Solution
= Solution
Apply part (b) to
$$
g(x,y)=
\begin{cases}
0,&y<x,\\
\uparrow,&y\geq x.
\end{cases}
$$
There is an index $m$ such that $f_{m,1}(y)\simeq g(m,y)$. Its <domain of a partial function> is exactly
$$
W_m=\operatorname{dom}f_{m,1}=\{0,1,\ldots,m-1\}.
$$
Therefore
$$
\boxed{|W_m|=m.}
$$