On 4 Jan., 10:54, Zuhair <zaljo...@gmail.com> wrote: > On Jan 4, 10:22 am, Virgil <vir...@ligriv.com> wrote: > > > > > > > In article > > <3c133339-6b4c-4f74-937f-804bdaad3...@t5g2000vba.googlegroups.com>, > > > Zuhair <zaljo...@gmail.com> wrote: > > > On Jan 4, 5:33 am, Virgil <vir...@ligriv.com> wrote: > > > > In article > > > > <6302ee90-f0a2-4be5-9dbb-c1f999c3a...@c16g2000yqi.googlegroups.com>, > > > > > Zuhair <zaljo...@gmail.com> wrote: > > > > > Since all reals are distinguished by finite initial > > > > > segments of them, > > > > > Some reals are distinguished by finite initial segments of their decimal > > > > representations, most are not.
Those are not different numbers. Such objects cannot appear in any Cantor list as entries or diagonal
> > > Of course all reals are to be represented by *INFINITE* binary decimal > > > expansions, so 0.12 is represented as 0.120000...
It is impossible to represent any real number by an infinite expansion that is not defined by a finite word. > > > > So we are not speaking about the same distinguishability criterion.
There is no other criterion. > > which mean that your objection is irrelevant to my argument. I think > that the argument that I've presented
that you have parroted without understanding its implications
> shows some COUNTER-INTUITIVENESS > to uncountability, that's all.
Have you ever seen that Cantor's argument works without distinguishability? Why must b_n =/= a_nn? Never wondered why that is required at a finite n?Anybody who pretends that there are numbers that cannot be distinguished is outside of mathematics and even outside of Cantor's argument and its implications.