# An Interesting Serendipitous Real Number

• Published in 2000
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.

## Other information

key
AnInterestingSerendipitousRealNumber
type
article
2020-09-21
date_published
2000-11-14
publisher
Springer, London
doi
10.1007/978-1-4471-0751-4_8
fulltext_html_url
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.},
}