for x,y > 7 twins(x+y) <= twins(x) + twins(y)
in [Math]
|
From: Jesse F. Hughes on 15 May 2010 09:27 Transfer Principle <lwalke3(a)lausd.net> writes: > My claim is that if someone posted a line of _borderline_ > rigor, a more reputable poster is more likely to be given > the benefit of the doubt (i.e., have the post treated as > if it were of full mathematical rigor) than one who has > received a five-letter label. Yes, when we've seen that a poster is evidently knowledgeable about mathematics, then we are likely to assume further mathematical writing can be made rigorous. If we've seen a poster is not knowledgeable, then we would prefer more explicit reasoning in his arguments. But, if either poster made a claim that simply contradicted established theorems, then we would require clear proof. In neither case would we assume that the poster really meant to use the symbols in an unconventional manner by interpreting them in an unspecified theory. That is bending the principle of charity past the breaking point, so that it becomes the pandering assumption that no one is ever wrong, they are just right in ways that aren't evident. -- Jesse F. Hughes "Mistakes are big part of the discovery process. I make lots of them. Kind of pride myself on it." -- James S. Harris
From: master1729 on 15 May 2010 11:20 jim burns wrote : > > (I briefly tried to google the post I was thinking > of. > Maybe you would have more luck at that.) > > > I've once seen a newbie poster make some claim > about > > something -- it might have been something about a > > factoring method faster than the known methods. > Some > > of the posters thought that the method was > promising > > though unlikely to work. Then another poster (not > the > > OP, and not myself) pointed out that had the OP > been > > JSH instead of a newbie, writing an identical > thread, > > then he wouldn't have been given the time of day, > and > > there would have been more ad hominem than actual > > considerations of the proof. > > What have you got here? A third poster "pointed out" > that what you believed was true? Is this supposed to > be > evidence of some kind? I see someone agreeing with > you, > nothing more. (I'm curious: who is this mysterious > poster?) who is ? who 'are' ! this has been pointed out a few times by people such as newbies , nonregular posters , students and others ; to call some names of ' others ' : quasi, galathaea and of course myself. on the other hand , i have to say it happens linear to the amount of posts , but not a high % ... on the other hand again , its not because it was not said , that it was not so ! in fact , it appears galathaea ( and perhaps quasi ) have LEFT sci.math for such opinions , despite that both were NOT cranks. thats as close to a proof one can get ...
From: master1729 on 15 May 2010 11:51 lwalke wrote : > On May 10, 10:09 am, James Burns <burns...(a)osu.edu> > wrote: > > [S]uppose that Poster Y asserts that 1 > 0.999... > > and it is clear he means to use those symbols in > the > > standard way. > > What does Burns mean by "the standard way"? If by > "the > standard way," he means the definition in classical > analysis by which it is exactly equal to 1, then > Poster > Y's assertion is equivalent to "1>1" (substitution). > To > me, "1>1" is a statement which even I won't defend or > attempt to find a theory for. > > To me, simply by posting "1 > 0.999...," it is clear > he > _doesn't_ mean to use those symbols in the standard > way > at all. It's clear that Poster Y means to use the > symbols in a nonstandard way -- a way in which > 0.999... > differs by 1 by a nonzero infinitesimal. And so it's > up > to me to _find_ a way to use it that's rigorous and > not > ad hoc. > > > 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. > > But what exactly is Poster Y saying? I doubt that he > would be saying "1>1" -- which is what he would be > saying > if he means the standard definition of 0.999.... together with what i said about 0.999... thats a very good analysis !! another example is someone posting an equation ( say diff equation or functional equation ) and people responding by f(x) = 0 idiot ! whereas clearly the OP was looking for the 'intresting' solutions / a description of all solutions / the amount of solutions / closed form expressions or proof that it doenst have closed form solutions / qualitive properties / a solution finding method / ... despite that yes f(x) = 0 is a solution. the OP might argue that "0" is a constant rather than a function ... which is then followed by 5 letter insults and the subject has shifted from equations to name-calling and flame wars. and after the OP has ' defended ' himself , he probably insulted others and they will use that against him ... against him -> they will point out almost all of his posts contained no math only insults. if he stays , he might be considered a ***** or *****. or he leaves ... untill another person does the same , and people can reply with " yet another ***** , we have seen that before " , and will even link that person to the insults the other gave them ( unaware, unintentional ). > > (An analogy: Poster Z writes, "The positive integral > factors of 14 are 1,2,7, and 14." If I assume that > here > "integral" means "antiderivative," then the statement > makes no sense, until I find a definition, such as > the > adjectival form of "integral," which does make sense, > since I assume that Poster Z is rational.) and indeed that has happened ! tommy1729 defended the person using "integral". neilist attacked him. it started a flamewar between tommy1729 and neilist. almost nobody defended tommy1729. even those who shared the same opinion and realized and respected the OP using " integral " and even gave good answers to him , but they did not defend tommy1729 nor attacked neilist for bullying tommy1729 and the OP for calling them cranks. worse even , tommy1729 and neilist used to be friends , even once agreeing that certain posters where *****. i ( tommy1729 ) however didnt use the words often and asked neilist for a " better theory ". i never got one and that occured in the flamewars : " neilist is just a bully who never did math " and in fact , he actually never did post math , he only insulted others. i was the only one pointing that out , despite neilists rude behaviour. ( apart from perhaps quasi ) ( lwalke probably already knows that but jim might not ) more striking is that neilist once said he liked my ideas. but he could not " repeat that " once the flame war started. > > I start from the assumption that Poster Y is > rational, > that the poster wouldn't write something as blatantly > false as "1>1" and search for a definition that does > make sense, such as "1 > 1-iota" for some nonzero > (infinitesimal) iota. Burns, on the other hand, > appears > to start from the opposite assumption, namely that > Poster Y is _irrational_, when he criticizes me for > searching for an infinitesimal theory. (But I could > be > wrong about Burns's assumption here.) > > > Why would you expect your newly introduced system > to > > change anyone's mind about Poster Y's crankhood? > > Have any of my newly introduced systems changed > anyone's > mind about Poster Y's "crank"-hood yet? Not yet -- > but > that could be because I have yet to post any theory > that > is sufficently rigorous and non-ad hoc. (The closest > that I have come is declaring that 0.999... is the > surreal 1-1/omega, but even this causes problems as > 1-1/omega doesn't work exactly as Poster Y wants it > to.) indeed ! however i explained why such threads are not so intresting ( apart for forum sociology ). all 0.99999... threads are similar , not only the responses but even more the OP's. lwalke tries to find a theory , but doesnt get help , not from the " opponents " but even ' less ' ( less than 0 ? :p ) from the OP. regards tommy1729
From: christian.bau on 15 May 2010 17:03 Let x be an element of S that is not real. Either x is greater than every real number, done. Or x is less than every real number, take -x, done. Or x is between two real numbers a and b. Take the set X of all reals < x. X is non-empty (it has element a) and has an upper bound b, therefore it has a least upper bound y. If x > y then 1 / (x - y) is greater than every real number. If x < y then 1 / (y - x) is greater than every real number. x = y is not possible because x is not real. The simplest model for the set S is the set of rational functions (quotient of two polynomials) with real coefficients. Identify the constant polynomials with the ordinary reals. Identify f (x) = x with inf. +, -, *, / are the operations on rational functions. And one rational function is less than another if its values for arbitrary large arguments are less. For example, inf / (inf + 1) would be represented by the rational function f (x) = x / (x + 1).
From: master1729 on 15 May 2010 14:56
jim burns wrote : > The particular example I had in mind of a poster > asserting that "1 > 0.999..." was BURT. I am not > having > much luck with groups.google, so I'll have to settle > for > the vague memory of an extended exchange with him, > where he made it clear he was correcting standard > usage, not creating a new system. I think that, in > this > case, it really is clear he _does_ mean to use those > symbols in the standard way. (No, he does not > /succeed/ > in using them the standard way, but he is trying to > do that.) as i already said to lwalke ; i dont defend burt. better known as the indefensible ' BURT ' for some reason with caps :). > > >>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. > > > > But what exactly is Poster Y saying? I doubt that > he > > would be saying "1>1" -- which is what he would be > saying > > if he means the standard definition of 0.999.... > > No. You can't do this. This whole line of argument > needs > to be thrown out. > > Consider a small boy waiting to visit Santa in a > department > store. Unbeknownst to the boy, his father is working > as > the store's Santa right now. Can we say, "The boy > does > not know that his father is Santa"? But, the boy's > father /is/ Santa. Isn't this the same as "The boy > does not know that his father is his father"? > Well, no, it isn't the same. dont tell musatov and inverse 19 about Santa. > > > (An analogy: Poster Z writes, "The positive > integral > > factors of 14 are 1,2,7, and 14." If I assume that > here > > "integral" means "antiderivative," then the > statement > > makes no sense, until I find a definition, such as > the > > adjectival form of "integral," which does make > sense, > > since I assume that Poster Z is rational.) > > > > I start from the assumption that Poster Y is > rational, > > that the poster wouldn't write something as > blatantly > > false as "1>1" and search for a definition that > does > > make sense, such as "1 > 1-iota" for some nonzero > > (infinitesimal) iota. Burns, on the other hand, > appears > > to start from the opposite assumption, namely that > > Poster Y is _irrational_, when he criticizes me for > > searching for an infinitesimal theory. (But I could > be > > wrong about Burns's assumption here.) > > I beg to differ. You start from the assumption that > Poster Y is /correct/. I start from the assumption > that > a poster /may be mistaken/. I think my assumption > does > much less violence to their point of view than yours > does. > how about / may be correct /. would that be 50 % burns and 50 % lwalke ? of course 0.00000000...1. is /mistaken/ > >>Why would you expect your newly introduced system > to > >>change anyone's mind about Poster Y's crankhood? > > > > Have any of my newly introduced systems changed > anyone's > > mind about Poster Y's "crank"-hood yet? Not yet -- > but > > that could be because I have yet to post any theory > that > > is sufficently rigorous and non-ad hoc. (The > closest > > that I have come is declaring that 0.999... is the > > surreal 1-1/omega, but even this causes problems as > > 1-1/omega doesn't work exactly as Poster Y wants it > to.) > > And yet, none of the criticisms I have seen of your > attempts to wipe away someone's crank-hood have > mentioned > insufficient rigor or excessive ad-hoc-ness. How do > you explain this? the posters are not familiar with ZFC ? making a consistant theory is harder than asking one ? i would not call a 0.99999... a crank or non-mathematician by that thread alone. but lets say in the case of 0.9999... it certain adds up the probabilities in the bad directions. > > Jim Burns regards tommy1729 |