Denote the class of surreal numbers **No**. We can create new "number", like the *gap* $\infty=\{\infty^L|\infty^R\}$, defined by $\infty^L=\{x:\exists n\in\mathbb N,x<n\}$ and $\infty^R=\{x:\forall n\in\mathbb N,x>n\}$. $\infty\notin$**No** because $\infty^L$ and $\infty^R$ are not sets, but classes. Apparently we can construct new numbers in the form $\{L|R\}$, where $L$ and $R$ are subclasses of **No** such that no $x\in L$ is $\geq$ any $y\in R$. Then we can use these new numbers to construct more numbers, and continue to expand **No** (possible indefinitely?). Is there any reason we do not do so?