English, Article, Journal or magazine article edition: On a Series of Goldbach and Euler Lluís Bibiloni; Pelegrí Viader; Jaume Paradís

User activity

Share to:
 
Bookmark: http://trove.nla.gov.au/version/153027
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • On a Series of Goldbach and Euler
Author
  • Lluís Bibiloni
  • Pelegrí Viader
  • Jaume Paradís
Physical Description
  • preprint
Notes
  • Theorem 1 of Euler’s paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum one. Euler attributes the Theorem to Goldbach. The proof is one of those examples of misuse of divergent series to obtain correct results so frequent during the seventeenth and eighteenth centuries. We examine this proof closely and, with the help of some insight provided by a modern (and completely dierent) proof of the Goldbach-Euler Theorem, we present a rational reconstruction in terms which could be considered rigorous by modern Weierstrassian standards. At the same time, with a few ideas borrowed from nonstandard analysis we see how the same reconstruction can be also be considered rigorous by modern Robinsonian standards. This last approach, though, is completely in tune with Goldbach and Euler’s proof. We hope to convince the reader then how, a few simple ideas from nonstandard analysis, vindicate Euler's work.
  • History of mathematics, infinite series, nonstandard analysis
  • RePEc:upf:upfgen:776
Language
  • English
Contributed by
OAIster

Get this edition

Other links

  • Set up My libraries

    How do I set up "My libraries"?

    In order to set up a list of libraries that you have access to, you must first login or sign up. Then set up a personal list of libraries from your profile page by clicking on your user name at the top right of any screen.

  • All (1)
  • Unknown (1)
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.

User activity


e.g. test cricket, Perth (WA), "Parkes, Henry"

Separate different tags with a comma. To include a comma in your tag, surround the tag with double quotes.

Be the first to add a tag for this edition

Be the first to add this to a list

Comments and reviews

What are comments? Add a comment

No user comments or reviews for this version

Add a comment