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. Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] 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.
