On Sunday, May 6, 2018 at 9:16:13 PM UTC-5, Russell Standish wrote: > > On Sun, May 06, 2018 at 06:19:01PM -0700, Brent Meeker wrote: > > But don't you take all arithmetic theories to include the axioms that > say > > every number has a successor? > > Just because every number has a successor does not entail the > existence of ω. > > This is otherwise known as "potential infinity" versus "actual > infinity". > > I've come across a similar sort of issue in studying what I call > "open dimensional systems". An open dimensional system is > still a finite dimensional system, but quite a distinct beast from the > usual fixed dimensional systems studied in dynamical systems > theory. Just doing a quick Google search indicates that I have been > unsuccessful in getting the term "open dimensional" adopted - it looks > like "unbounded dimensional" might have won the day :P. >
I will try to respond to Bruno more completely, but this is a bit of the conundrum. One can work up various models with different ideas about transfinite numbers. ZF set theory embraces infinity or transfinite numbers with all the issues that come with it. Other ideas are more restrictive. >From the perspective of physics these concerns in a sense flap in the breeze with little direct concern. LC > > Cheers > -- > > ---------------------------------------------------------------------------- > > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders > Visiting Senior Research Fellow [email protected] > <javascript:> > Economics, Kingston University http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
