Talk:Sequence of Powers of Number less than One

I’ve refactored this page which can be seen (temporarily) here. The motivation for this was to extend the therorm to include normed division rings. In summary what I have done is the following:
 * Separated the Real case from the Complex case
 * Added the normed division ring case
 * Dropped the rational case (it seems superfluous to me)
 * Expanded the theorem from:
 * $\size{x} < 1 \implies \sequence {x_n}$ is a null sequence
 * $\quad$to
 * $\size{x} < 1 \iff \sequence {x_n}$ is a null sequence

More controversatially I’d like to change the name of the theorem from ’Power of Number less than One’ to ‘Sequence of Powers of Number less than One’.

Is there any objection to the name change or any other of the changes? Leigh.Samphier (talk) 06:16, 1 January 2019 (EST)


 * All this makes sense, although we need to check carefully whether we do need the rational case -- as it is possible that this theorem for strictly rational terms may be one of the required steps in the justification of the derivation of real numbers as the limit of a Cauchy sequence of rationals. I haven't checked this, but it's worth doing.


 * Name change is good. Please feel free to go ahead. --prime mover (talk) 06:38, 1 January 2019 (EST)