For example, if we take the index set "I" = N and "X""i" = R, then the direct sum ⨁"i"∈N "X""i" is the space "l"2, which consists of all the sequences ("a""i") of reals with finite norm formula_38. Comparing this with the example for Banach spaces, we see that the Banach space direct sum and the Hilbert space direct sum are not necessarily the same. But if there are only finitely many summands, then the Banach space direct sum is isomorphic to the Hilbert space direct sum, although the norm will be different.