tag:blogger.com,1999:blog-26717801.post7719889395738184956..comments2023-12-15T01:18:40.855+11:00Comments on Expat@Large: Infinite But Not A Bit Funnyexpat@largehttp://www.blogger.com/profile/01250623536121293636noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-26717801.post-47733266728638833062009-06-29T02:47:04.200+10:002009-06-29T02:47:04.200+10:00We sorted this out by SMS, don't worry Sav. S...We sorted this out by SMS, don't worry Sav. Suffice to say he was right and I was wrong. He did "set theory" to university level. New Math was coming in for the year below at primary I think. We just memorized the times tables until high school.expat@largehttps://www.blogger.com/profile/01250623536121293636noreply@blogger.comtag:blogger.com,1999:blog-26717801.post-1993552780048210342009-06-28T09:03:45.846+10:002009-06-28T09:03:45.846+10:00well, ok, i'll just sit in the corner or how a...well, ok, i'll just sit in the corner or how about i just bring the beer over? xoxoxsavannahhttps://www.blogger.com/profile/04310843901371718758noreply@blogger.comtag:blogger.com,1999:blog-26717801.post-33585286558017331942009-06-28T01:08:22.022+10:002009-06-28T01:08:22.022+10:00Yeah, well DFW didn't say that, and that's...Yeah, well DFW didn't say that, and that's why I was confused and drifted off into a fantasy world of my own.<br /><br />LEM - law of excluded middle. Proving the null hypothesis to be true. Or false. Or not. I don't know, I need sleep... Brain hurts. Yes, God, I'm coming to thee!!!!!expat@largehttps://www.blogger.com/profile/01250623536121293636noreply@blogger.comtag:blogger.com,1999:blog-26717801.post-37808296068600269072009-06-27T22:12:45.125+10:002009-06-27T22:12:45.125+10:00Cantor's proof works whatever the numbers afte...Cantor's proof works whatever the numbers after the decimal point are: if we assume we have a list X1.a1a2a3a4a5..., X2.b1b2b3b4b5b like you said, then you construct a new number from the diagonal a1b2c3d4... by adding one to each digit modulo 10 (1->2, 2->3, ..., 9->0, 0->1) and then your new number differs from each one in your, supposedly complete, list, in at least one digit, and hence it's not on the list. Ergo, the list isn't complete, so our assumption that such a list could be constructed is false. <br /><br />What's a LEM? More than happy to talk maths over some beers some time - do you know what's non-orientable and swims? Möbius Dick! hahahaTomhttps://www.blogger.com/profile/14202479995274287665noreply@blogger.comtag:blogger.com,1999:blog-26717801.post-47747511773477399022009-06-27T18:32:29.768+10:002009-06-27T18:32:29.768+10:00OK, that was what I later on was afraid I hd done....OK, that was what I later on was afraid I hd done. Obviously I am not as smart as those guys, or you. <br /><br />But DFW explains what you said really badly in my opinion. Obviously, again, because I didn't get it. Things that are not all that contentious he gets ultra-worried about, but then skips over the crucial steps with a superficial blase attitude IMHO. A lot of teachers do that, at least mine must have. They place the emphasis on the wrong points. <br /><br />Actually, showing this new number is what he says Cantor does, but his explanation doesn't I thought, and diagram doesn't make any sense to me, with this X1.a1a2a3a4a5... X2.b1b2b3b4b5b... etc... Does this proof only work if the real numbers only have the same post decimal point number? Like does 'a' ALWAYS have to 9? Like 0.9999999 as in my attempt? He never *says* they have to be. This is why I went off on my tangent, trying to explain it to myself. <br /><br />As I said I am really dyslexic when I come to math notation, so his equations just do not help. It's yet another language I can't speak.<br /><br />But hang on, isn't Cantor's proof then sort a LEM? I thought DFW had earlier said they were not strong enough proofs for this level of abstraction. <br /><br />We need beers to sort this out together... Or not. We just need beers.expat@largehttps://www.blogger.com/profile/01250623536121293636noreply@blogger.comtag:blogger.com,1999:blog-26717801.post-72229534059451051942009-06-27T15:34:58.162+10:002009-06-27T15:34:58.162+10:00Close, but no cigar. Your argument would also work...Close, but no cigar. Your argument would also work for the set of integers (order them positive ones first, ascending, then zero and below, descending: you never get to start counting the negative ones - whereas you can construct a different countable set {0, 1, -1, 2, -2, ...) that has every integer in it, and can be "counted". Similarly, you can construct an ordering for rational numbers {0, 1/1, 2/1, 2/2, 1/2, 3/1, ...} and show every rational number occurs in it somewhere. <br /><br />Cantor's diagonal proof starts by assuming such a set exists for rationals, and then constructs a number that isn't inside it - and therefore such a set doesn't exist.Tomhttps://www.blogger.com/profile/14202479995274287665noreply@blogger.com