tag:blogger.com,1999:blog-8288194986820249216.post1077331870414662922..comments2024-03-29T15:22:58.020-07:00Comments on Abstract Heresies: Infinite CompositionJoe Marshallhttp://www.blogger.com/profile/03233353484280456977noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-8288194986820249216.post-52306279595524384552024-02-04T15:47:25.088-08:002024-02-04T15:47:25.088-08:00I'm not saying anything you don't already ...I'm not saying anything you don't already know, but these "infinite compositions" can be used as representations of computable real numbers, and the fact that you can't always round one to a float shows that in general, rounding a computable real to a float (or an integer) is not a computable function. Getting an infinite loop is very concrete evidence of trying to compute something that's theoretically not computable for some inputs.<br /><br />I happened to run up against the same problem when inadvertently trying to round a number exactly halfway between two floats using the representation and algorithms from John Harrison's Ph.D. thesis. I discuss some of these issues in the informal paper https://scholarship.claremont.edu/jhm/vol12/iss1/25/Brad Lucierhttp://www.math.purdue.edu/~luciernoreply@blogger.com