Talk:Sequence of Powers of Number less than One

I’ve refactored this page which can be seen (temporarily) leigh.Samphier/Sandbox/Sequence of Powers of Number less than One. 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)


 * All the old talk pages attached to the various subproofs of Power of Number less than One had been orphaned. I haven't a clue what they referred to, as I don't know where the pages went for all the various proofs.


 * What actually happened here? --prime mover (talk) 10:48, 26 July 2019 (EDT)


 * Oh yes and we still have this: Talk:Sequence of Powers of Number less than One/Proof 4 (which I just renamed) which I don't know what it's about at all. --prime mover (talk) 10:49, 26 July 2019 (EDT)


 * The talk pages were copied to the new pages on 5/Jan rather than being moved. Not sure why I did this, but I should have moved them so as not to lose the version history. Power of Number less than One/Proof 4 (now Talk:Sequence of Powers of Number less than One/Proof 4) was copied to Talk:Sequence of Powers of Number less than One/Necessary Condition/Proof 4.


 * Let me know if there are any other orphaned talk pages. —Leigh.Samphier (talk) 01:57, 27 July 2019 (EDT)


 * Thanks for that. I've deleted all those old talk pages now, and in due course we can delete this exchange so as to reduce the redlink count. Please feel free to keep up the good work. --prime mover (talk) 03:42, 27 July 2019 (EDT)