for x,y > 7 twins(x+y) <= twins(x) + twins(y)
in [Math]
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From: Jim Burns on 11 May 2010 00:21 {You've got a lot here I want to comment on, too much to get to in a single post, too much to get to tonight, also. I will return to this post a few times over the next few days.} master1729 wrote: >[Jim Burns:] >> Instead, suppose that Poster Y asserts that >> 1 > 0.999... and it is clear he means to use >> those symbols in the standard way. People tell him >> he is mistaken. People go on at great length >> explaining why he is mistaken, all to no avail. >> Eventually, he convinces people that he is not >> merely mistaken but a crank. Suppose that you >> find another mathematical system, another >> interpretation of "1 > 0.999..." in which it >> is true. Your use of "1 > 0.999..." is, in an >> important sense, not even the same thing >> Poster Y is saying. Why would you expect your >> newly introduced system to change anyone's mind >> about Poster Y's crankhood? > he convinces people that he is not merely > mistaken but a crank ... > thats an intresting sentense. > what would it mean actually ? I think you know what it means, even if you haven't thought about it. You have made it obvious that you consider certain people cranks. Ask yourself what it is about those certain people that brings you to think they are cranks. > that he is shown wrong but not willing to admit it ? > so suppose the thread has 100 posts and he is called > crank after 10 posts. > in other words , by the above , he is not willing > to admit he is wrong -> "crank" No. That isn't what you mean by crank, is it? (Merely) being wrong but not willing to admit it? That isn't what I mean by it, either, and I think most posters to sci.math or sci.logic mean more by "crank", also. http://en.wikipedia.org/wiki/Crank_%28person%29 In my opinion, what makes cranks distinct from other posters is the utter futility of trying to argue with them. NOTE: This is not to say cranks do not get argued with, not even that those who proclaim how useless it is to argue with them in fact stop arguing with them. Without having done any sort of survey, it looks to me as though cranks attract more responses, more attempts at reform, than "standard" posters do. There are several different methods for achieving this puncture-proof state of mind. (1) One can lack the basics of the discipline one intends to revolutionize and have no intention of acquiring them. (2) One can systematically re-interpret all criticism as support. (3) and more. > ( sidenote , even cranks who admitted mistakes are > often still called cranks , whereas others are just > people who where wrong/mistaken ... weird ... so > crank is probably just a description and insult to > people you dont like , justified by somewhat > controversial , wrong in some theory , or 'annoying' > ( not objective ! ) behaviour.(e.g. caps) ) I would be surprised if any cranks who admitted they were wrong continued to be called "cranks." Would you give me some examples, Tommy? {I'm going to have to close for now. I'm not done, though.} Jim Burns
From: James Burns on 11 May 2010 14:26 Jim Burns wrote: > master1729 wrote: >> [Jim Burns:] [...] >> that he is shown wrong but not willing to admit it ? >> so suppose the thread has 100 posts and he is called >> crank after 10 posts. >> in other words , by the above , he is not willing >> to admit he is wrong -> "crank" Another point: Ten posts seem much too early to decide that a poster is hopeless -- Do you have examples of this happening, or is this hypothetical? Perhaps ten posts could be a good sign, if a poster was repeating one of the so-often refuted arguments popular with cranks. Or it might be some poster only looked like a crank for a bit, and some other poster jumped to a conclusion a bit early. This does not show that there are no cranks, just that mistakes are possible in saying who they are. However, you aren't disputing that cranks exist, right, Tommy? That would be odd, since you have declared at least a couple of posters "indefensible" with respect to crankdom. [...] >> ( sidenote , even cranks who admitted mistakes are >> often still called cranks , whereas others are just >> people who where wrong/mistaken ... weird ... so >> crank is probably just a description and insult to >> people you dont like , justified by somewhat >> controversial , wrong in some theory , or 'annoying' >> ( not objective ! ) behaviour.(e.g. caps) ) > > I would be surprised if any cranks who admitted they > were wrong continued to be called "cranks." Would > you give me some examples, Tommy? It is sort of a defining feature of cranks that they do not admit they are wrong. See, for example, http://en.wikipedia.org/wiki/Crank_%28person%29 I would like to clarify something. If someone is a crank on one topic, it does not mean that they are a crank on all topics. When I say cranks do not admit to error, I mean that they do not admit to error on whatever topic they are cranks about. Jim Burns
From: James Burns on 11 May 2010 14:26 master1729 wrote: >[Jim Burns:] >> Instead, suppose that Poster Y asserts that >> 1 > 0.999... and it is clear he means to use >> those symbols in the standard way. People tell him >> he is mistaken. People go on at great length >> explaining why he is mistaken, all to no avail. >> Eventually, he convinces people that he is not >> merely mistaken but a crank. Suppose that you >> find another mathematical system, another >> interpretation of "1 > 0.999..." in which it >> is true. Your use of "1 > 0.999..." is, in an >> important sense, not even the same thing >> Poster Y is saying. Why would you expect your >> newly introduced system to change anyone's mind >> about Poster Y's crankhood? [...] > but - and now i make some sort of point - if he later > mentions that 1 > 0.99999999 is true because LH is an > infinitesimal larger , he could be considered correct. If he said that, either he is not using those symbols in the standard way -- when I specified that it is clear that he is using them in the standard way -- or he is wrong. There really isn't a third choice. There is room for argument, for clarification, and so on for most mathematical topics of interest (that is what makes them interesting). However, the topics that seem to attract cranks are not those topics. They are not cutting-edge topics. They are topics that are so well understood (by the mathematical community in general) that there is no room for serious disagreement. "1 = 0.999..." is a good example of this. /What that means/ is that the limit of the sequence of /real numbers/ (0.9, 0.99, 0.999, ...) is 1. /What that means/ is that, for every positive real number h, no matter how small, we can delete the first n elements, for some definite, finite number n, and all of the infinite number of elements left in the sequence will be h or closer to 1. And /that/ is quite provable from the axioms for the /real numbers/. If you come along later and say, "Yes, but -- what if the axioms were different?" then you are talking about something else, a statement about something other than the /real numbers/. That would be the same as my claiming that cats cannot breathe water, and you responding, "Yes, but -- if we call a goldfish a cat, then I have a cat at home doing very well in an aquarium." > and if he said so in the first post , he might not be > called crank , and some might even agree with him. > > but then something strange happens , since he didnt talk > about infinitesimals from the beginning , he became > " crank " and whatever he says is wrong !! I think you have this backwards. It is not "He is a crank, therefore whatever he says is wrong." It is much closer to "Whatever he says is wrong, therefore he is a crank." > people will then disagree more often and respond by > things like : > idiot (in caps) > or > there are only reals on my real number line , > no infinitesimals !! stupid ! > which is not fair. Please explain what is unfair about saying there are no infinitesimals in the reals (other than zero), when it is provable that there are no infinitesimals in the reals (other than zero). Jim Burns
From: Jesse F. Hughes on 11 May 2010 14:45 James Burns <burns.87(a)osu.edu> writes: > However, you aren't disputing that cranks exist, right, > Tommy? That would be odd, since you have declared > at least a couple of posters "indefensible" > with respect to crankdom. Are you sure you're not confusing Tommy (crank exemplar) with Transfer Principle/LWalker (crank messiah)? -- Jesse F. Hughes "What do you tremble your *soul* before it for?" he cried. "You don't learn algebra with your blessed soul. Can't you look at it with your clear simple wits?" -- D.H. Lawrence, /Sons And Lovers/
From: James Burns on 11 May 2010 15:34
Jesse F. Hughes wrote: > James Burns <burns.87(a)osu.edu> writes: > >>However, you aren't disputing that cranks exist, right, >>Tommy? That would be odd, since you have declared >>at least a couple of posters "indefensible" >>with respect to crankdom. > > Are you sure you're not confusing Tommy (crank exemplar) > with Transfer Principle/LWalker (crank messiah)? I don't think I'm mistaken, for what that's worth. It was an exchange between LWalker and Tommy, about expanding the range of posters deemed indefensible, that first got my attention. I responded first to Lwalker, but Tommy answered me, in part: : Surely , you must understand , you cannot simply : defend everyone. <705972730.11927.1272056531229.JavaMail.root(a)gallium.mathforum.org> If I have misunderstood Tommy, or even if he has just changed his mind since making that remark, I am willing to be corrected, but, so far, he hasn't done so. Jim Burns |