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Re: Dimension of the space of real sequences
Posted:
Nov 14, 2012 4:19 AM
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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
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>> all sequences of real numbers has uncountable dimension?
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>> Best regards,
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>>
>>
>> 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.
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