
Welcome to the International Skeptics Forum, where we discuss skepticism, critical thinking, the paranormal and science in a friendly but lively way. You are currently viewing the forum as a guest, which means you are missing out on discussing matters that are of interest to you. Please consider registering so you can gain full use of the forum features and interact with other Members. Registration is simple, fast and free! Click here to register today. 
3rd September 2020, 04:13 AM  #321 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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. 

3rd September 2020, 06:53 AM  #324 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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. 

3rd September 2020, 08:57 AM  #326 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947

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 
Master Poster
Join Date: Nov 2006
Posts: 2,235

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_infinity^{WP}: "∃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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260

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. 

4th September 2020, 09:37 AM  #331 
Master Poster
Join Date: Nov 2006
Posts: 2,235


__________________
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 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947

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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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, 09:47 AM  #334 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947

In the setbuilder 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 nonmembers 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 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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 
Master Poster
Join Date: Nov 2006
Posts: 2,235


__________________
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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, 10:12 AM  #341 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
Master Poster
Join Date: Nov 2006
Posts: 2,235


__________________
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, 11:35 AM  #345 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260

{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. 

4th September 2020, 11:50 AM  #346 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260

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 
Master Poster
Join Date: Nov 2006
Posts: 2,235

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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260

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 ... ... } 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 welldefine ∀ the members of set U (the term ∀ itself is actually not welldefined 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. 

4th September 2020, 12:08 PM  #349 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260

Yet, x does not stand for any particular members, including no members at all.
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. 

4th September 2020, 12:46 PM  #351 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947

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:
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260

K is indeed a set that is defined by its structure.
x is a placeholder for any given set, all we care about is that x is a set. 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 lefthand 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. 

4th September 2020, 01:19 PM  #353 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947

No. K is just any set. Your definitions impose no restrictions on K other than it being a set.
Quote:
Definition 1: A set K is a base 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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260

What do you mean by "fully quantified meaning"?
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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 
Master Poster
Join Date: Nov 2006
Posts: 2,235


__________________
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 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947


__________________
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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260

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 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,947

Where, exactly do either of your first two definitions impose any structure on K?
Quote:
Definition 1: A set K is a base 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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,260


__________________
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. 

Bookmarks 
Thread Tools  

