
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. 
22nd August 2020, 07:30 AM  #241 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

So N members are of the form (x∪{x}) (successors) OR not of the form (x∪{x}) (bases), which is a tautology but not a trivial one, since ~(x∪{x}) is actually a proper subset of forms in N, where (x∪{x}) is not one of these forms in N, where N is closed under succession since at least one of the (x∪{x}) forms does not have its largest (x∪{x}) form in N (the term "all" is not satisfied in N if N is an infinite set).
More details are given in http://www.internationalskeptics.com...&postcount=239 and http://www.internationalskeptics.com...&postcount=235. 
__________________
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. 

22nd August 2020, 11:55 AM  #242 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942

No, and no. The Axiom of Infinity establishes that there exists a set satisfying two properties. The two properties are:
These two properties do not in any way establish 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 

22nd August 2020, 12:05 PM  #243 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942


__________________
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 

22nd August 2020, 12:06 PM  #244 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259


__________________
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. 

22nd August 2020, 12:15 PM  #245 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259


__________________
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. 

22nd August 2020, 12:36 PM  #246 
Critical Thinker
Join Date: Jul 2007
Posts: 267

First Axiom of Doronity
There exists a set whose members are unknown.

22nd August 2020, 02:06 PM  #247 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942

The two statements are completely consistent. The Axiom itself (not the two properties) asserts some set exists.
The properties are two characteristics the set (asserted by the Axiom) must have. Neither Axiom itself nor the two properties give a precise definition for the set asserted to exist. 
__________________
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 

22nd August 2020, 02:08 PM  #248 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942


__________________
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 

22nd August 2020, 11:45 PM  #249 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

N members are welldefined, as given in http://www.internationalskeptics.com...&postcount=241 and its links.

__________________
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. 

22nd August 2020, 11:50 PM  #250 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

Done at http://www.internationalskeptics.com...&postcount=241 and its links.

__________________
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. 

23rd August 2020, 12:14 AM  #251 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

jsfisher and Hevneren,
N members are welldefined by the following rule: Any given N member is of the form (x∪{x}) OR not of the form (x∪{x}), which is a tautology. Please define some welldefined set that can't be N member according this tautology. 
__________________
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. 

23rd August 2020, 10:01 AM  #252 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942

I see. So you would like your set N to be a set of everything. All sets satisfy your rule so every set must be a member of N.
Alas, though, while that is surely not the set you had in mind, it is also not a set in any axiomatic set theory. This shouldn't be that hard, Doronshadmi. You just need a logic function M(x) such that M(x) is true if x is in N, and M(x) is false if x is not in N. Then, you can define N in a simple way: N = { x : M(x) }The only constraint is that M(x) must be consistent with the Axiom of Restricted Comprehension to insure that N is a set. 
__________________
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 August 2020, 12:57 AM  #253 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

No, you don't see that N can't be a set of everything, since if N is an infinite set at least one of the (x∪{x}) forms does not have its largest (x∪{x}) form in N (the term "all" is not satisfied in N if N is an infinite set, according to the following definition):
Definition: (x∪{x}) is called the largest successor in N iff (x∪{x}) does not have its successor in N. jsfisher, you still do not capture http://www.internationalskeptics.com...&postcount=241 and its links. jsfisher, you are the person at the adjacent table that is unaware of the paradise that he established on his table. jsfisher, you are the founder of set N by using base member and successor member as its inherent properties. 
__________________
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 August 2020, 03:59 AM  #254 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942

Of course it can't, but that's how you described it. You need to fix the description.
Quote:
Quote:

__________________
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 August 2020, 06:52 AM  #255 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

Well that's how you wrongly interpret it exactly because you ignore the following definition:
Definition 1: (x∪{x}) is called the largest successor in N iff (x∪{x}) does not have its successor in N. I use the term "in N" and not "of N", which enables to define the term "the largest successor" not with respect to "all" the possible successors in N, but only with respect to the successors that emerge from a given base member in N, as seen in the following example: Here is a bijective map between given infinite proper subsets in N, where for any such given infinte proper subset there is a distinct base member, and its other distinct members are defined according to (x∪{x}), such that no (x∪{x}) is the largest successor in any such given proper subset: Code:
N = { ∅, > {{∅}}, > ... < base members {∅}, > {{∅}, {{∅}} }, > ... {∅, {∅}}, > {{∅}, {{∅}}, {{∅}, {{∅}}}}, > ... {∅, {∅}, {∅, {∅}}}, > {{∅}, {{∅}}, {{∅}, {{∅}}}, {{∅}, {{∅}}, {{∅}, {{∅}}}}}, > ... ... ... } ZF was defined by persons that their aim was to establish definitions of order and cardinality that hold both for finite and infinite sets (in the name of generalization). It was done by using universal quantification (the term "For All") both for finite and infinite sets, where in the case of infinite sets universal quantification was arbitrarily forced on them without any reasoning. It can be seen right at the ZF Axiom of infinity, universal quantification (the term "For All") is arbitrarily plugged into this axiom even though a set, named, for example, as N by jsfisher (where any other name can be used) clearly does not have all of its successors, as shown above. It does not matter if the Axiom of Restricted Comprehension or other ZF axioms are used or not, the fundamental error was done by using universal quantification as a part of ZF Axiom of infinity. You can force the term "For All" as much as you like on an infinite set, a fundamental error it will stay. You are completely missing what you actually established in http://www.internationalskeptics.com...6&postcount=92 and http://www.internationalskeptics.com...&postcount=202 , don't you? Please read your http://www.internationalskeptics.com...6&postcount=92 post very carefully to actually understand your own words about bases and their successors. You still have no idea what a beautiful mathematical paradise you, jsfisher, established. 
__________________
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 August 2020, 09:39 AM  #256 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942

No, that definition is irrelevant to my point. You described the members of set N as either successors (of some nonspecific something) or not successors. You even admitted it was a tautology.
Your description admits all sets as members of your set N. If that isn't the description you want, then you need a better description for your set N. 
__________________
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 August 2020, 10:39 PM  #257 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

My description: Any given N member is of the form (x∪{x}) OR not of the form (x∪{x}), which is a tautology.
Definition 1: (x∪{x}) is called the largest successor in N iff (x∪{x}) does not have its successor in N. There is no all in my description exactly because for any given proper subset in N that its base member is, by definition, not a successor ( defined as ~(x∪{x}) ), does not have its largest successor in N by Definition 1, which means that the term "For All" (also called universal quantification that is notated by ∀) is not satisfied in N. So Definition 1 is relevant for N. Details are already given in http://www.internationalskeptics.com...&postcount=255 but you chose to ignore them.  B.T.W, ∀ 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. 

25th August 2020, 04:12 AM  #258 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942


__________________
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 

25th August 2020, 06:55 AM  #259 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

By using definition 1, no largest successor ( where successors are of the form (x∪{x}) ) is emerged from at least one base member of N ( where base members are of the form ~(x∪{x}) ), yet any given member of N is of the form (x∪{x}) OR ~(x∪{x}), which is tautology.
Please look at set N: Code:
N = { ∅, > {{∅}}, > ... < base members {∅}, > {{∅}, {{∅}} }, > ... {∅, {∅}}, > {{∅}, {{∅}}, {{∅}, {{∅}}}}, > ... {∅, {∅}, {∅, {∅}}}, > {{∅}, {{∅}}, {{∅}, {{∅}}}, {{∅}, {{∅}}, {{∅}, {{∅}}}}}, > ... ... ... } The lack of largest successors in N is exactly the property of an infinite set, therefore the term "For All" is not satisfied in N, and yet given any member of N, it is ~(x∪{x}) OR (x∪{x}), which a tautology. Moreover, you still do not capture the link between ∀ and Russell's Paradox, whether a given set is infinite or finite, in terms of ∀. Look how gross is ZF. From one hand ∃N (∅∈N ∧ ∀x∈N [(x∪{x})∈N]) But on the other hand the axiom schema of comprehension (https://en.wikipedia.org/wiki/Axiom_..._specification) is needed in order to avoid Russell's Paradox, exactly because ∀ is a part of the axiom of infinity. 
__________________
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. 

25th August 2020, 08:30 AM  #260 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942


__________________
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 August 2020, 03:46 AM  #261 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

Definition 1: Any given set that is not of the form (x∪{x}), is called a base set (if included in some set, it is called a base member in that set).
Definition 2: Any given set that is of the form (x∪{x}), is called a successor set (if included in some set, it is called a succesor member in that set). Definition 3: Given a successor member in some set, it is called largest successor member iff given a base member in that set, it has at least one successor member that does not have its successor member in that set. EDIT: The membership function of set N: Given set N, no one of its successor members has its largest successor member (M(x) returns false about largest successor members). Given set N, any one of its members is a base member OR a successor member that is not largest successor member (M(x) returns true about any base member OR any successor member that is not largest successor member). 
__________________
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. 

26th August 2020, 04:08 AM  #262 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942


__________________
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 August 2020, 04:34 AM  #263 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

I apologize, you replied during my editing of http://www.internationalskeptics.com...&postcount=261 .

__________________
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. 

26th August 2020, 06:11 AM  #264 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942

You have been scolded by multiple people multiple times about your rude post editing practices. Fixing typos and minor clarifications are entirely acceptable; substantial rewrites are not.
Still not a membership function. I note, too, your use of the word "returns"; it emphasizes the depth of your misunderstanding. 
__________________
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 August 2020, 06:21 AM  #265 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

No problem, without "returns":
The membership function of set N: Given set N, no one of its successor members has its largest successor member (M(x) is false about the membership of largest successor members). Given set N, any one of its members is a base member OR a successor member that is not largest successor member (M(x) is true about the membership of any base member OR any successor member that is not largest successor member). edit: Please see definitions 1,2,3 in http://www.internationalskeptics.com...&postcount=261 . 
__________________
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. 

26th August 2020, 06:25 AM  #266 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942


__________________
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 August 2020, 06:39 AM  #267 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

Well, here is an example of two base members and their successor members in set N:
Code:
N = { ∅, > {{∅}}, > ... < base members {∅}, > {{∅}, {{∅}} }, > ... {∅, {∅}}, > {{∅}, {{∅}}, {{∅}, {{∅}}}}, > ... {∅, {∅}, {∅, {∅}}}, > {{∅}, {{∅}}, {{∅}, {{∅}}}, {{∅}, {{∅}}, {{∅}, {{∅}}}}}, > ... ... ... } edit: Also see definitions 1,2,3 in http://www.internationalskeptics.com...&postcount=261 . 
__________________
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. 

26th August 2020, 06:55 AM  #268 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259


__________________
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. 

26th August 2020, 07:28 AM  #269 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942


__________________
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 August 2020, 07:40 AM  #270 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942

It demonstrates the computer sciency procedural perspective you have for things.
Your earlier attempts to describe your set, N, were nothing more than processes to enumerate the membership. You frequently express things as if a sequence of steps were required, and you more than once feigned denial with "it happens all at once". That excuse is not credible for a variety of reasons. 
__________________
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 

27th August 2020, 05:36 AM  #271 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

EDIT:
Let's put what is needed in one post, in order to define N as a set. Definition 1: Any given set that is not of the form (x∪{x}), is called a base set. Definition 2: Any given set that is of the form (x∪{x}), is called a successor set. Definition 3: Given a successor set in some set, it is called largest successor set iff given a base set in that set, it has at least one successor set that does not have its successor set, in that set.  The membership function of set N: Given set N, no one of its successor sets has its largest successor set (M(x) is false about the membership of largest successor sets). Given set N, any one of its members is a base set OR a successor set that is not largest successor set (M(x) is true about the membership of any base set OR any successor set that is not largest successor set).  Please support your claim, by details. An example: Code:
N = { ∅, > {{∅}}, > ... < base 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. 

27th August 2020, 06:07 AM  #272 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942

Still not a membership function.
M(x) : true if x is in N, and false if not (plus or minus a constraint or two consistent with the set theory axioms). Stop focusing on the irrelevant (i.e., whether there is a "largest successor"). Focus on membership: Is x in the set N or not? 
__________________
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 

27th August 2020, 06:30 AM  #273 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259


__________________
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. 

27th August 2020, 06:44 AM  #274 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942


__________________
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 

27th August 2020, 06:51 AM  #275 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259


__________________
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. 

27th August 2020, 07:05 AM  #276 
Master Poster
Join Date: Nov 2006
Posts: 2,235

Let's make it easy since doronshadmi is not understanding the simple items.
Which, if any, of the following items are in N? 1) The War of 1812 2) 10% GDP 3) Oranges 4) The ratio between the circumference of a circle and it's diameter 5) Beethoven's Fifth 6) {... 2, 1, 0, 1, 2, ...} 7) { {∅} ,{ { { {∅} } } } } 8) Double shot of espresso, 3 soy creams, 1 brown sugar, 97 degree, no whip Please note, since doronshadmi has used N before, I am confirming that I am not talking about the set of natural numbers (also known/written as N or N). 
__________________
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 August 2020, 07:10 AM  #277 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259


__________________
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. 

27th August 2020, 07:21 AM  #278 
Master Poster
Join Date: Nov 2006
Posts: 2,235

You miss the point.
They all can be part of set N. Specifically, they all can be elements of set N. Edit:  I did not ask about base set or a "pure" set. And again, you start making up your own definitions. All I asked was "Which, if any, of the following items are in N?" 
__________________
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 August 2020, 07:33 AM  #279 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,942


__________________
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 August 2020, 02:44 AM  #280 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,259

N does not have even one largest successor, this is exactly why N can't be but an infinite set that includes base sets OR successor sets that are not largest successors sets.
EDIT: Once again, universal quantification (the term "for all", notated by ∀) is not a property of N. Please read carefully what I wrote about Russell's Paradox and ∀, in the second part of http://www.internationalskeptics.com...&postcount=257 . As for N being a member of itself, it can be one of its base members, where the term ∀ is not a property of this base member (or any one of its members etc.) and so is the case about its successors, no one of them has its largest successor. Without ∀, N is its one of its base members without being failed by Russell's Paradox. 
__________________
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  

