In article <Q_OdnZ21K_FeyiXZnZ2dnUVZ_qOdnZ2d@speakeasy.net>, Hatto von Aquitanien <abbot@AugiaDives.hre> wrote:
> Gene Ward Smith wrote: > > > > > Hatto von Aquitanien wrote: > > > >> If we consider the > >> set of integers rather than natural numbers, I ask what it means to > >> rotate the members of that set to the left or right. > > > > Your question is gibberish. > > The question has clear meaning when discussing finite ordered sets. If you > don't understand what it means, the I will be happy to explain it to you. > This might help: > > http://documents.wolfram.com/mathematica/functions/RotateLeft > > If you still don't understand, let me know. I will try to help.
For a finite sequence of object arranged in a left to right ordering, any such left or right rotation is the result of a sequence of operations in which the rightmost element is successively moved to the left end.
To suppose that this can be done with any ordering for which either end does not exist, is silly.
That, of course, does not prohibit order isomorphisms from the naturally ordered set of integers to itself, but whether any of these isomorphs can be properly thought of as rotating the integers, I doubt.