  An emergent gapless Goldstone mode originates from continuous spontaneous
symmetry breaking, which has become a doctrine since the pioneering work by
Goldstone [J. Goldstone, Nuovo Cimento \textbf{19}, 154 (1961)]. However, we
argue that it is possible for a continuous symmetry group $\rm{U}(1)$ to make
an exceptional case, simply due to the well-known mathematical result that a
continuous symmetry group $\rm{U}(1)$ may be regarded as a limit of a discrete
symmetry group $Z_q$ when $q$ tends to infinity. As a consequence, spontaneous
symmetry breaking for such a continuous symmetry group $\rm{U}(1)$ does not
necessarily lead to any gapless Goldstone mode. This is explicitly explained
for an anisotropic extension of the ferromagnetic spin-1 biquadratic model. In
a sense, this model provides an illustrative example regarding the dichotomy
between continuity and discreteness.
