  We consider an agent interacting with an unknown environment. The environment
is a function which maps natural numbers to natural numbers; the agent's set of
hypotheses about the environment contains all such functions which are
computable and compatible with a finite set of known input-output pairs, and
the agent assigns a positive probability to each such hypothesis. We do not
require that this probability distribution be computable, but it must be
bounded below by a positive computable function. The agent has a utility
function on outputs from the environment. We show that if this utility function
is bounded below in absolute value by an unbounded computable function, then
the expected utility of any input is undefined. This implies that a computable
utility function will have convergent expected utilities iff that function is
bounded.
