On 28/03/2013 3:38 PM, fom wrote: > On 3/28/2013 7:48 AM, WM wrote: >>> >> If the set of all rationals exists, then that limit exists already in >> that set. Combining paths with loss of nodes is not useful to increase >> the number of paths. > > But no one is talking about whether the sequence > of rationals converging to a rational is in the > set of rationals. > > The issue is a representation of apparent geometric > completeness within an arithmetical system.
I don't think so. I think the issue is that Mueckenheim, whom someone decided to hire as a professor of mathematics at a third-rate institution, manages to obfuscate just enough the distinction between repeating and non-repeating decimals when he applies them to paths, and that he is too dense to comprehend that. Crayon marks, indeed.
> The issue is the logical form of such a construction. > > That you believe your crayon marks justify a material > belief in some abstract, non-material objects but deny > a material belief in other abstract, non-material > objects verges on sheer lunacy. > > Crayon marks have nothing to do with it. > > Belief has nothing to do with it. > > And, your ability to call certain crayon marks "names" > has nothing to do with it either. You failed your > science lesson on those days too. > >