tag:blogger.com,1999:blog-1227172931607686978.comments2018-04-20T07:25:45.941-04:00Math-Frolic!"Shecky Riemann"http://www.blogger.com/profile/07065658607024191185noreply@blogger.comBlogger242125tag:blogger.com,1999:blog-1227172931607686978.post-47491124770416324522018-04-19T14:40:45.935-04:002018-04-19T14:40:45.935-04:00Thanks John; I'm completely baffled what was h...Thanks John; I'm completely baffled what was happening, but merely converting the URL to a TinyURL seems to now make it work."Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-75438844815159300282018-04-19T14:27:17.244-04:002018-04-19T14:27:17.244-04:00For me, your digital commons link went to an Ameri...For me, your digital commons link went to an America First Twitter account, which is almost certainly not your intent.<br />John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-85678621660044703792018-04-15T17:09:01.431-04:002018-04-15T17:09:01.431-04:00Agreed!
In trying to show patterns to my students...Agreed!<br /><br />In trying to show patterns to my students, I love using this video which shows Bach's Toccata and Fugue: https://www.youtube.com/watch?v=ATbMw6X3T40<br /><br />This blew my mind when I fist saw it. And I really enjoy watching it even after way more than a dozen times...<br />MathOughtshttps://www.blogger.com/profile/05020281340534425685noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-1616789067819767422018-02-13T00:25:55.956-05:002018-02-13T00:25:55.956-05:00I regret that I am not familiar with the details o...I regret that I am not familiar with the details of the undecidability proofs, and so can't tell you how or whether the undecidability proof for the Generalized Continuum Hypothesis (GCH) differs from that for the Continuum Hypothesis (CH). I'm not sure I understand what you're getting at in your last paragraph, but maybe it's something like this: it is consistent with the other Gerry Myersonnoreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-37667820199885293982018-02-11T18:41:22.992-05:002018-02-11T18:41:22.992-05:00OK, thanks Gerry; I'm accustomed to seeing the...OK, thanks Gerry; I'm accustomed to seeing the Continuum Hyp. referring to the gap between the integers and the reals (or the power set of integers), but just didn't recall a "generalized" form that references the gap between any two power sets. I guess I wonder if the "proof" of undecidability is identical in both cases or slightly different, since the integers are "Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-1982064672127384762018-02-11T18:01:38.998-05:002018-02-11T18:01:38.998-05:00I think you've got the wrong end of the stick,...I think you've got the wrong end of the stick, concerning the continuum hypothesis. Aleph-one is, by definition, the next cardinality after aleph-zero. The continuum hypothesis is there are no sets of cardinality strictly between that of the integers (that's aleph-zero) and that of the reals. In other words, the continuum hypothesis is that the cardinality of the reals is aleph-one. <br /Gerry Myersonnoreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-71848144551491560642017-12-24T22:57:06.826-05:002017-12-24T22:57:06.826-05:00Math is currently described as being the "sci...Math is currently described as being the "science of patterns"; or the language that describes patterns, ones that exist either in nature or are theorized abstractions.<br /><br />While I do not claim to be a mathematician, you can look at a number as data point related to other points that make up a pattern, that is, a mathematical object.<br /><br />I think this "sensitivity"John CEhttps://www.blogger.com/profile/03629238394162397703noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-86556565691388875752017-10-28T22:33:49.430-04:002017-10-28T22:33:49.430-04:00It feels to me like an argument along the lines of...It feels to me like an argument along the lines of "Nothing is better than eternal happiness, and a ham sandwich is certainly better than nothing." An individual is a combination of atoms, so we'll count every possible combination of atoms as an "individual"...Denise Gaskinshttps://www.blogger.com/profile/11928843626113889088noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-12676662081907715232017-10-28T20:29:12.565-04:002017-10-28T20:29:12.565-04:00Yeah, I’m still confused by the sentence, “If ther...Yeah, I’m still confused by the sentence, “If there are n atoms, there are 2^n - 1 combinations of individuals.” The sentence prior to that makes sense to me, but by their definition, an individual is a “combination of atoms,” so the 2nd sentence really translates to: “If there are n atoms, there are 2^n - 1 combinations of, combinations of atoms.” I can agree there are 2^n - 1 “combinations” ("Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-58247526125908462652017-10-28T20:08:16.927-04:002017-10-28T20:08:16.927-04:00With that definition, I'd quibble with using t...With that definition, I'd quibble with using the word "individual." I can see counting you and me and the moon and the solar system as individuals. But the combination of my right thumb and your left foot? Nope.Denise Gaskinshttps://www.blogger.com/profile/11928843626113889088noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-51244039805383904892017-10-28T16:14:12.177-04:002017-10-28T16:14:12.177-04:00Since for a combination to exist under this assump...Since for a combination to exist under this assumption it is sufficient that its constituents exist, there's no problem..mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-64842594089639631902017-10-28T16:04:45.977-04:002017-10-28T16:04:45.977-04:00Doesn't this argument assume that all possible...Doesn't this argument assume that all possible combinations exist in the universe? If we are missing a few of the possibilities (and we must be, for how could there be more individuals than atoms?), then we can't draw any conclusion.Denise Gaskinshttps://www.blogger.com/profile/11928843626113889088noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-9389184125656627492017-10-25T09:58:25.938-04:002017-10-25T09:58:25.938-04:00
Ahh, thanks for the input and the spelling correc...<br />Ahh, thanks for the input and the spelling correction! (now changed)"Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-57522486439707160022017-10-25T09:13:12.361-04:002017-10-25T09:13:12.361-04:00My own understanding runs as follows:
(a) there a...My own understanding runs as follows:<br /><br />(a) there are a finite number of atoms<br />(b) we define an "individual" as a (non void) group of atoms<br />(c) therefore the total number of individuals must be odd.<br /><br />Of course, if you define a void set of atoms as an individual, the total number becomes even :-)<br /><br />Needless to say, an individual is not a person nor .mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-1115520517676315892017-08-29T09:35:05.953-04:002017-08-29T09:35:05.953-04:00A little history midway through this old piece of ...A little history midway through this old piece of mine: http://bit-player.org/bph-publications/SciAm-1984-01-Hayes-hailstone.pdf. <br /><br />Best source: The Ultimate Challenge: The 3x+1 Problem, ed. by Jeff Lagarias, published by AMS, reprints an article by Collatz himself "On the Motivation and Origin of the (3n+1)-Problem."bit-playerhttps://www.blogger.com/profile/10925013458053903295noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-91749921063476322402017-08-23T07:48:43.210-04:002017-08-23T07:48:43.210-04:00I think I'll use this as a math history assign...I think I'll use this as a math history assignment this semester. Pick a name, make a case! I'll find it difficult to choose, but I think have it narrowed down to Robinson or Thurston.<br /><br />Of course, might be benefits to having a statue of an immigrant as well.John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-53160185150425773642017-02-15T09:38:11.534-05:002017-02-15T09:38:11.534-05:00OK, thanks, he actually does that in a number of h...OK, thanks, he actually does that in a number of his books, which is partly why I think, despite his multi-talents and prolific writing, he never gained the following that Martin Gardner had being a much more succinct, smooth writer.<br /><br />"Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-76037136278972547832017-02-15T08:26:58.449-05:002017-02-15T08:26:58.449-05:00Be warned: I did not appreciate Reflections. It st...Be warned: I did not appreciate <i>Reflections</i>. It startes good, but in the second half of the book Smullyan rambled too much..mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-7736910154782454472017-02-14T04:29:32.050-05:002017-02-14T04:29:32.050-05:00Even if Smullyan published books until last year, ...Even if Smullyan published books until last year, I think his pop fame was in the 80s: this could be a reason why there are so few obituaries. I am startled that the Washington Post did not have one, but as for the other newspapers it's just a matter of "things of the past", rather than canary. After all, I don't think that neither the Donald nor his friends care a damn whether .mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-50306128816195763852016-10-20T23:00:59.869-04:002016-10-20T23:00:59.869-04:00Thanks a lot for motivating. The collection of boo...Thanks a lot for motivating. The collection of books stands at 155 now. My librarian is gracious enough to acquire most of them...JOSEPH VARGHESE Kureetharahttps://www.blogger.com/profile/02019655032384454831noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-27696669425364180212016-09-17T21:32:45.771-04:002016-09-17T21:32:45.771-04:00A bit less work, "next to last".A bit less work, "next to last".Neil Ostrovehttps://www.blogger.com/profile/03638059691645940108noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-82894715544898243032016-09-02T20:10:02.754-04:002016-09-02T20:10:02.754-04:00Not a computer genius here, not by far, but I had ...Not a computer genius here, not by far, but I had a recent problem when I used an ad blocker in a Chrome application. I wanted to open my Outlook work email account using a bookmark of the site.<br /><br />The site was locked, I was blocked, and then immediately a new attempt to reopen was initiated by the computer. The blocking and the re-initiation to open kept going in a cyclic fashion, until MathOughtshttps://www.blogger.com/profile/05020281340534425685noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-7745110449384394752016-08-16T17:29:59.530-04:002016-08-16T17:29:59.530-04:00Agreed. Love Numberphile. Thanks for the other lin...Agreed. Love Numberphile. Thanks for the other links.MathOughtshttps://www.blogger.com/profile/05020281340534425685noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-88095204154438564242016-07-03T22:37:13.094-04:002016-07-03T22:37:13.094-04:00have you had any news on this challenge, i can'...have you had any news on this challenge, i can't seem to find what the challenge even is,<br /><br /><br />thanks,<br /><br />gabegggnoreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-57101081410594299372016-06-15T01:34:34.456-04:002016-06-15T01:34:34.456-04:00Sublime.
Sublime.<br />David Langahttps://www.blogger.com/profile/09034899335717111526noreply@blogger.com