# An Interesting Serendipitous Real Number

- Published in 2000
- Added on

In the collection

This is the story of a remarkable real number, the discovery of which was due to a misprint. Namely, in the mid-seventies, while Ciprian was at the University of Bucharest, one of his former students approached him with the following question: If \(x_1 \gt 0\) and \(x_{n+1} = \left(1 + \frac{1}{x_n}\right)^n\), can \(x_n \to \infty\)?

## Comment

Known as the Foias constant.

## Links

- https://link.springer.com/chapter/10.1007/978-1-4471-0751-4_8
- https://link.springer.com/content/pdf/10.1007%2F978-1-4471-0751-4_8.pdf

## Other information

- key
- AnInterestingSerendipitousRealNumber
- type
- article
- date_added
- 2020-09-21
- date_published
- 2000-07-24
- publisher
- Springer, London
- doi
- 10.1007/978-1-4471-0751-4_8
- fulltext_html_url
- https://link.springer.com/chapter/10.1007/978-1-4471-0751-4_8
- identifier
- 10.1007/978-1-4471-0751-4_8
- pages
- 119-126

### BibTeX entry

@article{AnInterestingSerendipitousRealNumber, key = {AnInterestingSerendipitousRealNumber}, type = {article}, title = {An Interesting Serendipitous Real Number}, author = {John Ewing and Ciprian Foias}, abstract = {This is the story of a remarkable real number, the discovery of which was due to a misprint. Namely, in the mid-seventies, while Ciprian was at the University of Bucharest, one of his former students approached him with the following question: If \(x{\_}1 \gt 0\) and \(x{\_}{\{}n+1{\}} = \left(1 + \frac{\{}1{\}}{\{}x{\_}n{\}}\right)^n\), can \(x{\_}n \to \infty\)?}, comment = {Known as the Foias constant.}, date_added = {2020-09-21}, date_published = {2000-07-24}, urls = {https://link.springer.com/chapter/10.1007/978-1-4471-0751-4{\_}8,https://link.springer.com/content/pdf/10.1007{\%}2F978-1-4471-0751-4{\_}8.pdf}, collections = {fun-maths-facts}, url = {https://link.springer.com/chapter/10.1007/978-1-4471-0751-4{\_}8 https://link.springer.com/content/pdf/10.1007{\%}2F978-1-4471-0751-4{\_}8.pdf}, year = 2000, urldate = {2020-09-21}, publisher = {Springer, London}, doi = {10.1007/978-1-4471-0751-4{\_}8}, fulltext_html_url = {https://link.springer.com/chapter/10.1007/978-1-4471-0751-4{\_}8}, identifier = {10.1007/978-1-4471-0751-4{\_}8}, pages = {119-126} }