Virgil
Posts:
9,012
Registered:
1/6/11


Re: Dimension of the space of real sequences
Posted:
Nov 13, 2012 8:20 PM


In article <ken.pledger61ED7B.13480914112012@news.eternalseptember.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. 

