The introduction starts off by taking about the continued fraction associated to a number. Would it be better to define a continued fraction intrinsically, say that every CF represents (evaluates to/converges to) a real number and then sy that every real number has a CF? Thue Siegel Roth (talk) 21:11, 8 February 2012 (UTC)
It's probably a matter of taste but I like it better the way it is. The Generalized continued fraction article would probably be the best place to cover convergence issues. The way I thinking about it is that, for example, a decimal expansion is really a infinite series, but we don't (I hope) start our article on the decimal system with material on convergence tests.--RDBury (talk) 06:30, 9 February 2012 (UTC)
I don't copmment much on Wikipedia, but wanted to say that I thought the example was great. It would probably be more encyclopedic to present the general case, but using a specific example, at least for me, was much more edifying. Good job.Zipperfish (talk) 16:12, 15 March 2013 (UTC)
"In lieu in the introduction, could be replaced by in place" — Preceding unsigned comment added by 188.8.131.52 (talk) 14:01, 5 July 2014 (UTC)
Contradicts itself in "Continued fraction expansions of pi"
It says: The third convergent of π is [...] 355/113. Then later on it says "The third convergent, therefore, is 333/106." I think the first statement should say "The fourth convergent ..." Olliehaffenden (talk) 10:49, 17 July 2014 (UTC)
Yes, you are right. 355/113 is the fourth convergent, not the third. I have changed the text in the article. Gandalf61 (talk) 14:51, 17 July 2014 (UTC)