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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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Shmuel (Seymour J.) Metz

Posts: 3,365
Registered: 12/4/04
Re: Dimension of the space of real sequences
Posted: Nov 14, 2012 7:23 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In <ken.pledger-61ED7B.13480914112012@news.eternal-september.org>, on
11/14/2012
at 01:48 PM, Ken Pledger <ken.pledger@vuw.ac.nz> said:

>In article <agfvqlFbot6U1@mid.individual.net>,
> JosÚ 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?


No. See Hamel basis in
<http://en.wikipedia.org/wiki/Basis_%28linear_algebra%29#Related_notions>.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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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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