  The "compositeness" or "elementarity" is investigated for s-wave composite
states dynamically generated by energy-dependent and independent interactions.
The bare mass of the corresponding fictitious elementary particle in an
equivalent Yukawa model is shown to be infinite, indicating that the wave
function renormalization constant Z is equal to zero. The idea can be equally
applied to both resonant and bound states. In a special case of zero-energy
bound states, the condition Z = 0 does not necessarily mean that the elementary
particle has the infinite bare mass. We also emphasize arbitrariness in the
"elementarity" leading to multiple interpretations of a physical state, which
can be either a pure composite state with Z = 0 or an elementary particle with
Z \ne 0. The arbitrariness is unavoidable because the renormalization constant
Z is not a physical observable.
