Cantor Confusion
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From: William Hughes on 11 Oct 2006 11:42 mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > > > > Let set S be > > > > 0.1 > > 0.11 > > 0.111 > > ... > > > > Note that every member of set S has a finite number > > of ones. Therefore, 0.111... is not a member of set S. > > > > Then it is asserted that every member of set S is covered > > by some member of set S, but that no single member > > of set S covers every member of set S. > > > > Since 0.111... is not a member of set S, it is not > > asserted that it is covered by a member of set S. > > > > > You are correct. That is > > > impossible. > > > > > > > But this is a red herring. What we want is > > > > > > > > Given two sets, a linear set A and another set B, such > > > > that for every x in B there is a y in A such that y covers x. > > > > Then there is a y in A such that for every x in B, y > > > > covers x. > > > > > > > > It is easy to show that this can be false, if and only if > > > > A is a linear set with no largest element. I.e. it is > > > > not true. > > > > > > What is implied? Not my assertion is false but the assertion s false > > > that there are finished infinte sets. > > > > No, what is implied is that an infinite set with a linear ordering > > might not have a largest element. > > That is correct. But every element of the natural numbers is finite. > Hence every element covers its predecessors. If 0.111... is covered by > "the whole list", then it is covered by one element. That, however, is > excuded. > Since no one has claimed that '0.111... is covered by "the whole list"', I fail to see the relevence of a sentence that starts out 'If 0.111... is covered by "the whole list"'. - William Hughes > Regards, WM
From: Tony Orlow on 11 Oct 2006 11:49 Wendy Covington wrote: > Re: Parents > Posted: Oct 11, 2006 11:20 AM Plain Text Reply > > > I am DESPERATLY seeking advice. I am not the typical parent. I do not like rigid traditional academics although I do believe that tradition is a good thing. (Which is why I am considering religous school even though our family is agnostic) > > My 12 year old has always attended a Waldorf school and we have LOVED it. There is NOTHING like it!! However, my husband is a University professor and we had to relocate for a job. We are now in South Florida, Ft. Lauderdale. We enrolled our child in a Montessori school. (No offence to Montessori folks) but we do not like this education at all. > > Here is a fundemental problem, espically for a child not raised in Montessori, while I recognize the value and principal of "self-directed" learning or "co-op" learning. The REALITY must also be ideal. > > In order for a child to succeed in the socratic environment, they must be taught HOW. In other words, it has to be modeled and then the children can break away into their own groups without a teacher sitting with them. Initially though, I feel a teacher needs to be present to essentialy teach them how to utilize this environment. > > I won't go into the details here, although if anyone is curious I will answer any questions you may have about the variation of waldorf vs. montessori (I think it is vast and it would better serve parents if they understood this, the two are often times considered similar because they are both "alternative") > > However I will say this: > There are two ways to arrive at a destination (making a metaphore to a car trip) you can take the highway, and the drive will lack in scenery and expirence but you will get there or you can take the scenic back road and enjoy. > > Up to this point my son has had the pleasure of the scenic route and he is doing very well, not just academically (Which people over-value because while important the whole person is JUST as valuable) still, he entered this new school at a 7-8 grade level, which at their school is really a 8-9 grade level. This was from waldorf. He also loves music, himself, the earth, his friends. In other words, he is not just smart, he is happy. > > Now, he is doing terriable and we are doing homework all night and all weekend. I have called 100 schools and searched 100 hours on the internet for a solution. I am open to anything. I found a school in miami that talks about the "whole child" It is called the Cushman School. However, this would mean spending 5 hours of car time each day, I have a one year old also and I am not sure that is a good solution for either child, to spend so much of their life in the car. > > Does anyone have and suggestions? > > Thank you!!! Public school. :)
From: guenther vonKnakspot on 11 Oct 2006 11:50 Wendy Covington wrote: > Re: Parents > Posted: Oct 11, 2006 11:20 AM Plain Text Reply > > > I am DESPERATLY seeking advice. I am not the typical parent. I do not like rigid traditional academics although I do believe that tradition is a good thing. (Which is why I am considering religous school even though our family is agnostic) > > My 12 year old has always attended a Waldorf school and we have LOVED it. There is NOTHING like it!! However, my husband is a University professor and we had to relocate for a job. We are now in South Florida, Ft. Lauderdale. We enrolled our child in a Montessori school. (No offence to Montessori folks) but we do not like this education at all. > > Here is a fundemental problem, espically for a child not raised in Montessori, while I recognize the value and principal of "self-directed" learning or "co-op" learning. The REALITY must also be ideal. > > In order for a child to succeed in the socratic environment, they must be taught HOW. In other words, it has to be modeled and then the children can break away into their own groups without a teacher sitting with them. Initially though, I feel a teacher needs to be present to essentialy teach them how to utilize this environment. > > I won't go into the details here, although if anyone is curious I will answer any questions you may have about the variation of waldorf vs. montessori (I think it is vast and it would better serve parents if they understood this, the two are often times considered similar because they are both "alternative") > > However I will say this: > There are two ways to arrive at a destination (making a metaphore to a car trip) you can take the highway, and the drive will lack in scenery and expirence but you will get there or you can take the scenic back road and enjoy. > > Up to this point my son has had the pleasure of the scenic route and he is doing very well, not just academically (Which people over-value because while important the whole person is JUST as valuable) still, he entered this new school at a 7-8 grade level, which at their school is really a 8-9 grade level. This was from waldorf. He also loves music, himself, the earth, his friends. In other words, he is not just smart, he is happy. > > Now, he is doing terriable and we are doing homework all night and all weekend. I have called 100 schools and searched 100 hours on the internet for a solution. I am open to anything. I found a school in miami that talks about the "whole child" It is called the Cushman School. However, this would mean spending 5 hours of car time each day, I have a one year old also and I am not sure that is a good solution for either child, to spend so much of their life in the car. > > Does anyone have and suggestions? Unless you posted this as a joke, a rather confusing one mind you, or as part of an elaborate prank, I would suggest you reduce the intake of whatever substances induced you to post in this of all possible newsgroups. Regards. ps. Maybe a "rigid traditional" school where they beat some common sense into it would do your child better, least he become a confused adult like yourself seems to be. > > Thank you!!!
From: Tony Orlow on 11 Oct 2006 11:56 mueckenh(a)rz.fh-augsburg.de wrote: > Dik T. Winter schrieb: > >> In article <1160562822.815626.82270(a)c28g2000cwb.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: >> > Dik T. Winter schrieb: >> ... >> > > What *might* be a sensible definition of a limit for a sequence of sets of >> > > naturals is, that (given each A_n is a set of naturals), the limit >> > > lim{n = 1 ... oo} A_n = A >> > >> > Yes, in that manner the definition runs. Cantor does not write n = >> > 1...oo but puts only the n (he uses nue) under the limit. But the >> > meaning is clearly this one. >> > >> > > exists if and only if for every p in n, there is an n0, such that either >> > > (1) p in A_n for n > n0 >> > > or >> > > (2) p !in A_n for n > n0. >> > > In the first case p is in A, in the second case p !in A. >> > > >> > > With that definition, indeed, >> > > lim{n = 1 ... oo} A_n = N, >> > > but also >> > > lim{n = 1 ... oo} {n + 1, ..., 10n} = 0. >> > > >> > > I do not think you are meaning that definition. So what *is* your >> > > definition? >> > >> > I do *not* believe that omega exists or is a useful notion. Therefore I >> > do not give a definition, but, if necessary during the discussion, I >> > use the only posdsible one as given by Cantor (see above). >> >> So the definition I gave for a limit of a sequence of sets you agree >> with? Or not? I am seriously confused. With the definition I gave, >> lim{n = 1 .. oo} {n + 1, ..., 10n} = {}. > > Sorry, I don't understand your definition. But considering the vase and > its balls, set theory seems to allow *every* limit, just according to > the suitability for defending ZFC. > > Regards, WM > I don't understand this definition either. You write lim{n=1 .. oo}. Is that supposed to be a sum over that range, or do you mean lim(n->oo)? Does 1 belong there? Also, you are looking for a limit of what, a set of balls from n+1 through 10n? Are you looking for the limit of the *size* of that set, which would be 10-(n+1)+1, or 9n? If you want to put this in limit terms, with the corrections I suggest, you have the size of the set being lim(n->oo: 9n). That's not 0 by any stretch of the imagination. Tony
From: William Hughes on 11 Oct 2006 11:56
Wendy Covington wrote: > Re: Parents > Posted: Oct 11, 2006 11:20 AM Plain Text Reply > > > I am DESPERATLY seeking advice. I am not the typical parent. I do not like rigid traditional academics although I do believe that tradition is a good thing. (Which is why I am considering religous school even though our family is agnostic) > > My 12 year old has always attended a Waldorf school and we have LOVED it. There is NOTHING like it!! However, my husband is a University professor and we had to relocate for a job. We are now in South Florida, Ft. Lauderdale. We enrolled our child in a Montessori school. (No offence to Montessori folks) but we do not like this education at all. > > Here is a fundemental problem, espically for a child not raised in Montessori, while I recognize the value and principal of "self-directed" learning or "co-op" learning. The REALITY must also be ideal. > > In order for a child to succeed in the socratic environment, they must be taught HOW. In other words, it has to be modeled and then the children can break away into their own groups without a teacher sitting with them. Initially though, I feel a teacher needs to be present to essentialy teach them how to utilize this environment. > > I won't go into the details here, although if anyone is curious I will answer any questions you may have about the variation of waldorf vs. montessori (I think it is vast and it would better serve parents if they understood this, the two are often times considered similar because they are both "alternative") > > However I will say this: > There are two ways to arrive at a destination (making a metaphore to a car trip) you can take the highway, and the drive will lack in scenery and expirence but you will get there or you can take the scenic back road and enjoy. > > Up to this point my son has had the pleasure of the scenic route and he is doing very well, not just academically (Which people over-value because while important the whole person is JUST as valuable) still, he entered this new school at a 7-8 grade level, which at their school is really a 8-9 grade level. This was from waldorf. He also loves music, himself, the earth, his friends. In other words, he is not just smart, he is happy. > > Now, he is doing terriable and we are doing homework all night and all weekend. I have called 100 schools and searched 100 hours on the internet for a solution. I am open to anything. I found a school in miami that talks about the "whole child" It is called the Cushman School. However, this would mean spending 5 hours of car time each day, I have a one year old also and I am not sure that is a good solution for either child, to spend so much of their life in the car. > > Does anyone have and suggestions? > > Thank you!!! This ended up as a followup to an accidental duplicate post in a discussion of infinite sets. I take it this is not what you intended! However, while we're here: 5 hours of car time is too much for you, let alone the children. Three suggestions: - home school - send your child to public school and supplement - give it some time. Any move is a big adjustment. After a few months your child may settle down just fine. - William Hughes |