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Topic: Sequence limit
Replies: 72   Last Post: Nov 26, 2013 12:07 AM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Sequence limit
Posted: Nov 14, 2013 12:06 AM

In article <l614vg\$r43\$1@dont-email.me>,
Timothy Murphy <gayleard@eircom.net> wrote:

> Bart Goddard wrote:
>

> >>> > It's clear that the upper limit is 1,
> >>> > since n pi mod Z will be distributed evenly in [0,1),
> >>> > and so will infinitely often be in the range (1/3,2/3).

> >
> >>> I don't think this is true. |Sin(n)| is probably
> >>> distributed evenly, but raising to (1/n) power is going
> >>> to crowd things toward 0.

> >>
> >> This sounds ambiguous to me. Do you mean that you don't think it's
> >> true that the upper limit is 1 or do you mean that you don't think
> >> it's true that it's clear that the upper limit is 1?

> >
> > Neither. Obviously the thing I don't think is true is the
> > sentence to which I'm responding:

>
> > That the values
> > of |sin n|^(1/n) are evenly distributed. You could
> > infer this by my coment about the (1/n) power pushing
> > things toward zero.

>
> You seem to be responding to yourself.
> I did not say that "|sin n|^(1/n) is evenly distributed".
>

> > It has already been proven that the limit is 1.
>
> I think I missed this proof.
> What was the essential idea?

Note that for any fixed value, x, between 0 and 1, lim x ^(1/n) = 1
--

Date Subject Author
10/3/13 Bart Goddard
10/3/13 Karl-Olav Nyberg
10/3/13 quasi
10/3/13 quasi
10/3/13 Karl-Olav Nyberg
10/3/13 quasi
10/4/13 Roland Franzius
10/4/13 quasi
10/5/13 Roland Franzius
10/5/13 quasi
10/26/13 Roland Franzius
10/26/13 karl
10/26/13 Roland Franzius
10/26/13 gnasher729
10/27/13 karl
10/3/13 quasi
10/4/13 Leon Aigret
10/4/13 William Elliot
10/4/13 quasi
10/4/13 William Elliot
10/4/13 quasi
10/4/13 David C. Ullrich
10/4/13 Robin Chapman
10/5/13 Bart Goddard
10/4/13 Bart Goddard
10/4/13 Peter Percival
10/5/13 Virgil
10/4/13 Bart Goddard
10/6/13 David Bernier
10/6/13 Virgil
10/6/13 Bart Goddard
10/7/13 Mohan Pawar
10/7/13 Bart Goddard
10/7/13 gnasher729
10/7/13 Richard Tobin
10/7/13 Robin Chapman
10/7/13 Michael F. Stemper
10/7/13 Michael F. Stemper
10/7/13 David Bernier
10/7/13 fom
10/8/13 Virgil
10/8/13 fom
10/8/13 Virgil
10/8/13 fom
10/4/13 fom
10/4/13 quasi
10/4/13 quasi
10/9/13 Shmuel (Seymour J.) Metz
10/10/13 Bart Goddard
11/5/13 Shmuel (Seymour J.) Metz
11/6/13 Bart Goddard
11/11/13 Shmuel (Seymour J.) Metz
11/12/13 Bart Goddard
11/15/13 Shmuel (Seymour J.) Metz
11/15/13 Bart Goddard
11/6/13 Timothy Murphy
11/8/13 Bart Goddard
11/8/13 Paul
11/8/13 Bart Goddard
11/9/13 Paul
11/9/13 quasi
11/9/13 quasi
11/9/13 quasi
11/13/13 Timothy Murphy
11/13/13 quasi
11/14/13 Timothy Murphy
11/14/13 Virgil
11/14/13 Roland Franzius
11/26/13 Shmuel (Seymour J.) Metz
11/9/13 Roland Franzius
11/9/13 Paul