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Old 22nd August 2020, 07:30 AM   #241
doronshadmi
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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.
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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; 22nd August 2020 at 07:57 AM.
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Old 22nd August 2020, 11:55 AM   #242
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Originally Posted by doronshadmi View Post
The two properties are:

1) One property establishes sets, which are not of the form (x∪{x}) (where ∅ is an example of such set).

2) The other property establishes sets, which are of the form (x∪{x}).

No, and no. The Axiom of Infinity establishes that there exists a set satisfying two properties. The two properties are:
  1. The set contains the empty set as a member.
  2. For all members, x, of the set, x U {x} is also a member.

These two properties do not in any way establish sets.
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Old 22nd August 2020, 12:05 PM   #243
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Originally Posted by doronshadmi View Post
It is a membership function that does not need a gate (yes/no) keeper.
Then it is not a membership function.

Your repeated attempts to redefine things demonstrate no failures in Mathematics, only your lack of understanding of Mathematics. Mathematics is not wrong just because you imagine it to be different from what it is.
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Old 22nd August 2020, 12:06 PM   #244
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Originally Posted by jsfisher View Post
The Axiom of Infinity establishes that there exists a set satisfying two properties.
Originally Posted by jsfisher View Post
These two properties do not in any way establish sets.
Well, no consistency in your previous post.
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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; 22nd August 2020 at 12:17 PM.
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Old 22nd August 2020, 12:15 PM   #245
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Originally Posted by jsfisher View Post
Then it is not a membership function.

Your repeated attempts to redefine things demonstrate no failures in Mathematics, only your lack of understanding of Mathematics. Mathematics is not wrong just because you imagine it to be different from what it is.
jsfisher, you are stacked with your gate keeper and don't aware of the amazing N paradise that you established.

This paradise, if used carefully, may help us to understand how complexity (successors) emerges from simplicity (bases).
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That is also over the matrix, is aware of the matrix.

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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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Old 22nd August 2020, 12:36 PM   #246
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First Axiom of Doronity

There exists a set whose members are unknown.
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Old 22nd August 2020, 02:06 PM   #247
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Originally Posted by doronshadmi View Post
Well, no consistency in your previous post.
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.
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Old 22nd August 2020, 02:08 PM   #248
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Originally Posted by doronshadmi View Post
jsfisher, you are stacked with your gate keeper and don't aware of the amazing N paradise that you established.

This paradise, if used carefully, may help us to understand how complexity (successors) emerges from simplicity (bases).

Paradise? The person at the adjacent table wants what you're having.


If you want to use this set, N, of yours (and it looks like you have settled on N for its name), then you need to define it. Please do.
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Old 22nd August 2020, 11:45 PM   #249
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Originally Posted by Hevneren View Post
There exists a set whose members are unknown.
N members are well-defined, as given in http://www.internationalskeptics.com...&postcount=241 and its links.
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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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Old 22nd August 2020, 11:50 PM   #250
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Originally Posted by jsfisher View Post
Please do.
Done at http://www.internationalskeptics.com...&postcount=241 and its links.
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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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Old 23rd August 2020, 12:14 AM   #251
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jsfisher and Hevneren,

N members are well-defined 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 well-defined set that can't be N member according this tautology.
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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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Old 23rd August 2020, 10:01 AM   #252
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Originally Posted by doronshadmi View Post
jsfisher and Hevneren,

N members are well-defined 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.
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.
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Last edited by jsfisher; 23rd August 2020 at 10:07 AM.
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Old 24th August 2020, 12:57 AM   #253
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Originally Posted by jsfisher View Post
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.
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.

Originally Posted by jsfisher View Post
Paradise? The person at the adjacent table wants what you're having.
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.
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That is also over the matrix, is aware of the matrix.

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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 August 2020 at 01:24 AM.
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Old 24th August 2020, 03:59 AM   #254
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Originally Posted by doronshadmi View Post
No, you don't see that N can't be a set of everything
Of course it can't, but that's how you described it. You need to fix the description.

Quote:
...the term "all" is not satisfied...
Set theory says otherwise. You don't get to redefine things to your liking. You do, however, get to define this set N you continually reference.



Quote:
jsfisher, you are the person at the adjacent table that is unaware of the paradise that he established on his table.
You completely missed the movie reference, didn't you? Next time you hear a loud swooshing sound, look up.
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Old 24th August 2020, 06:52 AM   #255
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Originally Posted by jsfisher View Post
Of course it can't, but that's how you described it.
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
{∅},                  ---> {{∅}, {{∅}} }, ---> ...
{∅, {∅}},             ---> {{∅}, {{∅}}, {{∅}, {{∅}}}}, ---> ...
{∅, {∅}, {∅, {∅}}},  ---> {{∅}, {{∅}}, {{∅}, {{∅}}}, {{∅}, {{∅}}, {{∅}, {{∅}}}}}, ---> ...
...                         ...
}
In other words, set N has at least one such proper subset that does not have its largest successor, and by definition 1 universal quantification (the term "For All") can't be used on N.


Originally Posted by jsfisher View Post
Set theory says otherwise.
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.

Originally Posted by jsfisher View Post
You don't get to redefine things to your liking.
You can force the term "For All" as much as you like on an infinite set, a fundamental error it will stay.


Originally Posted by jsfisher View Post
You completely missed the movie reference, didn't you?
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.
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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 August 2020 at 07:16 AM.
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Old 24th August 2020, 09:39 AM   #256
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Originally Posted by doronshadmi View Post
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.
No, that definition is irrelevant to my point. You described the members of set N as either successors (of some non-specific 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.
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Old 24th August 2020, 10:39 PM   #257
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Originally Posted by jsfisher View Post
No, that definition is irrelevant to my point. You described the members of set N as either successors (of some non-specific something) or not successors. You even admitted it was a tautology.
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.

Originally Posted by jsfisher View Post
Your description admits all sets as members of your set 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 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.
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That is also over the matrix, is aware of the matrix.

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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 August 2020 at 12:38 AM.
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Old 25th August 2020, 04:12 AM   #258
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Originally Posted by doronshadmi View Post
My description: Any given N member is of the form (x∪{x}) OR not of the form (x∪{x}), which is a tautology.
So which is it: You are telling us that everything is a member of your set N, or you are not telling us what things are not members? Your choice, but neither describe a specific set.

How's that membership function coming along?
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Old 25th August 2020, 06:55 AM   #259
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Originally Posted by jsfisher View Post
So which is it: You are telling us that everything is a member of your set N, or you are not telling us what things are not members? Your choice, but neither describe a specific set.

How's that membership function coming along?
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
{∅},                  ---> {{∅}, {{∅}} }, ---> ...
{∅, {∅}},             ---> {{∅}, {{∅}}, {{∅}, {{∅}}}}, ---> ...
{∅, {∅}, {∅, {∅}}},  ---> {{∅}, {{∅}}, {{∅}, {{∅}}}, {{∅}, {{∅}}, {{∅}, {{∅}}}}}, ---> ...
...                         ...
}
Given any base member (where a base member is of the form ~(x∪{x}) ), no largest successor (where a successor is of the form (x∪{x}) ) is emerged from it.

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.
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That is also over the matrix, is aware of the matrix.

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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 August 2020 at 07:43 AM.
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Old 25th August 2020, 08:30 AM   #260
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Originally Posted by doronshadmi View Post
By using definition 1....

You still have not defined your set N. A membership function would be an important step towards that goal.
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Old 26th August 2020, 03:46 AM   #261
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Originally Posted by jsfisher View Post
You still have not defined your set N. A membership function would be an important step towards that goal.
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).
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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; 26th August 2020 at 04:31 AM.
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Old 26th August 2020, 04:08 AM   #262
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Originally Posted by doronshadmi View Post
The membership function of set N:

Given set N, no one of its successor members has its largest successor member.
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).
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Old 26th August 2020, 04:34 AM   #263
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Originally Posted by jsfisher View Post
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).
I apologize, you replied during my editing of http://www.internationalskeptics.com...&postcount=261 .
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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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Old 26th August 2020, 06:11 AM   #264
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Originally Posted by doronshadmi View Post
I apologize, you replied during my editing of http://www.internationalskeptics.com...&postcount=261 .
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.
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Old 26th August 2020, 06:21 AM   #265
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Originally Posted by jsfisher View Post
Still not a membership function. I note, too, your use of the word "returns"; it emphasizes the depth of your misunderstanding.
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 .
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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; 26th August 2020 at 06:24 AM.
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Old 26th August 2020, 06:25 AM   #266
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Originally Posted by doronshadmi View Post
No problem, without "returns":

The membership function of set N:
....
Still not a membership function.
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Old 26th August 2020, 06:39 AM   #267
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Originally Posted by jsfisher View Post
Still not a membership function.
Well, here is an example of two base members and their successor members in set N:

Code:
N = {
∅,                    ---> {{∅}}, ---> ...   <-- base members
{∅},                  ---> {{∅}, {{∅}} }, ---> ...
{∅, {∅}},             ---> {{∅}, {{∅}}, {{∅}, {{∅}}}}, ---> ...
{∅, {∅}, {∅, {∅}}},  ---> {{∅}, {{∅}}, {{∅}, {{∅}}}, {{∅}, {{∅}}, {{∅}, {{∅}}}}}, ---> ...
...                         ...
}
As can be seen, set N members are of the form ~(x∪{x}) (base members) OR (x∪{x}) (successor members) (M(x) is true), but no largest successor member is a member of set N (M(x) is false).

edit:

Also see definitions 1,2,3 in http://www.internationalskeptics.com...&postcount=261 .
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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; 26th August 2020 at 06:44 AM.
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Old 26th August 2020, 06:55 AM   #268
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Originally Posted by jsfisher View Post
I note, too, your use of the word "returns"; it emphasizes the depth of your misunderstanding.
B.T.W what exactly is the problem of using the word "returns"?

Function M(x) returns the truth value false if x is not a member of set N.

Function M(x) returns the truth value true if x is a member of set N.
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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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Old 26th August 2020, 07:28 AM   #269
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Originally Posted by doronshadmi View Post
Well, here is an example of two base members and their successor members in set N:

Code:
N = {
∅,                    ---> {{∅}}, ---> ...   <-- base members
{∅},                  ---> {{∅}, {{∅}} }, ---> ...
{∅, {∅}},             ---> {{∅}, {{∅}}, {{∅}, {{∅}}}}, ---> ...
{∅, {∅}, {∅, {∅}}},  ---> {{∅}, {{∅}}, {{∅}, {{∅}}}, {{∅}, {{∅}}, {{∅}, {{∅}}}}}, ---> ...
...                         ...
}
How do you know that is actually a set?

You need to decide what it is you mean by this set N of yours, be specific, then provide a definition for it as a set. A membership function would be a convenient way to do that.
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Old 26th August 2020, 07:40 AM   #270
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Originally Posted by doronshadmi View Post
B.T.W what exactly is the problem of using the word "returns"?
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.
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Old 27th August 2020, 05:36 AM   #271
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Originally Posted by jsfisher View Post
How do you know that is actually a set?

You need to decide what it is you mean by this set N of yours, be specific, then provide a definition for it as a set. A membership function would be a convenient way to do that.
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).

-------------------------------

Originally Posted by jsfisher View Post
Still not a membership function.
Please support your claim, by details.



An example:

Code:
N = {
∅,                    ---> {{∅}}, ---> ...   <-- base sets
{∅},                  ---> {{∅}, {{∅}} }, ---> ...
{∅, {∅}},             ---> {{∅}, {{∅}}, {{∅}, {{∅}}}}, ---> ...
{∅, {∅}, {∅, {∅}}},  ---> {{∅}, {{∅}}, {{∅}, {{∅}}}, {{∅}, {{∅}}, {{∅}, {{∅}}}}}, ---> ...
...                         ...
}
As can be seen, set N members are of the form ~(x∪{x}) (base sets) OR (x∪{x}) (successor sets) (M(x) is true), but no largest successor set is a member of set N (M(x) is false).
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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 August 2020 at 07:06 AM.
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Old 27th August 2020, 06:07 AM   #272
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Originally Posted by doronshadmi View Post
...
The membership function of set N:
...
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?
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Old 27th August 2020, 06:30 AM   #273
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Originally Posted by jsfisher View Post
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?
It is relevant.

If x is largest successor, then M(x) : false.

If x is not largest successor, then M(x) : true.
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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 August 2020 at 06:35 AM.
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Old 27th August 2020, 06:44 AM   #274
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Originally Posted by doronshadmi View Post
It is relevant.

If x is largest successor, then M(x) : false.

If x is not largest successor, then M(x) : true.
Whether x is a largest successor isn't the same question as whether x is a member.
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Old 27th August 2020, 06:51 AM   #275
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Originally Posted by jsfisher View Post
Whether x is a largest successor isn't the same question as whether x is a member.
x is largest successor is the same as x is not a member.

x is ~largest successor is the same as x is a member.
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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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Old 27th August 2020, 07:05 AM   #276
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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).
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Old 27th August 2020, 07:10 AM   #277
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Originally Posted by Little 10 Toes View Post
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).

Only (7) as a base set.

Any N member is a "pure" set ( represented only by "{" or "}" (where ∅ is {} in terms of "pure" sets) ).
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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 August 2020 at 07:16 AM.
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Old 27th August 2020, 07:21 AM   #278
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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?"

Last edited by Little 10 Toes; 27th August 2020 at 08:14 AM.
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Old 27th August 2020, 07:33 AM   #279
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Originally Posted by doronshadmi View Post
x is largest successor is the same as x is not a member.

x is ~largest successor is the same as x is a member.

You have been outspoken that there is no largest successor. That means that any set I choose is going to be "~largest successor". That means that any set I choose (including N) is going to be a member of N.
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Old 29th August 2020, 02:44 AM   #280
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Originally Posted by jsfisher View Post
You have been outspoken that there is no largest successor. That means that any set I choose is going to be "~largest successor". That means that any set I choose (including N) is going to be a member of N.
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.
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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 August 2020 at 03:40 AM.
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