3 ms·
We can effectively calculate all of the rationals to arbitrary precision, but we can't do that with all of the reals. Most of the reals have no effective proced
by roywiggins 8y ago
We can effectively calculate all of the rationals to arbitrary precision, but we can't do that with all of the reals. Most of the reals have no effective procedure to calculate their decimal expansion.
- mike00632 8y agoRight, but we're getting away from illustrating the point of the paper, which isn't about number computability (interestingly) but about cardinality of sets. The intractability of this machine learning problem could have more to do with an absence of a successor function in the Real numbers than about the cardinality of uncomputable numbers. Or it could be a consequence of properties of differing infinite sets in general, like the difference between the Reals and the power set of the Reals. What I'm trying to get at is that we're not just talking about infinite decimal expansions.