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 International Skeptics Forum Continuation Deeper than primes - Continuation 1/3*9

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 24th September 2020, 05:30 AM #561 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 Originally Posted by jsfisher I skipped any treatment of the natural numbers because I don't need any. You are the one insisting it be there, I have shown it isn't required. Yes, that is what I wrote and what you already quoted. Repeating it was unnecessary. No, N is defined by the previous expression. Restating it again does not add value. And you made an error in the process. Be that as it may, though, I am confident you have no idea how the expression actually achieves the goal. You recognize the individual "words" by you don't comprehend their collective meaning. Yep, proof you don't comprehend their collective meaning. Oh? Are you unfamiliar with the phrase, vacuously true? F : ∅ → X is an injective map from the empty set to any set X. A function F is an injective map from the not necessarily distinct sets A to B iff:∀a∈A (∃b∈B (F(a) = b ∧ ∀c∈A (F(a) = F(c) ⇒ a = c)))Nothing there forbids A or B from being empty. You have missed my correction in http://www.internationalskeptics.com...&postcount=559 and replied to an irrelevant post. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.
 24th September 2020, 05:56 AM #562 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,964 Originally Posted by doronshadmi You have missed my correction in http://www.internationalskeptics.com...&postcount=559 and replied to an irrelevant post. If you need to make extensive corrections to a post (i.e., other than slight typos), then make a new post. Also, be kind enough to highlight the important corrections you think you are making. __________________ 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
 24th September 2020, 06:05 AM #563 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 Originally Posted by jsfisher If you need to make extensive corrections to a post (i.e., other than slight typos), then make a new post. Also, be kind enough to highlight the important corrections you think you are making. http://www.internationalskeptics.com...&postcount=559 is a new post, where you replied to the older one. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 24th September 2020 at 06:11 AM.
 24th September 2020, 06:15 AM #564 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,964 Originally Posted by doronshadmi It is a new post, where you replied to the older one. No, it was not a new post. It was an substantial edit to an existing post. And I replied to the version of the post in place at the time I hit the Quote button. It is rude for you to dismiss my post in its entirety, too. If it comments on mistakes of yours that have been corrected, point out in response to my post how your mistakes were corrected. If it comments on things you thought were correct in the first place, comment on that. I await the mitigation to your rudeness. __________________ 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
 24th September 2020, 06:44 AM #566 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 Originally Posted by jsfisher I skipped any treatment of the natural numbers because I don't need any. You can't skip on these sets, as shown in http://www.internationalskeptics.com...&postcount=559. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 24th September 2020 at 06:45 AM.
 24th September 2020, 07:33 AM #567 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 The relevant details are as follows: jsfisher, in order to establish the minimal set satisfying the requirements of the Axiom of Infinity, one first has to show that all the natural numbers (which are defined by von Neumann's treatment of the natural numbers in terms of sets) are actually establish a set that satisfying the requirements of the Axiom of Infinity. So at the first stage the following definitions are restricted only to all the members of this minimal set, such that the initial member is the empty set (v=∅) and the rest of the members are defined as v⋃{v}, which are all finite sets: Definition 1: |v| = |v| iff there is bijection from v to v. Definition 2: |v| < |v⋃{v}| iff (there is an injective non-surjective function from v to v⋃{v}) OR (injective function from v to v⋃{v} that is based on empty function) (in case that v=Ø) Definitions 1 and 2 look trivial at first glance, but these are the functions among the finite sets, which define all the natural numbers by von Neumann's treatment. Since ∀v ∈ V(v∪{v} ∈ V ∧ |v∪{v}| can't be but < |V|) |V| is not established, simply because it can't be defined as the cardinality of all V members, which are all the finite sets by von Neumann's treatment of all the natural numbers. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 24th September 2020 at 07:43 AM.
 24th September 2020, 08:11 AM #568 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,964 Just a reminder: Originally Posted by jsfisher No, it was not a new post. It was an substantial edit to an existing post. And I replied to the version of the post in place at the time I hit the Quote button. It is rude for you to dismiss my post in its entirety, too. If it comments on mistakes of yours that have been corrected, point out in response to my post how your mistakes were corrected. If it comments on things you thought were correct in the first place, comment on that. I await the mitigation to your rudeness. __________________ 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
 24th September 2020, 09:08 PM #569 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,240 I'm starting this message at 9:13pm local time according to my tablet. I am purposely waiting and stalling a few minutes to have the forum clock to change. Edit: the system clock is 7-8 minutes behind. This would confirm that the time on the post is not when you start writing it, but when you submit/save/post it. Edit 2: trying to see what the edit time is based off. Waiting about 30mins. Looks like it's based off the save button. __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did. Last edited by Little 10 Toes; 24th September 2020 at 09:25 PM.
 25th September 2020, 06:52 PM #570 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,240 And what the deal about waiting almost two hours before posting the final "edit"? __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.
 27th September 2020, 08:38 AM #572 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 Originally Posted by jsfisher ... especially since my observations about the post I responded to were still valid after all of Doronshadmi's editing. Let's see. 1) He ignores the minimal set that satisfies the requirements of the Axiom of Infinity. 2) This minimal set is exactly the von Neumann's treatment of the natural numbers in terms of sets (let's call this set V (which, of course, can be replaced by any other chosen name)). 3) All the members of set V are finite sets. 4) There are four functions, divided into two types, among V members, as follows: a) 2 functions from a given member to itself: a.1) Empty function from Ø to itself. a.2) Bijective function from v (where v≠Ø) to itself. a.3) Bijective function from v⋃{v} to itself. b) 2 functions from a given member to a different member: b.1) Injective non-surjective function from v to v⋃{v} (in case that v≠Ø). b.2) Injective function from v to v⋃{v} (in case that v=Ø, where all v⋃{v} in V are finite sets, according to von Neumann's treatment of the natural numbers in terms of sets). Originally Posted by jsfisher Every element of v ⋃ {v} is an element of V. The identity function is a perfectly adequate injection from v ⋃ {v} to V. Therefore (under my definition): |v ⋃ {v}| ≤ |V| But by (1) to (4) there can't be injection from v⋃{v} to V, which means that: ∀v ∈ V(v∪{v} ∈ V) ∧ (|v∪{v}| < |V|). No wonder that jsfisher ignores "weak limit cardinal" as seen in http://www.internationalskeptics.com...&postcount=451. Quote: ( https://en.wikipedia.org/wiki/Limit_cardinal ) In mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This means that one cannot "reach" λ from another cardinal by repeated successor operations. λ is an ad hoc invention out of nowhere, that all of its purpose is to establish the Cantorian transfinite system by hook or by crook. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 27th September 2020 at 09:14 AM.
 29th September 2020, 02:45 AM #573 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 The foundations of mathematics Please look at http://www.internationalskeptics.com...&postcount=478 in order to understand better why ZF(C) is not the actual foundations of mathematics. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.
 29th September 2020, 08:08 AM #574 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 Originally Posted by jsfisher Not all closed curves are circles, but all circles are closed curves. Not all injections are bijections, but all bijections are injections. closed curves = one-to-one functions circles = one-to-one AND onto functions So, according to you, not all one-to-one functions are one-to-one AND onto functions (in this case we have |A| < |B|) , but all one-to-one AND onto functions are one-to-one functions (in this case we have |A| = |B|). Originally Posted by jsfisher You can, in fact, use those meanings to show that the expression |A| <= |B| is identical to (|A| < |B|) OR (|A| = |B|) By using your analogy: (not all one-to-one functions are one-to-one AND onto functions) OR (all one-to-one AND onto functions are one-to-one functions) Since all the members of the von Neumann's treatment of the natural numbers in terms of sets are finite sets, only the following part of his analogy holds: (not all one-to-one functions are one-to-one AND onto functions) which means that only all one-to-one functions that are not one-to-one AND onto functions, are used in case of |v∪{v}| < |V|, exactly because v∪{v} can't be but a finite set, the von Neumann's treatment of the natural numbers in terms of sets. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 29th September 2020 at 08:18 AM.
 2nd October 2020, 01:51 PM #576 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 Originally Posted by jsfisher On two previous occasions, I posted some cryptic hieroglyphics suggesting they may be useful sometime later. Now that the thread's star celeb is working on his monologue, re-presenting past nonsense, I will close out my participation in this arc of the thread explaining those two posts for anyone who really cares. You close your participation in this arc by a monologue that does not satisfy fundamental things for anyone who really cares: 1) You have proved that N exists, such that Ø is its one and only one member that is not a successor of the rest of N members, where all the members of set N are themselves sets, such that for all x (where x is any arbitrary member of N), x⋃{x} is also a member of N. 2) All along the way you ignored the existence of all the finite sets that are definitely members of N. 3) Whether you like it or not, all these finite sets that are members of set N, satisfying the requirements of the Axiom of Infinity. 4) If you disagree with (3), you actually disagree with the existence of all the natural numbers in terms of sets (as defined by the von Neumann's treatment of the natural numbers, where their initial set is Ø, as written in (1)). 5) By not ignoring all the finite sets of N, one can easily understand http://www.internationalskeptics.com...&postcount=567, which very simply addresses the fact that no x⋃{x} has the cardinality of N. 6) Your entire framework is based on injective function (≤), which according to it x⋃{x} (which is a finite member of N, if N is indeed the minimal set that satisfying the requirements of the Axiom of Infinity) has the cardinality of N, but http://www.internationalskeptics.com...&postcount=572 very simply shows why |x⋃{x}| = |N| is not established. 7) You take injection as some generalization, which somehow enables bijection to sneak in order to establish |x⋃{x}| = |N|, but http://www.internationalskeptics.com...&postcount=574 shows why this generalization has no basis. 8) No wonder that you ignores "weak limit cardinal" as seen in http://www.internationalskeptics.com...&postcount=451. Quote: ( https://en.wikipedia.org/wiki/Limit_cardinal ) In mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This means that one cannot "reach" λ from another cardinal by repeated successor operations. λ is an ad hoc invention out of nowhere, that all of its purpose is to establish the Cantorian transfinite system by hook or by crook. ==================================== Is there any alternative to jsfisher's framework? The answer is yes, as can be seen, for example, in https://en.wikipedia.org/wiki/Alternative_set_theory. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 2nd October 2020 at 01:57 PM.
 14th October 2020, 07:35 AM #577 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 |A| ≤ |B| is identical to (|A| < |B|) OR (|A| = |B|). p="|A| < |B|" q="|A| = |B|" Code: ```p OR q -------- F F --> F T F --> T F T --> T T T --> T``` Logically < can be replaced by ≤, but ≤ can't be replaced by <. Some example: 1) 1<2 and 1≤2 are both true (T OR F --> T of the truth table above). 2) 1≤1 is true, but it's not true that 1<1 (F OR T --> T of the truth table above). -------------------- 3) T OR T --> T is possible only if |A| is a variable for values that are < or = |B|. -------------------- Since all the members of the von Neumann's treatment of the natural numbers in terms of sets, satisfying the requirements of the Axiom of Infinity, they can't be ignored by any one that works under ZF(C). Option (3) above is impossible, since given any arbitrary x (where x is some set by the von Neumann's treatment of the natural numbers in terms of sets) |x⋃{x}| can't be but < |N| (T OR F --> T of the truth table above) if N is claimed to be a set with infinitely many members. -------------------- One claims: "You can't pick parts from a truth table in order to support your argument, since the whole truth table must be taken". Well, in this case how, for example, 1<2 and 1≤2 are both true by the whole OR truth table? -------------------- Maybe I am mixing things up, so please correct my mistakes. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 14th October 2020 at 07:57 AM.
 25th October 2020, 03:51 AM #578 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,265 By ZFC, the minimal set satisfying the requirements of the axiom of infinity, is the intersection of all inductive sets. In case that the axiom of infinity is expressed as ∃I (Ø ∈ I ∧ ∀x (x ∈ I ⇒ x ⋃ {x} ∈ I)) the intersection of all inductive sets (let's call it K) is defined as set K = {x∈I : ∀y ((Ø ∈ y ∧ ∀z ((z ∈ y ⇒ z ⋃ {z} ∈ y))) ⇒ x ∈ y)}. The members of set K can be defined by von Neumann's construction of the natural numbers in terms of sets (https://en.wikipedia.org/wiki/Natura..._on_set_theory). So K satisfying the requirements of the axiom of infinity, where all of its members are finite sets, such that only Ø is not a successor of the rest of K's members. In that case ∀k ∈ K (k ∪ {k} ∈ K), where |k ∪ {k}| can't be but < |K|, if |K| = λ = weak limit cardinal (such that λ is neither a successor cardinal nor zero). In that case how λ is formally defined as the cardinality of all k in K ? __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 25th October 2020 at 03:54 AM.

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