phyti Posted June 23, 2016 Posted June 23, 2016 https://drive.google.com/file/d/0ByCTeSH4WyfPTWtMWEtGQjVPQ3c/view?usp=sharing
imatfaal Posted June 23, 2016 Posted June 23, 2016 ! Moderator Note Nope - we do not allow this. You need to post your summary and enough detail here to allow members to partake of the discussion without visiting other sites and especially without downloading. Please do so - otherwise I will be forced to lock thread.
Strange Posted June 23, 2016 Posted June 23, 2016 Like all his other attempts, it is trivially wrong anyway.
imatfaal Posted June 23, 2016 Posted June 23, 2016 Like all his other attempts, it is trivially wrong anyway. That sounds dangerously like the fallacy of poisoning the well - or have you taken the plunge and read the file?
Strange Posted June 23, 2016 Posted June 23, 2016 That sounds dangerously like the fallacy of poisoning the well - Would I ... ? I did look at the document. The argument appears to be: if we do something different from Cantor's diagonal argument it doesn't result in a contradiction, therefore the diagonal argument is flawed. 1
phyti Posted July 8, 2016 Author Posted July 8, 2016 The paper has been revised many times, and the one linked was not the latest. After reducing it to the bare essentials, it's up for criticism. https://drive.google.com/file/d/0ByCTeSH4WyfPSXRtdUR6OC04RjQ/view?usp=sharing -3
mathematic Posted July 9, 2016 Posted July 9, 2016 Using measure theory, it is easy to see that the number of reals in the unit interval is uncountable. Proof: Measure of unit interval = 1. Any set with a countable number of points has measure 0. Therefore unit interval has more than a countable number of points.
blue89 Posted July 9, 2016 Posted July 9, 2016 (edited) NOTE: any question has not been detected!/found!.. hi, I am functional analysist. this theorie simply is being evaluated at functional analysis (rather than real analysis (measure theorie (!) , I would request you to remember that functional analysis own (especially sometimes) will contain (already) real analysis. in other words , already mathematics own has a very different language/spesification in comparison with other parts of scence. ok. (I would express (only) cantor theorie and how to find its proof. cantor theorie says ; if any function is continuos at a closed interval. -->> it will be regular continuous at that interval. proof. binali musayev,nizami mustafayev ,murat alp; analysis III . (this source is not written in english language) NOT: the relation with functional ananlysis is just assessments own. (the proof at above is being told using metric spaces' Axioms/spesifications.otherwise it is already related basic analysis. (not progressive to functional analysis or real analysis) related phrases and explanations relevant key words. 1) remember please ,being closed & opened & margin values & limit values & compact ..etc. are all being assessed at both topology and functional analysis. 2) any functional analysist would be highly interested in whether any space/interval is complete or not. (this is too much important. and it is not important which space it was ,e.g: Lebesgue Space ,lp or lq (1/p+1/q=1) , c,C[a,b],integral space , or other new spaces (like mines ,I am trying to create a new one!) ..etc. 4) I recommend that you check these words : lipschitz, cauchy sequences, functional (cauchy) sequences,linear&nonlinear ,convergence, divergence. (all these are basic at real) regards. Edited July 9, 2016 by blue89
swansont Posted July 9, 2016 Posted July 9, 2016 The paper has been revised many times, and the one linked was not the latest. After reducing it to the bare essentials, it's up for criticism. https://drive.google.com/file/d/0ByCTeSH4WyfPSXRtdUR6OC04RjQ/view?usp=sharing ! Moderator Note Was there something in "You need to post your summary and enough detail here to allow members to partake of the discussion without visiting other sites and especially without downloading" that you didn't understand? Post the salient points of the material you wish to discuss here, or this gets locked.
wtf Posted July 9, 2016 Posted July 9, 2016 Phyti, I found a couple of problems in your paper. 1) Your tree does not contain all binary sequences. For example, what node of the tree contains the sequence 101010101..., that is, alternating 1's and 0s'? The solution is that real numbers are represented as paths in the infinite binary tree, not nodes. Although there are only countably many nodes in the tree, there are uncountably many paths. 2) You wrote: "For large values of k the "end" of the list effectively accelerates into the future ..." This of course is incoherent. Does the sequence of natural numbers 1, 2, 3, ... "accelerate into the future?" This is simply meaningless. 1
andrewcellini Posted July 9, 2016 Posted July 9, 2016 "With time implicit in Cantor's constructive method" What?
phyti Posted July 10, 2016 Author Posted July 10, 2016 Phyti, I found a couple of problems in your paper. 1) Your tree does not contain all binary sequences. For example, what node of the tree contains the sequence 101010101..., that is, alternating 1's and 0s'? The solution is that real numbers are represented as paths in the infinite binary tree, not nodes. Although there are only countably many nodes in the tree, there are uncountably many paths. 2) You wrote: "For large values of k the "end" of the list effectively accelerates into the future ..." This of course is incoherent. Does the sequence of natural numbers 1, 2, 3, ... "accelerate into the future?" This is simply meaningless. You begin at L, toss a coin, which selects 0 or 1, move 1 segment/branch, repeat... The choice is always the same, and it's always from L! Repeating 10101... would continue along the lower portion of the tree. The acceleration is just a description for his task, he has more to change than what he has changed. Cantor's list has no end, thus he can't reach it by any means, just as he can't write the greatest integer. I'm just using HIS method to show where it doesn't lead.
andrewcellini Posted July 10, 2016 Posted July 10, 2016 So no comment on what you think time has to do with Cantor's argument? 1
phyti Posted July 11, 2016 Author Posted July 11, 2016 So no comment on what you think time has to do with Cantor's argument? In the real world, how long would it take him to write any infinite sequence? Given 0 precedes 1, the tree begins with a repeating zero and ends with a repeating 1, so all sequences will be included between those two. How can p (green) be in the tree, when Cantor says it isn't in L?
Strange Posted July 11, 2016 Posted July 11, 2016 In the real world, how long would it take him to write any infinite sequence? That isn't relevant to a mathematical proof. 1
Carrock Posted July 11, 2016 Posted July 11, 2016 In the real world, how long would it take him to write any infinite sequence? In the real world, how long does it take to write/generate the unbounded finite sequence 1,2,3,4,5,[...]? ([...] represents the numbers I didn't have time to write) It's impractical to continue up to even the number of electrons in the observable universe (or some finite number you choose) and you will never reach infinity as each successive number is finite. Much of mathematics is shorthand for something impractical or impossible to work out with basic arithmetic using pencil and paper.. If you think the above math is ok, what is the problem with being unable to write every term in an infinite sequence? [crossposted with Strange]
wtf Posted July 11, 2016 Posted July 11, 2016 (edited) You begin at L, toss a coin, which selects 0 or 1, move 1 segment/branch, repeat... The choice is always the same, and it's always from L! No, an infinite sequence is NEVER a node in the tree. It's obvious that any node in the tree represents a FINITE sequence. An infinite sequence is a PATH through the tree, and not a node. If you don't see this you don't understand the infinite binary tree. Edited July 11, 2016 by wtf
phyti Posted July 12, 2016 Author Posted July 12, 2016 In the real world, how long does it take to write/generate the unbounded finite sequence 1,2,3,4,5,[...]? ([...] represents the numbers I didn't have time to write) It's impractical to continue up to even the number of electrons in the observable universe (or some finite number you choose) and you will never reach infinity as each successive number is finite. Much of mathematics is shorthand for something impractical or impossible to work out with basic arithmetic using pencil and paper.. If you think the above math is ok, what is the problem with being unable to write every term in an infinite sequence? [crossposted with Strange] You gave the correct word (red). The ellipsis was invented for just that reason. Since there is no largest integer, no one can write it. Sequences are not laid down instantaneously, so it's a real question as to how long to form one that has no end. . No, an infinite sequence is NEVER a node in the tree. It's obvious that any node in the tree represents a FINITE sequence. An infinite sequence is a PATH through the tree, and not a node. If you don't see this you don't understand the infinite binary tree. No, an infinite sequence is NEVER a node in the tree. It's obvious that any node in the tree represents a FINITE sequence. An infinite sequence is a PATH through the tree, and not a node. If you don't see this you don't understand the infinite binary tree. If you read below the tree, it says each sequence corresponds to a unique path.
wtf Posted July 12, 2016 Posted July 12, 2016 (edited) You gave the correct word (red). The ellipsis was invented for just that reason. Since there is no largest integer, no one can write it. Sequences are not laid down instantaneously, so it's a real question as to how long to form one that has no end. . Do you believe in functions? For example if we say that f(x) = x^2, do you believe in f? Because an infinite sequence is just a function whose domain is the natural numbers. All the mappings from elements of the domain to elements of the range exist at the same time, as mathematical sets. There is no time involved. Of if you like you can think of a function as a machine. Input a value and get out a value. For the squaring function, input 5 and the machine outputs 25. If you have a sequence, it's just a function where you input n and the machine outputs the n-th element of the sequence. If you read below the tree, it says each sequence corresponds to a unique path. You're right, but then I don't understand what is the point of showing the tree. The set of nodes is countable, but the set of paths is uncountable. Edited July 12, 2016 by wtf
imatfaal Posted July 13, 2016 Posted July 13, 2016 ! Moderator Note There is still nothing here to discus. Agreed. Phyti - last warning. Despite members taking the time to go off site to read your paper you have still not done the other members the courtesy of posting a summary here. Do so in next post or I will lock thread.
phyti Posted July 14, 2016 Author Posted July 14, 2016 There is still nothing here to discus. You are right, there is nothing to discuss here. From the feedback; lacking clarity and too much detail.
John Cuthber Posted July 14, 2016 Posted July 14, 2016 You are right, there is nothing to discuss here. From the feedback; lacking clarity and too much detail. If the decision was down to me I might give you the benefit of the doubt and assume that you didn't see that mod note when you posted a reply to my comment. The decisionisn't down to me. If you hurry, you might be able to avoid getting your thread axed if you actually tell us what the F*** you are talking about.
Sensei Posted July 14, 2016 Posted July 14, 2016 There is still nothing here to discus. The first time, I have to agree with you... phyti, you *HAVE TO* attach your paper here on forum for review, not just link, otherwise nothing to discuss.. If you don't follow rules, you soon will be gone from the forum. You are right, there is nothing to discuss here. From the feedback; lacking clarity and too much detail. You didn't give people chance to see what you have in mind. You just gave them link to website, instead of what you worked on really. You cannot give link, without description the everything what is inside. Basically you have to reveal everything what link is about, so everybody can understand it, without having to click on link. Make screen-shots of PDF all pages (or use application for this purpose), and attach in reply.
imatfaal Posted July 15, 2016 Posted July 15, 2016 ! Moderator Note thread locked you had your chance and you blew it. Do not reintroduce this topic.
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