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

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 3rd September 2020, 04:13 AM #321 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi I take the property (x ∪ {x}) right from the axiom above, as follows: Definition 1: A set K is a base set iff K property is ~(x∪{x}). How can you determine whether K is of the form x ∪ {x} or not? (By the way, (x ∪ {x}) is not a property and ~(x∪{x}) is not a valid formula. You don't negate sets.) __________________ 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 September 2020, 04:16 AM #322 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi Each one of the given definitions simply declares the existence of some set that satisfies a given property. No, they don't. They give names to things. Neither "declares the existence" of anything. __________________ 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 September 2020, 06:25 AM #323 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher How can you determine whether K is of the form x ∪ {x} or not? Originally Posted by jsfisher; No, the formula (x ∪ {x}) appears without "the need to first define it as a successor" because it is unnecessary to give it a name. Is (x∪{x}) a wff? __________________ 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; 3rd September 2020 at 06:31 AM.
 3rd September 2020, 06:53 AM #324 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi Is (x∪{x}) a wff? Not in propositional calculus, no. "Cup" is a set-valued binary operator, and x and {x} are sets. That makes x ∪ {x} a set and not a true/false ;proposition. __________________ 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 September 2020, 07:23 AM #325 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher Not in propositional calculus, no. "Cup" is a set-valued binary operator, and x and {x} are sets. That makes x ∪ {x} a set and not a true/false ;proposition. A∪B = {x : x∈A OR x∈B} A=x B={x} and we get A∪B = {x : x∈x OR x∈{x}} Definition 1: A set K is a base set iff K ≠ {x : x∈x OR x∈{x}}. Definition 2: A set K is a successor set iff K = {x : x∈x OR x∈{x}}. __________________ 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; 3rd September 2020 at 07:33 AM.
 3rd September 2020, 08:57 AM #326 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi Definition 1: A set K is a base set iff K ≠ {x : x∈x OR x∈{x}} So, what is "x" thing (the non-bold, non-italic version)? __________________ 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
 4th September 2020, 08:33 AM #327 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher So, what is "x" thing (the non-bold, non-italic version)? Whet are the iff yes/no logical foundations of "x" and "x ∪ {x}" things in the following expression? : ∃I (∅∈I ∧ ∀x∈I [(x ∪ {x})∈I]) __________________ 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.
 4th September 2020, 09:05 AM #328 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi Whet are the iff yes/no logical foundations of "x" and "x ∪ {x}" things in the following expression? : ∃I (∅∈I ∧ ∀x∈I [(x ∪ {x})∈I]) Yes/no logical foundations? Where did that come from? I asked what was x in your definition. You cannot just introduce x ∪ {x} (in whatever form you care to represent set union) without telling us what x is. If you leave x unknown, as you have, then your definition isn't. The Axiom of Infinity does include x ∪ {x}, but if first tells us about x. That's the ∀x∈I part. So, what's your x? __________________ 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
 4th September 2020, 09:13 AM #329 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,230 Originally Posted by doronshadmi Whet are the iff yes/no logical foundations of "x" and "x ∪ {x}" things in the following expression? : ∃I (∅∈I ∧ ∀x∈I [(x ∪ {x})∈I]) That makes no sense. "What are the 'if and only if' yes/no foundations of 'x' and 'x ∪ {x}" things in the following expression"? There are none. Axiom_of_infinityWP: "∃I (∅ ∈ I ∧ ∀ x ∈ I [(x ∪ {x}) ∈ I]). In words, there is a set I (the set which is postulated to be infinite), such that the empty set is in I, and such that whenever any x is a member of I, the set formed by taking the union of x with its singleton {x} is also a member of I. Such a set is sometimes called an inductive set." (I use square brackets in the for readability). No iff or yes/no there. __________________ 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.
 4th September 2020, 09:24 AM #330 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 x is a placeholder for any given set (without any information about its members). x∪{x} = {x : x∈x AND {x∈x}} Definition 1: A set K is a base set iff K ≠ {x : x∈x AND {x∈x}}. Definition 2: A set K is a successor set iff K = {x : x∈x AND {x∈x}}. __________________ 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; 4th September 2020 at 09:43 AM.
 4th September 2020, 09:37 AM #331 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,230 Originally Posted by doronshadmi x is a placeholder for a set. x∪{x} = {x : x∈x AND {x∈x}} Definition 1: A set K is a base set iff K ≠ {x : x∈x AND {x∈x}}. Definition 2: A set K is a successor set iff K = {x : x∈x AND {x∈x}}. Define x. Define x. What is the difference between x and x? __________________ 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.
 4th September 2020, 09:37 AM #332 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi x is a placeholder of any given set. You need to quantify that in some way. Otherwise, x is just an unknown. The "right hand side" of your definitions are not allowed to contain unknowns. You can have unknowns on the left, after all those are the things you intend to define, but by the time you get to the right, it all needs to be fixed. __________________ 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
 4th September 2020, 09:43 AM #333 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher You need to quantify that in some way. Otherwise, x is just an unknown. The "right hand side" of your definitions are not allowed to contain unknowns. You can have unknowns on the left, after all those are the things you intend to define, but by the time you get to the right, it all needs to be fixed. x is a placeholder for any given set (without any information about its members). Originally Posted by jsfisher The Axiom of Infinity does include x ∪ {x}, but if first tells us about x. That's the ∀x∈I part. Once again you force "for all" (universal quantification). __________________ 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; 4th September 2020 at 09:52 AM.
 4th September 2020, 09:47 AM #334 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by Little 10 Toes Define x. Define x. What is the difference between x and x? In the set-builder notation Doronshadmi is using, x has a defined meaning. It is simply a variable representing each possible member of the set being defined; everything following the colon provides the conditions all members of the set must meet (and which all non-members fail to meet). E.g.,{ w : w is an even whole number } = { 0, 2, 4, 6, ... } __________________ 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
 4th September 2020, 09:54 AM #335 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi x is a placeholder for any given set (without any information about its members). Then your definition fails to define anything. Whether K is equal to some set involving x cannot be decided since x is not known. You'd need to quantify x in some way, formally, right there in the definition. (This is the second time I have provided that hint.) __________________ 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
 4th September 2020, 09:58 AM #336 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher { w : w is an even whole number } = { 0, 2, 4, 6, ... } In this example w meaning can also be "no members". __________________ 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.
 4th September 2020, 10:02 AM #337 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,230 Originally Posted by doronshadmi In this example w meaning can also be "no members". How? Are you saying that even whole numbers don't exist? __________________ 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.
 4th September 2020, 10:04 AM #338 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher Then your definition fails to define anything. Whether K is equal to some set involving x cannot be decided since x is not known. You'd need to quantify x in some way, formally, right there in the definition. (This is the second time I have provided that hint.) Here we come again to ∀. __________________ 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.
 4th September 2020, 10:05 AM #339 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi In this example w meaning can also be "no members". It is correct exactly as presented. You didn't understand the example at all, did you? Stop pretending. __________________ 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
 4th September 2020, 10:06 AM #340 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by Little 10 Toes How? Are you saying that even whole numbers don't exist? My mistake of writing a misleading post , I mean that generally w meaning can also be "no members", where w in jsfishr's example and x in my post are used for the same purpose, to define a set according its structure and not according to its members. __________________ 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; 4th September 2020 at 10:56 AM.
 4th September 2020, 10:12 AM #341 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi Here we come again to ∀. Seems like an inconvenient choice, but, hey, knock yourself out. __________________ 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
 4th September 2020, 10:42 AM #342 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher Seems like an inconvenient choice, but, hey, knock yourself out. Can you tell me please for what set the expression "x" stands for, by adding "∀" to "x"? If you can't do it, it means that x is a placeholder for any given set (without any information about its members). __________________ 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.
 4th September 2020, 10:49 AM #343 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi Can you tell me please for what set the expression "x" stands for, by adding "∀" to "x"? You might have a better time of it if you focused on the second definition. __________________ 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
 4th September 2020, 11:24 AM #344 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,230 Originally Posted by doronshadmi My mistake of writing a misleading post , I mean that generally w meaning can also be "no members", where w in jsfishr's example and x in my post are used for the same purpose, to define a set according its structure and not according to its members. And this is wrong. Edit: and VERY Dishonest. You changed the post at 10:56am after 3 other posts. __________________ 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; 4th September 2020 at 11:26 AM.
 4th September 2020, 11:35 AM #345 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher You might have a better time of it if you focused on the second definition. {x : x∈A OR x∈B} is the general logical structure of A∪B, where x is a placeholder for any given member (including no members at all), and so is the case about A and B, they are placeholders for sets, without any information about their members, exactly because x is such placeholder. Here it is: A∪B = {x : x∈A OR x∈B} Now let's go to the general logical structure of x∪{x} x is a placeholder for any given set (without any information about its members). x∪{x} = {x : x∈x AND {x∈x}} Definition 1: A set K is a base set iff K ≠ {x : x∈x AND {x∈x}}. Definition 2: A set K is a successor set iff K = {x : x∈x AND {x∈x}}. __________________ 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; 4th September 2020 at 01:24 PM.
 4th September 2020, 11:50 AM #346 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by Little 10 Toes And this is wrong. You are right, my use of x is different than jsfisher's use of w. jsfisher uses w in order to define the members of a given set. I use x as a part of the general logical structure of x∪{x}, which enables me to define N members in terms base sets or successor sets that are not largest successor sets, according to their structures, no matter what members N members have. __________________ 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.
 4th September 2020, 12:01 PM #347 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,230 I notice that once again, you do not mention your dishonesty. __________________ 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.
 4th September 2020, 12:08 PM #348 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 EDIT: Let's put what we have until now, in one post. {x : x∈A OR x∈B} is the general logical structure of A∪B, where x is a placeholder for any given member (including no members at all), and so is the case about A and B, they are placeholders for sets, without any information about their members, exactly because x is such placeholder. Here it is: A∪B = {x : x∈A OR x∈B} Now let's go to the general logical structure of x∪{x} x is a placeholder for any given set (without any information about its members). x∪{x} = {x : x∈x AND {x∈x}} Definition 1: A set K is a base set iff K ≠ {x : x∈x AND {x∈x}}. Definition 2: A set K is a successor set iff K = {x : x∈x AND {x∈x}}. Definition 3: A successor set K is a largest successor set in X iff K∈X AND K successor set ∉ X. Let M(y) be the membership function of set N. If y is largest successor set, then M(y) : false. If y is not largest successor set, then M(y) : true. Not being largest successor set in N is: (successor set that has its successor set) OR (base set) An example: Code: ```N = { ∅, ---> {{∅}}, ---> ... <-- base sets {∅}, ---> {{∅}, {{∅}} }, ---> ... <-- successor sets {∅, {∅}}, ---> {{∅}, {{∅}}, {{∅}, {{∅}}}}, ---> ... <-- successor sets {∅, {∅}, {∅, {∅}}}, ---> {{∅}, {{∅}}, {{∅}, {{∅}}}, {{∅}, {{∅}}, {{∅}, {{∅}}}}}, ---> ... <-- successor sets ... ... }``` As can be seen, set N members are (base sets) OR (successor sets that have their successor sets) (M(y) is true), but no largest successor set is a member of set N (M(y) is false). Moreover, if x=N, then N is not the same as (N∪{N}), and we can't define N as its own member, exactly as we can't define, for example, {} as its own member, since {}∪{{}}={{}}≠{}. In other words, ∀ and N have nothing to do with each other, which enables to define N as a set of infinitely many members that its cardinality is not any particular size. Without definition 2, the following is actually unknown: Any set that is the member of itself is actually a successor set of that set, for example: x={a,b,c,...} If {a,b,c,...} is a member of itself, then we get the set {a,b,c,...{a,b,c,...}} which is actually ({a,b,c,...}∪{{a,b,c,...}}) = (x∪{x}) ≠ x = {a,b,c,...} More general, no set is its successor set. ----------------------------------------------------- jsfisher, another unknown thing by mathematicians that do not define successor set, is ∀ as the cause of Russell's Paradox, and this time please do not skip on it. ∀ is the cause of Russell's Paradox, whether a given collection of distinct objects is finite, or not. For example: U is a set of two distinct members, such that one of the members, called u, shaves ∀ the members of set U that do not shave themselves and only these members of set U (this is supposed to be his property in order to be a member of set U). Who shaves u? If u shaves himself, then he must not shave himself (shaves AND ~shaves himself, which is a contradiction) exactly because of the term ∀. If u does not shave himself, then he must shave himself (~shaves AND shaves himself, which is a contradiction) exactly because of the term ∀. So, because the term ∀ is used as a part of the terms that define u as a member U, u must be referred to himself, and we get the contradictions that actually prevents to well-define ∀ the members of set U (the term ∀ itself is actually not well-defined in case of U). The same problem holds also among infinite sets that the term ∀ is one of their properties, therefore the Axiom of Restricted Comprehension was add to ZF in order to avoid Russell's Paradox, but it is done without being aware of the fact that the term ∀ is the cause of any given contradictory self reference, whether it is used among finite or infinite 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; 4th September 2020 at 01:21 PM.
 4th September 2020, 12:08 PM #349 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi A∪B = {x : x∈A OR x∈B} The left-hand side provides the meaning for A and B used on the right. Quote: Definition 1: A set K is a base set iff K ≠ {x : x∈x AND {x∈x}}. Definition 2: A set K is a successor set iff K = {x : x∈x AND {x∈x}}. So, what's x? We are set on what K means; not at all set on x. __________________ 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
 4th September 2020, 12:17 PM #350 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher The left-hand side provides the meaning for A and B used on the right. Yet, x does not stand for any particular members, including no members at all. Originally Posted by jsfisher So, what's x? We are set on what K means; not at all set on x. K is defined by its structure, not by its members. Please carefully read http://www.internationalskeptics.com...&postcount=345 from start to end. __________________ 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; 4th September 2020 at 12:33 PM.
 4th September 2020, 12:46 PM #351 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi Yet, x does not stand for any particular members. What has that to do with anything? You clearly do not understand the notation, so please stop pretending you do. The set builder notation gives fully quantified meaning to your bold/italic x. Quote: K is defined by its structure, not by its members. No, K is defined by neither its structure nor its members. All we know about K, all we care about K, is that K is a set. Be that as it may, though, the question you are ducking is what is x. It is sitting as a free variable in your definitions; it needs to be bound or quantified in some way. What is x? __________________ 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
 4th September 2020, 01:04 PM #352 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher No, K is defined by neither its structure nor its members. All we know about K, all we care about K, is that K is a set. K is indeed a set that is defined by its structure. Originally Posted by jsfisher Be that as it may, though, the question you are ducking is what is x. It is sitting as a free variable in your definitions; it needs to be bound or quantified in some way. x is a placeholder for any given set, all we care about is that x is a set. Originally Posted by jsfisher What is x? x is a set. x is a placeholder for any given member, including no member at all. x∪{x} = {x : x∈x AND {x∈x}} The left-hand side provides the meaning for x used on the right. __________________ 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; 4th September 2020 at 01:27 PM.
 4th September 2020, 01:19 PM #353 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi K is indeed a set that is defined by its structure. No. K is just any set. Your definitions impose no restrictions on K other than it being a set. Quote: The left-hand side provides the meaning for x used on the right. Not in any of your definitions.Definition 1: A set K is a base set iff ... Definition 2: A set K is a successor set iff ...There's K on the left in both cases. No x, though. So what is x? You need to quantify it somehow. __________________ 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
 4th September 2020, 01:39 PM #354 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher What has that to do with anything? You clearly do not understand the notation, so please stop pretending you do. The set builder notation gives fully quantified meaning to your bold/italic x. What do you mean by "fully quantified meaning"? Originally Posted by jsfisher No, K is defined by neither its structure nor its members. All we know about K, all we care about K, is that K is a set. Really? In that case what is w if not a condition that defines the members of a given set, as seen in your example in http://www.internationalskeptics.com...&postcount=334 . __________________ 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.
 4th September 2020, 01:46 PM #355 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher No. K is just any set. Your definitions impose no restrictions on K other than it being a set. Yes, it imposes on set K a structure. Originally Posted by jsfisher Not in any of your definitions.Definition 1: A set K is a base set iff ... Definition 2: A set K is a successor set iff ...There's K on the left in both cases. No x, though. So what is x? You need to quantify it somehow. x is a placeholder for any given set, all we care about is that x is a set. __________________ 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.
 4th September 2020, 01:51 PM #356 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,230 Originally Posted by doronshadmi Yes, it imposes on set K a structure. x is a placeholder for any given set, all we care about is that x is a set. No! It does not matter if K has "a structure". __________________ 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.
 4th September 2020, 01:53 PM #357 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi What do you mean by "fully quantified meaning"? Everyone is better in Comic Sans:S = { x : P(x) } ⇔ ∀x ( x∈ S ⇔ P(x) ) Quote: Really? In that case what is w if not a condition that defines the members of a given set The set K was the subject. No w was involved. (And w, by the way, is a variable, not a condition.) __________________ 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
 4th September 2020, 01:58 PM #358 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 jsfisher, as seen in http://www.internationalskeptics.com...&postcount=348 there can be more than one notion about strings of symbols, but in your case, you do not understand the potential damage of ∀ on sets, finite or not. Also you do not understand the difference between N and N∪{N} that actually prevents N as a member of itself, without the need of any ad hoc axioms like the ZF axiom of specification https://en.wikipedia.org/wiki/Axiom_..._specification . __________________ 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.
 4th September 2020, 02:02 PM #359 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,920 Originally Posted by doronshadmi Yes, it imposes on set K a structure. Where, exactly do either of your first two definitions impose any structure on K? Quote: x is a placeholder for any given set, all we care about is that x is a set. So, I get free choice as to what set I want it to be? Excellent!!! I chose the empty set. Definition 1: A set K is a base set iff K ≠ {x : x∈∅ AND x∈{∅}}. Definition 2: A set K is a successor set iff K = {x : x∈∅ AND x∈(∅}}. By the way, I corrected, let's be generous and call it a typo, a typo in your definitions. Not quite up there with negated sets, but still.... __________________ 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
 4th September 2020, 02:04 PM #360 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,243 Originally Posted by jsfisher The set K was the subject. No w was involved. (And w, by the way, is a variable, not a condition.) Call it a variable, yet it is used to define the members of a given set. __________________ 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.

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