##However...##
-Some computable functions are just not definable in this way. The simplest function that *simply cannot* be defined using the resources we've so far developed is the [[!wikipedia Ackermann function]]:
+Some computable functions are just not definable in this way. We can't, for example, define a function that tells us, for whatever function `f` we supply it, what is the smallest integer `x` where `f x` is `true`.
+
+Neither do the resources we've so far developed suffice to define the
+[[!wikipedia Ackermann function]]:
A(m,n) =
| when m == 0 -> n + 1