for x,y > 7 twins(x+y) <= twins(x) + twins(y)
in [Math]
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From: Jesse F. Hughes on 15 May 2010 22:26 "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: > No idea the original context. Someone more interested might look > around Nov. 22, 2004, since that *might* be close to when I first > found it. A search on google for "mathforum 'enterprize'" (with quotes around the latter word) brings up the original thread, I think. For anyone who cares. -- "Kim liked the math I did for her and gave me quite a few groceries... likely so many groceries that they would have cost Kim about what she pays for two whole packages of cigarettes. Few people have ever rewarded me for my work as much as Kim did." -- Usenet nut
From: Jesse F. Hughes on 15 May 2010 22:52 Transfer Principle <lwalke3(a)lausd.net> writes: > But this would seem to imply that if I really wanted to > respect others' intelligence, I should tell other posters > that they are wrong! Yes, that's true. You work so hard to ensure that no one is ever wrong that you end up re-interpreting their claims so that their original meaning is lost. Your sense of charity denies faithfulness altogether. You want everyone to be right, but in order to do so, you change the meaning of some posters' words. For instance, when *some* posters say 1 > 0.999..., they surely believe they are saying something significant. Now, it is not significant to claim that this is true in some arbitrary theory. It is a triviality. Rather, it is most likely that they meant that, contrary to prevailing opinion, 1 really is greater than 0.999.... Now, either this means that the proof in the reals is invalid, or it means that the theory of the reals is somehow wrong. The former claim is simply false and the latter is vague and unclear. But these two interpretations respect the original posters' assertions more than your misplaced sense of charity. > Recall that I am willing to call a poster _wrong_, as long as there > aren't four or five other posters in the thread calling him wrong as > well. I'd much rather find a way for the poster to be right than > _repeat_ (and I emphasize the word _repeat_) that he is wrong. If a slew of others are already saying that someone is wrong, there's no need for you to say so, too. But finding a way that the poster is "right" makes little sense if, in fact, what he said was wrong. -- Jesse F. Hughes Jesse: Quincy, you should trust me more. Quincy (age 4): Baba, I never trust you. And I've got good reasons.
From: Tonico on 16 May 2010 05:28 On May 16, 5:02 am, Transfer Principle <lwal...(a)lausd.net> wrote: > On May 15, 6:27 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > > > Transfer Principle <lwal...(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. > > Thank you for admitting this. > > Let's go back to an explicit example of this. Months ago, > there was a poster named T.H. Ray, who wanted to give a new > definition of "function." According to Ray's definition, a > function is an object which "inheres changes." > > Predictably, other posters, including IIRC Hughes himself, > criticized Ray's use of "inheres." Naturally, the first > thing that Ray was asked to do is define "inheres." One > was skeptical that "inheres" is even a real word. > > Well, guess what? Today on my Page-a-Day word calendar is > the following entry: > > inhere \in-'hir\ v: to be inherent: to be a fixed element > or attribute. > > So "inhere" really is an English word! One might argue > that "inhere" is a back-formation of "inherent," but the > etymology reveals that "inherent" is actually the > adjectival form of the verb "inhere." (This is example > where the derived word is more common than the root word.) > > Suffice it to say that had an established mathematician > been the poster, he's less likely to be asked to define > "inheres" than a poster like Ray. Oh, what an excellent example of your strange heat to "deffend" real nonsenses! First, in mathematics we're really touchy about getting stuff defined...what to do! Anyone having studied mathematics seriously even at college level knows that this is a very important thing to require, and of course most other sciences also have a big need of this. Second, by the above if the OP were an actual mathematicis then he/she wouldn't have even attempted to define something using fuzzy, foggy words (real or not). For one, I can't remember even one single example of any mathematician, pro or not, having done that, and if there was ANY doubt about some stuff he gave he'd define it at once upon being asked to without trying to justify it by huntchs, pink feelings or "justice" > > So what was Ray really saying? He was simply defining a > function as an object in which change is _inherent_. In > fact, I can see where Ray is coming from. It's funny: you say this as if it really means something...;P Mathematicians are likely to be hardasses: how do you define that change and how do you define this property as being "inherent"? Would humans beings be considered functions since, for what we know, they keep on changing on so many levels - atomic, molecular, cellwise, characters, behaviour, etc. - ? Of course, this would make lots of things functions...and changing, or adopting, this new "definition", assuming we can make any sense out of it all, is going to add anything to our understanding of mathematics, analysis, sciences or whatever? If yes, HOW? You know, somehow I can see where this Ray guy is coming from, but I think it's not the same place you're thinking. If there is an > object whose attributes change with, say, time, then we > are saying that the attribute is a function of time. In > the real world, functions occur when one attribute can > be described by a variable that changes with respect to > some other variable (often time). > > Mathematicians, of course, prefer to be more abstract, > so they prefer definitions which refer to ordered pairs > and Cartesian products. In that other thread, Ray was > challenged for excluding the empty set (a degenerate > function), constant functions, and possibly even the > identity function. But once again, this shows yet again > a disconnect between mathematicians and the real world, > for non-mathematicians seldom consider something that > doesn't change as a "function," or consider the empty > set to be a "set" of anything, much less a function. Hmmm....I'd say non-mathematicians seldom consider functions at all, and this perhaps is the reason anyone trying to "redefine" function in such a clumsy, foggy way as the above one would make sure to all to know that he's not enough educated in these matters and thus he's dealing with stuff he doesn't know. Tonio
From: master1729 on 16 May 2010 06:27 lwalke wrote : > On May 15, 6:27 am, "Jesse F. Hughes" > <je...(a)phiwumbda.org> wrote: > > Transfer Principle <lwal...(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. > > Thank you for admitting this. > > Let's go back to an explicit example of this. Months > ago, > there was a poster named T.H. Ray, who wanted to give > a new > definition of "function." According to Ray's > definition, a > function is an object which "inheres changes." > > Predictably, other posters, including IIRC Hughes > himself, > criticized Ray's use of "inheres." Naturally, the > first > thing that Ray was asked to do is define "inheres." > One > was skeptical that "inheres" is even a real word. > > Well, guess what? Today on my Page-a-Day word > calendar is > the following entry: > > inhere \in-'hir\ v: to be inherent: to be a fixed > element > or attribute. > > So "inhere" really is an English word! One might > argue > that "inhere" is a back-formation of "inherent," but > the > etymology reveals that "inherent" is actually the > adjectival form of the verb "inhere." (This is > example > where the derived word is more common than the root > word.) > > Suffice it to say that had an established > mathematician > been the poster, he's less likely to be asked to > define > "inheres" than a poster like Ray. > > So what was Ray really saying? He was simply defining > a > function as an object in which change is _inherent_. > In > fact, I can see where Ray is coming from. If there is > an > object whose attributes change with, say, time, then > we > are saying that the attribute is a function of time. > In > the real world, functions occur when one attribute > can > be described by a variable that changes with respect > to > some other variable (often time). the irony is that bad knowledge of english is often considered a crank detector. here the ' people who dont want to be grouped ' ( is that grouping ? :p ) are in fact those who didnt know english. > > Mathematicians, of course, prefer to be more > abstract, > so they prefer definitions which refer to ordered > pairs > and Cartesian products. In that other thread, Ray was > challenged for excluding the empty set (a degenerate > function), constant functions, and possibly even the > identity function. But once again, this shows yet > again > a disconnect between mathematicians and the real > world, > for non-mathematicians seldom consider something that > doesn't change as a "function," or consider the empty > set to be a "set" of anything, much less a function. constant 'vs' function yes. i mentioned it yesterday in a reply to lwalke (here in this thread). the constant function is not ' intresting ' and it has no 'real' parameter. saying f(x) = 0 is same as f = 0. and here f is rather 'memory' than 'computation'. rather than being dependant on x , f(x) = 0 is actually independant of x. as for the empty set 'as a number' : x + [] = x x*[] = x so the empty set ( as a number representation ) cannot be 0 nor 1. g(x,[]) = g(x) similar to constant with respect to []. but that is not the 'ordinary' empty set. that more like a physicists / computer / mereologic algebra type of empty set. as seen in ' the real world ' ( consistant with my [] from my TST ) regards tommy1729
From: master1729 on 16 May 2010 06:58
Jesse F Hughes wrote : > the theory of real > analysis is perfectly > respectable and not "fake", whatever that means. > you admit not knowing what fake means , yet you are certain it isnt fake. reminds me of ullrich. telling people he was certain that their ideas are wrong. later asking an explaination. and even later saying he doesnt know what they mean. yet , certainly 'wrong' or 'false' ... whatever that means to someone who doesnt understand ' false ' or the proposed idea. regards tommy1729 |