Let $R$ be the ring of all the real-valued functions on $\mathbb { N } \times \mathbb { N }$. Show that $R$ contains a subring isomorphic to the polynomial ring $\mathbb { R } [ X , Y ]$.
Let $R$ be the ring of all the real-valued functions on $\mathbb { N } \times \mathbb { N }$. Show that $R$ contains a subring isomorphic to the polynomial ring $\mathbb { R } [ X , Y ]$.