 The Foundation Axiom and object circularity. We mentioned in connection with streams that according to standard set theory, streams of numbers do not exist.   Here is the reasoning. Recall that we defined a stream to be a pair of a number and another stream.   Suppose that a stream s exists, so that the set N∞ of streams is non-empty.   Recall that we have a function   fs : N → N∞   by recursion:  