A set of wave functions of the form C*exp(i k_n x) make a complete orthonormal basis on the interval [-L/2,L/2]. In the limit as L goes to infinity the discrete k_n become a continuum, and the set of basis states goes from being countable (k_n) to being continuous (k). An arbitrary state can be written as an integral of the basis states as opposed to a sum. The orthonormality and completeness conditions generalize to the continuum case by replacing sums by integrals and discrete delta functions by continuum delta functions.