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Topic: Dimension of the space of real sequences
Replies: 21   Last Post: Nov 19, 2012 10:22 AM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Dimension of the space of real sequences
Posted: Nov 13, 2012 8:20 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
<ken.pledger-61ED7B.13480914112012@news.eternal-september.org>,
Ken Pledger <ken.pledger@vuw.ac.nz> wrote:

> In article <agfvqlFbot6U1@mid.individual.net>,
> José Carlos Santos <jcsantos@fc.up.pt> wrote:
>

> > ....
> > Can someone please tell me how to prove that the real vector space of
> > all sequences of real numbers has uncountable dimension? ....

>
>
> Over what field? Over the reals, the dimension is surely countable,
> isn't it? Or am I misunderstanding something?
>
> Ken Pledger.



For every infinite

The SET of reals as a vector space over the rationals is of uncountable
dimension.
--




Date Subject Author
11/13/12
Read Dimension of the space of real sequences
Jose Carlos Santos
11/13/12
Read Re: Dimension of the space of real sequences
Mike Terry
11/14/12
Read Re: Dimension of the space of real sequences
Jose Carlos Santos
11/14/12
Read Re: Dimension of the space of real sequences
Mike Terry
11/13/12
Read Re: Dimension of the space of real sequences
Ken.Pledger@vuw.ac.nz
11/13/12
Read Re: Dimension of the space of real sequences
Virgil
11/14/12
Read Re: Dimension of the space of real sequences
Jose Carlos Santos
11/14/12
Read Re: Dimension of the space of real sequences
Shmuel (Seymour J.) Metz
11/13/12
Read Re: Dimension of the space of real sequences
archimede plutanium
11/14/12
Read Re: Dimension of the space of real sequences
Robin Chapman
11/14/12
Read Re: Dimension of the space of real sequences
David Bernier
11/14/12
Read Re: Dimension of the space of real sequences
Jose Carlos Santos
11/14/12
Read Re: Dimension of the space of real sequences
Robin Chapman
11/14/12
Read Re: Dimension of the space of real sequences
Jose Carlos Santos
11/14/12
Read Re: Dimension of the space of real sequences
quasi
11/14/12
Read Re: Dimension of the space of real sequences
Jose Carlos Santos
11/14/12
Read Re: Dimension of the space of real sequences
W^3
11/15/12
Read Re: Dimension of the space of real sequences
David C. Ullrich
11/15/12
Read Re: Dimension of the space of real sequences
Butch Malahide
11/15/12
Read Re: Dimension of the space of real sequences
W^3
11/18/12
Read Re: Dimension of the space of real sequences
David Bernier
11/19/12
Read Re: Dimension of the space of real sequences
David C. Ullrich

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