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We define the "BEC state" to be the many-body wavefunction where allparticles are in the same one-body state. Using an argument analogous toAnderson's Orthogonality Catastrophe, we argue that for interacting particlesthe amplitude of the BEC state within the many-body wavefunction goes to zeroin the thermodynamic limit. This does not mean that there is no condensate.However, we argue that, if the excitations satisfy the Landau criterion, thenthe absence of a finite amplitude for the BEC state, or the absence of acondensate, do not prevent the definition of the phase function \phi, fromwhich the superfluid velocity follows.

Zero BEC State Amplitude, and BEC Unnecessary to Define Phase \phi