tag:blogger.com,1999:blog-21503568.post461371005042887181..comments2023-11-03T06:32:28.410-04:00Comments on Staring At Empty Pages: Countable and uncountable sets, part 1Barry Leibahttp://www.blogger.com/profile/14205294935881991457noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-21503568.post-46448174759013466682008-10-30T08:04:00.000-04:002008-10-30T08:04:00.000-04:00Look at part 2 of this post, and use the same grid...Look at <A HREF="http://staringatemptypages.blogspot.com/2008/10/countable-and-uncountable-sets-part-2.html" REL="nofollow">part 2</A> of this post, and use the same grid and diagonal mapping as for the rational numbers. Instead of (numerator, denominator), the ordered pair becomes (f(0), f(1)), and you don't have to skip any points [(1, 2) and (2, 4) are distinct now].Barry Leibahttps://www.blogger.com/profile/14205294935881991457noreply@blogger.comtag:blogger.com,1999:blog-21503568.post-24043795842015930142008-10-29T12:05:00.000-04:002008-10-29T12:05:00.000-04:00Hey Barry. I have a question for you. What must y...Hey Barry. I have a question for you. What must you do to show that the set of all functions from {0,1} to the naturals is countable? I am not sure how to arrange my sets to show they are <BR/>1-1.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-21503568.post-50955755156540611752008-10-03T07:38:00.000-04:002008-10-03T07:38:00.000-04:00Ooh, Laurie, I'm sorry to've done that. My apolog...Ooh, Laurie, I'm sorry to've done that. My apologies to the cat (and to Bill, who I guess had to clean up the mess).<BR/><BR/>And having that on the same day at the VP debate probably wasn't a wise idea either. I'll avoid posting part 2 next Tuesday.Barry Leibahttps://www.blogger.com/profile/14205294935881991457noreply@blogger.comtag:blogger.com,1999:blog-21503568.post-7905695613075997932008-10-03T02:23:00.000-04:002008-10-03T02:23:00.000-04:00I'm sorry, but I got to: "It seems intuitive, then...I'm sorry, but I got to: "It seems intuitive, then, that the sets of natural numbers, integers, rationals and reals are all infinite." and my brain exploded. Scared the cat.Lauriehttps://www.blogger.com/profile/00682513110485580000noreply@blogger.comtag:blogger.com,1999:blog-21503568.post-74634321262670819932008-10-02T09:02:00.000-04:002008-10-02T09:02:00.000-04:00Thanks for bringing mathematics closer to the "lay...Thanks for bringing mathematics closer to the "lay" population, Barry. There's a desperate need to promote math literacy, and you definitely have the ability to help others in this area. Have you ever given any thought to writing some books for the general population explaining mathematics (as Asimov was able to do with science)?William M. Irwinhttps://www.blogger.com/profile/15810352494774053280noreply@blogger.com