The questions reads: If H1 and H2 are two Hilbert spaces, prove that one of them is isomorphic to a subspace of the other. (Note that every closed subspace of a Hilbert space is a Hilbert Space.) What I'm thinking is that every separable Hilbert space is isomorphic to L2. If I recall, a Hilbert space is separable iff it has a countable basis, so what of uncountable bases? Do I then consider a subspace of that space spanned by a countable subset of the uncountable basis?