  It is demonstrated that for the isospin $I=1/2$ $\pi$N scattering amplitude,
$T^{I=1/2}(s,t)$, $s={(m_N^2-m_\pi^2)^2}/{m_N^2}$ and $s=m_N^2+2m_\pi^2$ are
two accumulation points of poles on the second sheet of complex $s$ plane, and
are hence accumulation of singularities of $T^{I=1/2}(s,t)$. For
$T^{I=3/2}(s,t)$, $s={(m_N^2-m_\pi^2)^2}/{m_N^2}$ is the accumulation point of
poles on the second sheet of complex $s$ plane. The proof is valid up to all
orders of chiral expansions.
