In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 31 Jan., 23:35, david petry <david_lawrence_pe...@yahoo.com> wrote: > > > It is eminently reasonable to believe that the purpose of mathematics is to > > provide a rigorous and practically useful conceptual framework for > > reasoning quantitatively about real world phenomena.
There are any number of even quite famous mathematicians who would disagree, for example G.H. Hardy.
> The objects that exist in a conceptual framework are concepts; the > universe of mathematical objects is a collection of concepts.
And how does one manage to do Euclidean geometry without infinitely long lines and infinitely many ppnts on the circumdrence of circles, and so on.
That WM is incapable of conceiving of infinite sets does not prevent those less seriously handicapped from doing so.
And despite WMs debility a great many people both can and do.
> > In Cantor's argument, these facts are inversed. There is an infinite > list of infinite sequences.
Actually, Cantor's argument does not require that any such list exist. Cantor's merely says that IF such a list were to exist then it must also be incomplete.
But the standard real number system cannot be made to work properly in WM's world.
How can an ordered set be dense without the actuallity of infinity or points between points?
At what level does one say that for distinct numbers x and y that (x+y)/2 is no longer a number? --