On Sun, Aug 26, 2012 at 4:58 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Er --- why should the answer be not simply "oo" ( |N or aleph-null ) ?
Well the question is whether the answer is simply "aleph-null" or simply "2^aleph-null" (though I strongly suspect it is one or the other). The aleph-null vectors that each have a 1 in one position and zeroes everywhere else do not form a basis; for a set to be a basis, every vector has to be a *finite* linear combination of the basis vectors, and any vector with infinitely many non-zero entries is not in the span of these vectors. Andy
Admittedly, just how this might be justified in terms of a formal definition of "dimension" for a vector space is not something I have thought about.
WFL
On 8/26/12, Dan Asimov <dasimov@earthlink.net> wrote:
Let R^oo denote the real vector space that is the countable direct product of copies of the reals.
I.e., all countable-tuples of reals with componentwise addition.
Puzzle: What is the dimension of the real vector space R^oo ???
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