
Re: 1.28  The myth of the 'real' number line.
Posted:
Jul 11, 2014 2:20 AM


On Friday, July 11, 2014 12:35:45 AM UTC+2, dull...@sprynet.com wrote: > On Thu, 10 Jul 2014 10:19:11 0700 (PDT), John Gabriel > >On Thursday, July 10, 2014 6:56:19 PM UTC+2, dull...@sprynet.com wrote: > > > > > >> >> >> No. Saying N=epsf(x)L is nonsense, because N is not allowed > > >> >> >> to depend on x. > > > > > >> >Nonsense. Allowing N=epsf(x)L proves that N works for all x>N. > > > > > >> N is not allowed to depend on x. That's simply how the logic of "Ae EN (Ax ...) works. > > > > > >There is nothing that says N cannot be stated in terms of x. > > > > > >The definition is: "for every eps > 0 there exists N such that f(x)  L < eps for all x > N". > > > > _That_ is exactly what says N cannot depend on x. First "there exists > N such that", and then something about x. N is chosen _first_, > then given N it's suppoed to be true that something happens > for every x > N.
Wrong. N is influenced by the value of x even though it's chosen first.
> > > > You really really really need to learn simple basic > > elementary _logic_. > > > > Look. Is the following true or false? > > > > (*) There exists N such that every x is larger than N. > > > > I hope you agree that (*) is false. No N is larger than > > _every_ x. > > > > But by your (wrong) logic it's easy to show that > > (*) is true: Just let N = x  1. > > > > If N = x  1 then x > N. True, Does that say > > that there exists N which is larger than every x? > > No. It seys for every x there exists N which > > is larger than x. Very different statements. > > > > But if N is allowed to depend on x then the > > clear false statment (*) becomes true. > > N is simply not allowed to depend on x. > > For the same reason as in the definition > > of limit.

