Discrete functions (or, discrete signals in engineer talk) also form a vector space. Consider a discrete signal \(X[i]\), ie

\begin{eqnarray}

\ldots \, X[-3] , X[-2] , X[-1] , X[0] , X[1] , X[2] , X[3] , \ldots

\end{eqnarray}

The basic intuition is to think this signal as an infinite dimensional vector.