Definition talk:Continued Fraction/Expansion of Real Number

What does this page add which is not on the main page? --prime mover (talk) 08:34, 12 July 2017 (EDT)


 * This is to make clear what is meant when talking about the continued fraction of a real number. Take for example Condition for Rational to be a Convergent: the statement of the theorem links to Definition:Convergent of Continued Fraction, but it does not specify which continued fraction of $x$ we're talking about. There are plenty continued fractions converging to $x$, if we allow non-integers as partial quotients, but the theorem implicitly assumes the reader understands it is the one defined on this page.


 * This is the beginning of an attempt to remedy this ambiguity everywhere. The idea is to add a note at Definition:Convergent of Continued Fraction (and other pages) saying: "When dealing with real numbers, unless otherwise specified it is assumed we're talking about the usual continued fraction defined in Definition:Continued Fraction/Expansion of Real Number." --barto (talk) 08:52, 12 July 2017 (EDT)


 * What I'm trying to guard against is for an entire field of mathematics being duplicated on ProofWiki in different language with different terminology and from an infinitesimally different direction. --prime mover (talk) 10:06, 12 July 2017 (EDT)