On Wednesday, June 12, 2013 11:47:38 PM UTC-7, Norbert_Paul wrote: > Ross A. Finlayson wrote: > > > Do the integers, via their existence, contain elements infinite in extent? > > What do you mean by "integer", "existence", "containment", "inifinity" and "extent"? > > > > > If not, what is their extent? > > see above > > > > > A variety of classical era thinkers maintain a discussion on mathematics. > > I am not interested in philosophical discussions about math. > > I just stick to mathematics.
To refine to define the finite and non-finite, or infinite and non-infinite, usually non-finity is as shown with a set of ordinals that is Dedekind-finite or otherwise an unchanging amount of ordinals that is of to no limit ordinals, in infinite and transfinite ordinals. Defining infinity as change then non-infinity as dividing or divisible is so back to the non-infinite divides to itself, the infinite is only as to the related.
So, counting or division could be read first in forward inference: for defining the non-finite by the counted finite, or the infinite by the non-infinite divided continuum (here with the continuum as infinite).
This is plainly constructible, in terms of that the infinite (-ies) establish related rates of change as to the continuum.
Then where the coordinates as it were are counted outward or to the origin, for the nilpotent and as in to partial products and transformation, they at once establish in one the other, in bounds then space.