Virgil
Posts:
4,655
Registered:
1/6/11
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Re: Dimension of the space of real sequences
Posted:
Nov 13, 2012 8:20 PM
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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.
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