Re: abundance of irrationals!)

Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx> wrote in message news:<ITSnetNOTcom#virgil-1A8151.14060606042005@xxxxxxxxxxxxxxxxxxxxxxxx>...


> > >
> > > If, by "diagonal", you mean the non-terminating presumably decimal
> > > expression formed by taking then nth digit from the nth member of the
> > > sequence as its nth digit, ad infinitum, then that is the decimal
> > > expansion of 1/9.
> >
> > In case of series, the limit is contained? Whereas in case of
> > sequences the limit is not contained (in general)?
>
> NO! Where did you get the stupid notion that the limit need be
> "contained" in a series any more than in a sequence?

It is a stupid idea, in fact. And I am glad to see you are not sharing
it. But some people, even mathematicians, do not see a difference
between the limit

oo
SUM (1/2^k) = 1
k=1

and

SUM (1/2^k)
k e N

though they admit that

lim {n --> oo} 1/2^n = 0 while for every natural number

1/2^n > 0

Ins't that funny?

Regards, WM
.

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