In the Page 7 of the book Simplicial Homotopy theory by Jardine and Goerss they defined the simplex category of a simplicial set $X$ as the slice category $\Delta \downarrow X$. So objects of $\Delta \downarrow X$ are simplicial maps $\sigma: \Delta^n \rightarrow X$ or simplices of $X$ (by strong version of Yoneda Lemma) and morphisms are commutative diagrams of simplicial maps of the following form:
Then they said that the simplicial map $\theta$ is induced by a unique ordinal number map $\theta_{*}: [m] \rightarrow [n]$ where $[m], [n]$ are objects of the finite ordinal category, $\Delta$.
I am not able to guess a natural choice of such unique ordinal map $\theta_*:[m] \rightarrow [n]$ which will induce the simplicial map $\theta: \Delta^n \rightarrow \Delta^m$.
Thanks in Advance.