Hey,

Thanks for your patience.

Let me try again. Looking at the previous posts I saw that I had written the space incorrectly. I have the space:

It does not state that

´is a subset of a larger space!!!?

My confusion has to do with the textbook I'm using (and have been using since I started the course on Real Analysis). It is terrible and the formulation is not clear at all.

I know that a subspace of a vector-space

is a subset

such that when the addition and scalar multiplication of

are used to add and scalar-multiply the elements of

, then

is a vector-space. Hence by showing that

is closed under addition and multiplication then that would show the intended (as mentioned several times now).

Appreciate the help.