Thread: Infinite dimensional vector Space

Show that set of real sequence whose infinite sum is convergent is not a finite dimensional vector space over R

Originally Posted by math.dj

Show that set of real sequence whose infinite sum is convergent is not a finite dimensional vector space over R

For n=1,2,3,..., let be the sequence with a 1 in the n'th position and zeros everywhere else:

Check that these sequences form an infinite linearly independent set (in the vector space of real sequences with convergent sum).

to show that these sequences form a infinite linearly independent set what do i do?

Originally Posted by math.dj

to show that these sequences form a infinite linearly independent set what do i do?

For a given natural number N, show that the set is linearly independent. That shows that the dimension of the space is at least N. Since that holds for all N, it follows that the space is infinite-dimensional.

Thank you for your help ...U Rock