```Date: Mar 9, 2013 9:28 PM
Author: William Elliot
Subject: Re: Simple analytical properties of n/d

On Sat, 9 Mar 2013, Ross A. Finlayson wrote:> On Mar 8, 9:31 pm, William Elliot <ma...@panix.com> wrote:> > What's R_[0,1]?  So now your considering any function f:N -> [0,1]> > and want to discuss rang f.> >> > > Obviously and directly as N is countable, ran(f)> > > is countable,> > > Is ran(f) = [0,1]? > >> > Of course not, you showed that range f is countable and> > unable to be any uncountable set.> > Apply the antidiagonal argument to ran(f).Why?> the only item different from each is and, ran(f) includes 1.0. Huh?> Apply the nested intervals argument to ran(f).What's that?> The interval is [.0, .1], there's no missing element from ran(f)'s> [0,1].> > The antidiagonal argument and nested intervals argument don't support> that ran(f) =/= [0,1].> > In fact, remarkable among functions N -> R, is that the antidiagonal> argument and nested intervals argument, DON'T apply to f.It doesn't?  What if f:N -> [0,1] is the constant function f(N) = {0}?
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