Re: [math-fun] Infinite product vector space puzzle

Er --- why should the answer be not simply "oo" ( |N or aleph-null ) ? 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 ???

--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun