Let $T_1$ be non empty. Prove that $T_1$ is finite if there exists bijection from $T_1$ to another finite set $T_2$.
Now, we have $h : J_m \to T_1$
Assume another finite set $T_2$, so we have $h_1 : J_m \to T_2$.
Since both $h_1$ and $h_2$ are bijections, so is $h_1 \circ h^{-1}$
$J_m$ = ${\{1,2,3,...,m\}}$
Conversely, a similar idea can be used. But is this even correct?
Thanks