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 International Skeptics Forum Deeper than primes - Continuation 2

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 26th November 2014, 09:30 PM #201 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi Dear jsfisher, This is my last post to you on this fine subject. Thank you. Too bad you could not define your terms, though. Quote: Fortunately Mathematics is not restricted only to your arbitrary |N| observation. I have no such arbitrary observation, nor would Mathematics be restricted by it. Neither your re-definitions nor your straw change the value of 0.999.... __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 26th November 2014, 11:17 PM #202 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 http://www.internationalskeptics.com...&postcount=110 is aimed to those who are interested in the discussed fine subject, which is rigorously defined by the abstract mathematical fact of the strict difference among carnality |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... Using ∞ (as currently done among mathematicians) in order to deduce conclusions in terms of infinity is not accurate enough, simply because it does not use the well established mathematical proof of |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... different levels of infinity, where each one of them is defined in no more than one step (no process of more than one step is involved) . __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 27th November 2014 at 12:18 AM.
 27th November 2014, 07:16 AM #203 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi http://www.internationalskeptics.com...&postcount=110 is aimed to those who are interested in the discussed fine subject, which is rigorously defined by the abstract mathematical fact of the strict difference among carnality |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... You keep using those words, but do not understand what they mean. Quote: Using ∞ (as currently done among mathematicians) in order to deduce conclusions in terms of infinity is not accurate enough... No, it is you who do not understand how infinity is used in something like 0.999.... (In fact, it isn't used at all, but that nuance escapes you, doesn't it.) As a result, you make things up in support of your own confusion, and you erect strawmen in attempts to discredit the actual meaning of things. The things you make up, you cannot ever define, either. That indicates that you, yourself, have no idea what you are saying. Quote: ...simply because it does not use the well established mathematical proof of |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... different levels of infinity, where each one of them is defined in no more than one step (no process of more than one step is involved) . There's another phrase you misuse and don't understand. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 29th November 2014, 05:22 AM #204 realpaladin Master Poster     Join Date: Apr 2007 Posts: 2,585 What? All the other posters already left Doron? I can understand that; all the talk in the world of being peaceful does not balance the acts of strife and opposition that Doron really commits. Doron, again. If you are in a discussion, you *MUST* listen to the other side and you *MUST* concede when you are *WRONG*. If you are unable to do so, then on *any* board on the Internet, people will simply ignore you. If you look at the preceding weeks, you will find that, with the exception of Apathia, each and everyone, in just about any tone of voice possible, from friendly to arrogant, has asked you the same same thing: - Define your concepts. Not *show* your concepts, which you keep doing, but *defining* them. Put borders around them, explain why these borders are valid etc. Whatever you think, whatever you say, if you can not participate in a discussion, then in a few years, when you are gone from the planet, everything you have ever said is just stored and ignored. It won't have mattered that you existed. To change that, participate, not just direct, and concede when you are wrong. __________________ "All is needed (and it is essential to my definitions) is to understand the actuality beyond the description, for example: Nothing is actually" - Doron Shadmi "But this means you actually have nothing." - Realpaladin ---
 30th November 2014, 05:12 AM #205 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Dear Dessi, Let's simplify http://www.internationalskeptics.com...&postcount=158 as follows: The serial solution: |1| worker puts |N| stones along an infinite road by speed |N|. The parallel solution: |N| workers put |N| stones along an infinite road by speed |1|. So, in both cases the mission is accomplished by one step (|1| worker with speed |N| = |N| workers with speed |1|). By using one step for each cardinal number of the forms |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... it is clear that no mission of lower cardinality is accomplished if observed from higher cardinality, or in other words, the power of lower cardinality is insignificant in order to reach the power of higher cardinality. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 30th November 2014 at 05:38 AM.
 30th November 2014, 09:45 AM #206 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi Dear Dessi, Let's simplify http://www.internationalskeptics.com...&postcount=158 as follows: The serial solution: |1| worker puts |N| stones along an infinite road by speed |N|. The parallel solution: |N| workers put |N| stones along an infinite road by speed |1|. Do you know what these two processes have in common with the evaluation of 0.999...? Absolutely nothing. Why do you keep bringing it up? Do you know what's curious about your so-called solutions (aside from their irrelevance to the infinite series topic)? You so desperately try to make aleph-null behave like an integer, which it isn't, so they are mathematically meaningless. All that aside, though, why haven't you found a place for aleph-one in any of this? Considering how much mathematics has been ignored to this point, forcing in aleph-one and some of its higher-numbered friends should be easy for you. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 30th November 2014, 09:47 AM #207 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi So, in both cases the mission is accomplished by one step (|1| worker with speed |N| = |N| workers with speed |1|). Not even close. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 1st December 2014, 08:20 AM #208 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher You so desperately try to make aleph-null behave like an integer Not even close. You are simply missing the one step notion, no matter what cardinality>0 (finite or infinite) is used. As a result Originally Posted by doronshadmi By using one step for each cardinal number of the forms |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... it is clear that no mission of lower cardinality is accomplished if observed from higher cardinality, or in other words, the power of lower cardinality is insignificant in order to reach the power of higher cardinality. is not in your scope. Here is a concrete example (your rhetoric question) that supports my argument about you: Originally Posted by doronshadmi Do you know what these two processes have in common with the evaluation of 0.999...? Absolutely nothing. It is clearly seen that you are totally missing the fact that there is one step in both parallel and serial solutions, no matter what cardinality>0 (finite or infinite) is used for a given solution. Moreover, you are totally missing the fact that a given solution in a given cardinality>0 is not satisfied if observed from higher cardinality (as written in my first quote in this post). Generally your mathematical universe is the result of no more than one level for each observation (you systematically avoiding observations of lower levels from higher levels, so there is no wonder that my theorem is not in your scope). __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 1st December 2014 at 08:50 AM.
 1st December 2014, 08:26 AM #209 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi Not even close. Perhaps you don't understand your own posts. Your wrote, among other things, "|N| workers". You are, in fact, using aleph-null as if it were an integer. I am even more than close; I am dead on. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 1st December 2014, 08:54 AM #210 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher Perhaps you don't understand your own posts. Your wrote, among other things, "|N| workers". You are, in fact, using aleph-null as if it were an integer. I am even more than close; I am dead on. Perhaps you don't understand your own posts, so let me help you. Please change "|N| workers" to "|N| integers", and walla, you have no argument. Generally, you are far far away from http://www.internationalskeptics.com...&postcount=110. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 1st December 2014 at 09:15 AM.
 1st December 2014, 09:40 AM #211 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi Please change "|N| workers" to "|N| integers", and walla, you have no argument. No, the same argument remains: Whether workers or integers, you are still trying to use |N| as if it were an integer. Be that as it may, it still has no relevance to the valuation of 0.999.... (Walla?? Half a city in Washington State?) __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 1st December 2014, 10:39 AM #212 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher No, the same argument remains: Wrong, there is a collection of |N| integers, where |N| is not one of them. Originally Posted by jsfisher you are still trying to use |N| as if it were an integer. jsfisher, I am not going to argue with you about your own trivial mistakes. You are on your own in this trivial loop. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 1st December 2014 at 10:41 AM.
 1st December 2014, 11:41 AM #213 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi Wrong, there is a collection of |N| integers, where |N| is not one of them. There are infinitely many integers and the cardinality of the set of integers is aleph-null. However, it is incorrect to say the number of integers is aleph-null or anything semantically equivalent, including "|N| integers". As a colloquial convenience, the phrase and its semantic equivalents, "the number of integers is infinite", may be used, but never as a prelude to using 'inifinity' as an ordinary number. Be that as it may, it is still irrelevant to the valuation of 0.999.... __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 1st December 2014, 02:34 PM #214 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher but never as a prelude to using 'inifinity' as an ordinary number. |N| is a transfinite number, so you simply have no argument. You so desperately try to convince yourself that I define |N| as an ordinary number, but no matter how hard you try you are still closed under your own misleading wishful thinking loop. jsfisher, you are far far away from http://www.internationalskeptics.com...&postcount=110. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 1st December 2014 at 02:56 PM.
 1st December 2014, 02:38 PM #215 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher Be that as it may, it is still irrelevant to the valuation of 0.999.... Your inabilities are clearly demonstrated in http://www.internationalskeptics.com...&postcount=208. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com )
 1st December 2014, 05:47 PM #216 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi Your inabilities are clearly demonstrated in http://www.internationalskeptics.com...&postcount=208. Ah, another Doron-classic massively re-edited post! One step or a billion (or, dare I say it, infinitely many steps), it is still a process you are chasing. Moreover, whether the steps are performed sequentially or all in parallel, or any combination of the two, it is still the same number of steps. But what of that, either way, you remain fixated on process. And it still is irrelevant to the valuation of 0.999.... No process, no algorithm, just a simple limit. So simple that only rational numbers are needed. The rest of the reals (and most* of the rationals for that matter) are never needed to establish 0.999... as identical to 1. The only way for you demonstrate that 0.999... and 1 are not identical is to show that 1 does not satisfy the N/epsilon requirement for the limit of the partial summations corresponding to 0.999.... *"Most" takes a figurative meaning in this parenthetical remark. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 1st December 2014, 11:46 PM #217 realpaladin Master Poster     Join Date: Apr 2007 Posts: 2,585 Ah, I see we are back to Doron being snide and insulting again... I wonder what has happened to the Doron that all of his friends and family said to be a peace-loving person. Doron, how is communicating with others working out for you? What? Everyone left already? __________________ "All is needed (and it is essential to my definitions) is to understand the actuality beyond the description, for example: Nothing is actually" - Doron Shadmi "But this means you actually have nothing." - Realpaladin ---
 2nd December 2014, 04:31 AM #218 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher The only way for you demonstrate that 0.999... and 1 are not identical is to show that 1 does not satisfy the N/epsilon requirement for the limit of the partial summations corresponding to 0.999... This is another example that supports my argument about your one-level mathematical universe, as very simply addressed in http://www.internationalskeptics.com...&postcount=208. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 2nd December 2014 at 04:35 AM.
 2nd December 2014, 05:57 AM #219 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi This is another example that supports my argument about your one-level mathematical universe, as very simply addressed in http://www.internationalskeptics.com...&postcount=208. Doron, you do not get to redefine the meanings of things to conform to your misunderstandings. The valuation of 0.999... stands at 1. Your attempts to distract with irrelevant references to power sets doesn't change that. (Curious, though. You used to reject Cantor's Theorem. It was just wrong; Cantor was just wrong. Now, you embrace it, even though it lacks utility for your purpose. How flexible of you.) __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 2nd December 2014, 06:22 AM #220 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher You used to reject Cantor's Theorem. Since you are living in the past in a frozen one-level observation of this fine subject, you and only you are responsible to your arbitrary limitations, as easily demonstrated in http://www.internationalskeptics.com...&postcount=208. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 2nd December 2014 at 06:34 AM.
 2nd December 2014, 06:29 AM #221 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher (Curious, though. Curiosity is clearly not one of your features , in this case. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com )
 2nd December 2014, 06:36 AM #222 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher The valuation of 0.999... stands at 1. If observed only from |N|. http://www.internationalskeptics.com...&postcount=110 is simply not in your |N|_only scope. jsfisher, you simply have no argument anymore, so you are digging in the past and desperately try to convince yourself that real mathematics fits to your |N|_only scope. Originally Posted by jsfisher Doron, you do not get to redefine the meanings I do not redefine anything. My argument is true if |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... is true. Simple as that, as clearly shown in http://www.internationalskeptics.com...&postcount=202. Your ∞ hands waving does not hold water. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 2nd December 2014 at 06:58 AM.
 2nd December 2014, 07:08 AM #223 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi If observed only from |N|. Doesn't matter how it is "observed." Doron, you don't get to redefine mathematics to accommodate your personal confusion. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 2nd December 2014, 07:22 AM #224 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher Doesn't matter how it is "observed." Doron, you don't get to redefine mathematics to accommodate your personal confusion. Dear jsfisher. This is the beautiful thing here, I do not redefine anything. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 2nd December 2014 at 07:24 AM.
 2nd December 2014, 08:38 AM #225 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi Dear jsfisher. This is the beautiful thing here, I do not redefine anything. Sure you did. The decimal notation 0.999... has a well-defined meaning, that of a series. The series has a value determined by the limit of the partial summation sequence corresponding to the series. The determination of limits is well-defined. The consequence of all that is that 0.999... is identical in value to 1. Your attempt to "observe" it differently is a redefinition. I can observe 4 differently as 5; that doesn't make it 5. Moreover, your appeal to cardinal numbers is unwarranted since they have no function in establishing the value of 0.999.... __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 2nd December 2014, 09:33 AM #226 realpaladin Master Poster     Join Date: Apr 2007 Posts: 2,585 Originally Posted by doronshadmi Dear jsfisher. This is the beautiful thing here, I do not redefine anything. If all the colors are only to be seen through a new blue lens, then all the colors are redefined as shades of blue. __________________ "All is needed (and it is essential to my definitions) is to understand the actuality beyond the description, for example: Nothing is actually" - Doron Shadmi "But this means you actually have nothing." - Realpaladin ---
 2nd December 2014, 01:02 PM #227 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher Sure you did. Sure I did not. Originally Posted by jsfisher Your attempt to "observe" it differently is a redefinition. Not at all, it is based on the well defined mathematical fact that |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... Originally Posted by jsfisher I can observe 4 differently as 5; that doesn't make it 5. Even in this simple case you fail. Observing 4 from 5 simply enables one to know that 5 > 4. There is nothing in this observation that can be interpreted as if 4 is 5. Originally Posted by jsfisher Moreover, your appeal to cardinal numbers is unwarranted since they have no function in establishing the value of 0.999.... They have a function in establishing the value of 0.999..., but it clearly not in the scope of one that interpretes 4 as 5. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 2nd December 2014 at 01:08 PM.
 2nd December 2014, 01:36 PM #228 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi Not at all, it is based on the well defined mathematical fact that |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... You keep repeating that, but you never actually show how it (whatever "it" actually is) is based on those inequalities. How do you connect Cantor's Theorem to the definition for limits in such a way that 0.999... and 1 are not identical? __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 2nd December 2014, 10:54 PM #229 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher You keep repeating that, but you never actually show how it (whatever "it" actually is) is based on those inequalities. All you have to do is to deduce a given mathematical framework in terms of cardinality, in order to provide a given solution. For example: Finite or infinite cardinality: A given solution that is satisfied by at least some cardinality > |1|, is not satisfied by some cardinality ≤ |1|. Infinite cardinality: A given solution that is satisfied by at least some cardinality > |N|, is not satisfied by some cardinality ≤ |N|. A given solution that is satisfied by at least some cardinality > |P(N)|, is not satisfied by some cardinality ≤ |P(N)|. A given solution that is satisfied by at least some cardinality > |P(P(N))|, is not satisfied by some cardinality ≤ |P(P(N))|. A given solution that is satisfied by at least some cardinality > |P(P(P(N)))|, is not satisfied by some cardinality ≤ |P(P(P(N)))|. etc. ... at infinitum. Originally Posted by jsfisher How do you connect Cantor's Theorem to the definition for limits in such a way that 0.999... and 1 are not identical? A given solution that is satisfied by at least some cardinality > |N|, is not satisfied by some cardinality ≤ |N|. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 2nd December 2014 at 11:08 PM.
 3rd December 2014, 07:00 AM #230 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi Originally Posted by jsfisher You keep repeating that, but you never actually show how it (whatever "it" actually is) is based on those inequalities. All you have to do is to deduce a given mathematical framework in terms of cardinality, in order to provide a given solution.... So you are unable to make clear whatever "it" actually is. Telling us all what it's based on and could be deduced from is just hand-waving without ever defining "it". Quote: Originally Posted by jsfisher How do you connect Cantor's Theorem to the definition for limits in such a way that 0.999... and 1 are not identical? A given solution that is satisfied by at least some cardinality > |N|, is not satisfied by some cardinality ≤ |N|. And this is relevant to the definition for limits just how? __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost Last edited by jsfisher; 3rd December 2014 at 07:28 AM. Reason: fixed quote tags
 3rd December 2014, 12:39 PM #231 realpaladin Master Poster     Join Date: Apr 2007 Posts: 2,585 Originally Posted by doronshadmi A given solution that is satisfied by at least some cardinality > |N|, is not satisfied by some cardinality ≤ |N|. I am not entirely sure why the at least is emphasized by an underscore... The greater than symbol already signifies this. And as for the logic... this is the same as stating: If it is not black, then it is a different color... __________________ "All is needed (and it is essential to my definitions) is to understand the actuality beyond the description, for example: Nothing is actually" - Doron Shadmi "But this means you actually have nothing." - Realpaladin ---
 3rd December 2014, 01:01 PM #232 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by realpaladin I am not entirely sure why the at least is emphasized by an underscore... The greater than symbol already signifies this. And as for the logic... this is the same as stating: If it is not black, then it is a different color... And you aren't even going to ask what it means to satisfy a solution, now are you? Nor how a solution might be satisfied by a cardinal number, either, right? __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 3rd December 2014, 02:01 PM #233 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 Originally Posted by jsfisher So you are unable to make clear whatever "it" actually is. Telling us all what it's based on and could be deduced from is just hand-waving without ever defining "it". This "it" is simply cardinality, and it measures the minimal needed values that satisfy a given value, for example: 0.9+0.09+0.009 that has |3| values can't satisfy value 1, and in this case at least 0.9+0.09+0.009+... that has |N|+1 = |N| values, satisfies value 1. In case that the minimal needed values that satisfy 1 is at least |P(N)|+1 = |P(N)|, 0.9+0.09+0.009+... that has |N|+1 = |N| values, can't satisfy value 1. In case that the minimal needed values that satisfy 1 is at least |P(P(N))|+1 = |P(P(N))|, no |P(N)|+1 = |P(N)| of such values satisfy value 1. Etc. ... ad infinitum. Originally Posted by jsfisher And this is relevant to the definition for limits just how? It is about the ability to satisfy a given value, as explained above. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 3rd December 2014 at 02:17 PM.
 3rd December 2014, 02:41 PM #234 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 20,093 Originally Posted by doronshadmi This "it" is simply cardinality, and it measures the minimal needed values that satisfy a given value Just how do values satisfy a given value? What values would satisfy 42, just as an example? Quote: for example: 0.9+0.09+0.009 that has |3| values No, that is an expression of three values (and, no, I don't need to extract the absolute value of 3). The expression has a value, and that is 0.999. Quote: ...can't satisfy value 1 "Satisfy value 1"? Perhaps you meant "equal" in place of "satisfy value"? Quote: ...and in this case at least 0.9+0.09+0.009+... that has |N|+1 = |N| values, satisfies value 1. 0.9 + 0.09 + 0.009 + ... is an infinite series. The only thing important in determining the value of the series is the limit of the related sequence of partial summations. No infinity is needed to establish that the limit is 1 and thus 0.999... is identical to 1. (By the way, your assertion of |N| + 1 terms are involved is just bizarre. So is your usage of the phrase, "at least".) Quote: In case that the minimal needed values that satisfy 1 is at least |P(N)|+1 = |P(N)|, 0.9+0.09+0.009+... that has |N|+1 = |N| values, can't satisfy value 1. And what case would that be? Again, series, limits, value without every visiting any flavor of infinity. Quote: ... It is about the ability to satisfy a given value, as explained above. Your use of that highlighted word is novel. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost Last edited by jsfisher; 3rd December 2014 at 04:04 PM. Reason: Minor plural problem
 4th December 2014, 04:43 AM #236 realpaladin Master Poster     Join Date: Apr 2007 Posts: 2,585 Originally Posted by jsfisher And you aren't even going to ask what it means to satisfy a solution, now are you? Nor how a solution might be satisfied by a cardinal number, either, right? It's Doron... I am waaay beyond that already... __________________ "All is needed (and it is essential to my definitions) is to understand the actuality beyond the description, for example: Nothing is actually" - Doron Shadmi "But this means you actually have nothing." - Realpaladin ---
 4th December 2014, 04:45 AM #237 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,577 http://www.internationalskeptics.com...postcount=4298 is defined by using different values of cardinality as an essential factor of a given solution, and it is definitely not in the scope of a framework that uses only each cardinal number separately from the other cardinal numbers, in order to provide a given solution. Originally Posted by jsfisher 0.9 + 0.09 + 0.009 + ... is an infinite series. More accurately, 0.9 + 0.09 + 0.009 + ... is an infinite series of countable |N| values and it is < 1 if it used among an infinite series of uncountable |P(N)| values. In order to understand it all you have to do is to realize, for example, how 0.9 + 0.09 + 0.009 finite series of countable |3| values is < 1 if it used among an infinite series of countable |N| values like 0.9 + 0.09 + 0.009 + ... The same principle holds for both cases. __________________ As long as Comparison is impossible because of the imbalance of one's mind, new glasses will not help. ---- If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) Last edited by doronshadmi; 4th December 2014 at 05:34 AM.
 4th December 2014, 04:52 AM #238 psionl0 Skeptical about skeptics     Join Date: Sep 2010 Location: 31°57'S 115°57'E Posts: 10,779 Originally Posted by jsfisher 0.999... stands at 1. Just to be technically accurate, the limit of 0.999... stands at 1. No matter how many 9's you add to the string, the sum will never add up to 1. 0.999... is a convergent countably infinite series. Trying to make more of it than that like doronshadmi is doing or making an unprovable assertion that an infinite string of 9's would still add up to < 1 is to just generate meaningless confusing jargon. __________________ "The process by which banks create money is so simple that the mind is repelled. Where something so important is involved, a deeper mystery seems only decent." - Galbraith, 1975
 4th December 2014, 04:58 AM #240 psionl0 Skeptical about skeptics     Join Date: Sep 2010 Location: 31°57'S 115°57'E Posts: 10,779 Originally Posted by doronshadmi My terms are rigorously defined by the fact that |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... As your diagram in http://www.internationalskeptics.com...&postcount=158 showed, this is true only as long as N is some finite subset of the set of natural numbers. You haven't demonstrated this to be true for a countably infinite set of natural numbers. I'd go as far as to say that if N is the set of all natural numbers, then all of the supersets that you generate are also countably infinite. __________________ "The process by which banks create money is so simple that the mind is repelled. Where something so important is involved, a deeper mystery seems only decent." - Galbraith, 1975

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