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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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Robin Chapman

Posts: 258
Registered: 5/29/08
Re: Dimension of the space of real sequences
Posted: Nov 14, 2012 4:19 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 14/11/2012 01:34, plutanium.archimedis@gmail.com wrote:
> On Tuesday, November 13, 2012 5:27:34 PM UTC-5, José Carlos Santos wrote:
>> Hi all,
>>
>>
>>
>> Can someone please tell me how to prove that the real vector space of
>>
>> all sequences of real numbers has uncountable dimension?
>>
>>
>>
>> Best regards,
>>
>>
>>
>> Jose Carlos Santos

>
> Isn't the set Del^i_j , where the sequence is 1 in the i-th spot and 0
>
> everywhere else linearly-independent?


Yes; it's also countable.



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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