tag:blogger.com,1999:blog-2811876938195306723.post7828380282322012566..comments2023-07-07T01:27:13.382-07:00Comments on Absolutely Regular: A harder analysis exerciseAryehhttp://www.blogger.com/profile/14913393383227385317noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2811876938195306723.post-17993584970385448972007-01-28T20:11:00.000-08:002007-01-28T20:11:00.000-08:001/4, 3/4, 1/13... I'll leave the formula as a puzz...1/4, 3/4, 1/13... I'll leave the formula as a puzzle for people who haven't taken college math yet. :)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2811876938195306723.post-63218284975357303392007-01-28T17:16:00.000-08:002007-01-28T17:16:00.000-08:00Well, it's not a real contradiction -- I just trie...Well, it's not a real contradiction -- I just tried hard to word it as one :)<br /><br />And yes, you're absolutely right. Can you exhibit a specific point x in [0,1] that belongs to C but is not the endpoint of any segment comprising E?Aryehhttps://www.blogger.com/profile/14913393383227385317noreply@blogger.comtag:blogger.com,1999:blog-2811876938195306723.post-56840899285157923952007-01-28T15:49:00.000-08:002007-01-28T15:49:00.000-08:00I'm somewhat confused as to why this is supposed t...I'm somewhat confused as to why this is supposed to be a contradiction. Each segment in E corresponds to two points in C, but the converse is not necessarily true.<br /><br />Another way to think about it: the construction of C is not (apologies if my quasi-formal notation is incomprehensible) {xeC|En s.t. x is a boundary of a region excluded from the nth step of the construction of C}, but rather {xeC|~En s.t. x is excluded from C in the nth step of the construction of C}.Anonymousnoreply@blogger.com