
Re: Dimension of the space of real sequences
Posted:
Nov 14, 2012 2:22 AM


On 14112012 0:00, Mike Terry wrote:
>> Can someone please tell me how to prove that the real vector space of >> all sequences of real numbers has uncountable dimension? > > You need to exhibit an uncountable set of vectors that are linearly > independent  i.e. no finite linear combination of the vectors can be zero. > > I imagine there must be lots of ways to exhibit such a set, but as a hint > for the approach that occured to me: think "reals" (= "Dedekind cuts": > uncountably many of these...) composed from rationals (countably many of > these, like the countable number of terms in a sequence...).
Great hint. Thanks.
Best regards,
Jose Carlos Santos

