prominently) in those articles is fictitious. I am presently attempting to verify whether in fact they are fictitious. The outcome of that research will dictate whether or not I decide to pursue developing the article particularly if I cannot locate any other references of comparable notability. There is a 1981 book referenced as "The Mathematical Work of John Wallis" (AMS Chelsea Publishing) by J. F. Scott which may provide a reference but if the symbol cannot be referenced in either its symbolic or linguistic form (ie "the inverse of infinity" or the "reciprocal of infinity") in the original Wallis document (which may well be unreferencable) than I will most likely not pursue inclusion via further development.YWA2014 (talk) 01:45, 14 July 2014 (UTC)


 * To D.Lazard, Tsirel|Boris Tsirelson:

I have confirmed references for the symbol 1/∞ in the 1656 Wallis Book "Arithmetica Infinitorum". They can easily be directly referenced, the current situation in the infinitesimal and Wallis articles is that they are indirectly referenced via two sources which are both by authors with minimal publications in the area of mathematics. The use of the symbol in conjunction with the infinity symbol in the referenced work strongly suggests that the symbol was one of, if not, the first representations of differential (or indivisibles as they were referred to at that time) as they were used in the process of integration. Whatever nomenclature was used at that time to describe the symbol or expression, it clearly was a symbolic representation of some concept that was used as part of the concept of integration as it was thought of and referred to symbolically at that time. So, my initial research supports the statement in the infinitesimal article that the symbol 1/∞ was used to represent the concept of infinitesimal by Wallis...this finding directly contradicts D. Lazards statement that it is not and confirms that the most prominent reference is authentic. Wallis can be referenced as one of the heavy hitters in the development of Calculus, he preceded Newton and is credited with inspiring Newton's work...Newton's notation has its own article. Wallis' notation preceded it and was instrumental in the conceptual development of Calculus...that alone in my opinion should be enough to warrant inclusion.YWA2014 (talk) 04:50, 14 July 2014 (UTC)

Thanks for the comments, please note that what is below has virtually no references and was not researched for more than 10 minutes because I wanted to get an idea of what the initial reactions would be first and then determine if there would be a willingness to discuss the article's inclusion before I invested the work into developing it...and yes I pretty much wrote it off of the top of my head for the same reasons. So I appreciate the initial reactions and comments because that was my intent. I will start addressing them based on my impression of their relative significance as reasonable concerns. Notability: I completely agree that this is the primary issue that needs to be addressed. The blurb that I wrote below conveys the impression that the only references that can be cited are from Wallis' work and that that article is sufficient to address the notability. I should hope that if I can produce other notable references for where this "expression" or "symbol" has been used in the evolution of Calculus then at some point we could all agree upon a reasonable threshold of notability for its inclusion based on the number of significant references that can be cited.YWA2014 (talk) 02:08, 13 July 2014 (UTC)


 * @ DLazard - I appreciate your expressing your concerns but if its OK with you I think we should try to address them via a gentlemen's reference citation duel. With that in mind in order to support your assertion that this combination of symbols is more an expression than symbol can you reference anything to support your claim? My initial reaction to this is that there are distinct mathematical symbols that can be viewed also as expressions in the sense that they are combinations of unique symbols and symbols that are used in expressions.  An example of this would be the operator dy/dx or Laplacian.  Likewise, if you could please provide a reference to support your assertion that 1/∞ = 0. Finally the statement "1/∞ is not and has never been an infinitesimal"...I think that this one is the most significant of your concerns and the onus is on me to demonstrate a connection with supporting references.  I will surely agree that if the score is tied or 0/0 and even if I cannot demonstrate a significant advantage via references that the article does not warrant inclusion.YWA2014 (talk) 03:02, 13 July 2014 (UTC)

It's not clear to me that this article establishes the notability of 1/∞. Yes, John Wallis is notable, and the idea of taking a reciprocal of infinity is, while not a part of contemporary mathematics, certainly part of its historical development, as the lone reference proves. But this article does not establish that it was an influential concept. The article suggests that 1/∞ was important to Wallis and that through him it may have influenced the development of calculus. (I ignore the paragraph about Zeno, which is unreferenced and quite likely wrong.) Fine; but did 1/∞ ever take on a life of its own? How many people wrote about it and thought about it? I suspect that the lack of documentation on 1/∞ is because the idea simply is not that important, and that it therefore is not notable. Anything interesting that can be said about it can be said in the article on Wallis (and indeed is likely there already). Ozob (talk) 14:43, 12 July 2014 (UTC)


 * I agree. If at all, this could be some lines in an article on the history of mathematics. Boris Tsirelson (talk) 17:50, 12 July 2014 (UTC)

I understand your concerns here and agree that in its present state the article would surely not warrant inclusion...however, would you both agree that if were possible to provide a threshold of significant references that we all deem are reasonably sufficient that the article would then warrant inclusion? My purpose for posting the bare bones article is to gauge whether or not there is any support for the assertion that 1/∞ is historically tied to the evolution of Calculus and the use of infinitesimals. In the article I mention a connection with the differential symbol dx used to represent the concept of infinitesimal in differential and integral calculus (which has a unique article)...I should hope that you all would agree that if a connection can be demonstrated between 1/∞ and dx via references that it would support the inclusion of the article.YWA2014 (talk) 02:52, 13 July 2014 (UTC)


 * To Ozob:

My response to the lack of notability claim based on my current research as this notation is at least as notable than Newton's fluxion notation. This assessment is based on the fact that Wallis' notation preceded Newton's and was instrumental to the conceptual development of Calculus. Wallis' work and its associated notation can be referenced as being described as one of Newton's primary influences in his development of Calculus...I feel this alone warrants inclusion, I will be working on looking for additional references to the notation to further support notability.YWA2014 (talk) 05:00, 14 July 2014 (UTC)


 * Newton's notation is in current use; physicists and engineers use the notation $$\dot x$$ for a derivative all the time. Wallis' notation is not.  If you want to make a convincing argument that the notation 1/∞ is notable enough to deserve its own article, you will have to show that someone other than Wallis used it.  If that cannot be done then I suggest you expand the relevant portion of the John Wallis article.  Ozob (talk) 06:24, 14 July 2014 (UTC)


 * To Ozob: One more reference of a notable mathematician that has used it seems reasonable as a threshold to me...however

what would the threshold be for unique secondary historical references? There are two in the infinitesimal article but I would say that only the JF Scott reference would be notable and countable towards a threshold. YWA2014 (talk) 08:11, 14 July 2014 (UTC)


 * There are no strict thresholds. If you can show that this concept meets the general notability guideline, then it qualifies for an article.  I realize that the GNG does not precisely specify what is notable and what isn't, but it's the fundamental Wikipedia policy on what warrants an article and what doesn't.  Ozob (talk) 19:59, 14 July 2014 (UTC)


 * To Ozob: Got it, and understand that it is going to involve a judgement call...just wanted to

see if we could try to pin down a threshold as much as possible so I have an idea of how hard I am going to have to dig. Thanks for your guidance.YWA2014 (talk) 08:57, 15 July 2014 (UTC)

= 1/ ∞ =

The origin of the symbol 1/∞ is commonly attributed to the 17th century English mathematician John Wallis who introduced it in his 1655 book Treatise on the Conic Sections. The symbol, which denotes the reciprocal, or inverse, of ∞, is the symbolic representation of the mathematical concept of an infinitesimal. In the Treatise on the Conic Sections Wallis also discusses the concept of a relationship between the symbolic representation of infinitesimal 1/∞ that he introduced and the concept of infinity for which he introduced the symbol ∞. The concept suggests a thought experiment of adding an infinite number of lines have infinitesimal width to form a finite plane. This concept was the predecessor to the modern method of integration used in integral calculus.

The conceptual origins of the concept of the infinitesimal 1/∞ can be traced as far back as the Greek philosopher Zeno of Elea, whose Zeno's dichotomy paradox was the first mathematical concept to consider the relationship between a finite interval and an interval approaching that of an infinitesimal-sized interval.

Subsequent to its introduction by Wallis the symbolic representation of the concept of infinitesimal was used in different forms such as Newton's fluxion notation and Leibniz's differential notation. Emphasis on the symbolic representation of the infinitesimal was of less concern and importance as the introduction of the concept of limits was introduced with their associated notation.