Originally Posted by

**frater_cp** Hi Opalg. Thank you for you hint.

I know that if I take this set of finite linear combinations you proposed I can use it as a set, say called M. Then I must show that this set M is countable and this set is dense in X.

So it is easy to argue that this set is countable since there are finite number of operations to multiply rational coefficients to basis vectors and then sum them.

But I must now take this set M and show it is dense in X by using the fact that rational numbers Q are dense in R (reals), but I do not know how to show this with norm estimates. So not sure how to write this in "analysis language".

Can you help me please?