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19th September 2020, 01:01 PM  #521 
ETcorngods survivor
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Posts: 22,920

Are you unable to tell us what you mean? Use your words. Examples are not definitions. Dodges are not definitions.

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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 

19th September 2020, 01:42 PM  #522 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,920

Oh, what the heck. Let's dissect your latest heralded post to see just how much correctness it contains.
This is not a set description within the rules of ZF or ZFC.
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So, let's see. Every part, every single part of your post, Doronshadmi, is riddled with mistakes, omissions, and just plain nonsense. There is nothing there for you to point to and be proud. Please stop linking back to it as if it merited high praise. It is linebyline garbage. And stop pretending. 
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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 

19th September 2020, 03:12 PM  #523 
Penultimate Amazing
Join Date: Mar 2008
Posts: 13,243

V = { v : (v is not nonfinite member of von Neumann ordinals) } = The set of all natural numbers in terms of sets.
In that case the set of all natural numbers in terms of sets, is undefined within the rules of ZF or ZFC. In other words, you are dishonest with yourself. V is not the cardinality of V simply because ∀v ∈ V(v∪{v} ∈ V ∧ v∪{v} < V). In simple words: For all v∪{v} in V, v∪{v} is too small in order to be valued as V. So, exactly as the von Neumann set of ordinals it is too big to be a set, so is the case of all natural numbers in terms of sets, it is too small to be a set. No wonder that λ was invented out of nowhere (as seen in http://www.internationalskeptics.com...&postcount=451) in order to cover that for all v∪{v} in V, v∪{v} is too small in order to be valued as V. Without the ad hoc invention out of nowhere of V=λ as a weak limit cardinal (such that λ is neither a successor cardinal nor zero) ZF(C) does not hold water. 
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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. 

19th September 2020, 04:10 PM  #524 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,920

This is not a valid definition for your set, V. It violates the Axiom of Restricted Comprehension, for example.
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Getting to all the ordinals that von Neumann had in mind, as you insist on doing, is an extremely difficult and long route. It is also working backwards, as you are prone to do. And it also requires accepting as given all the things you are trying to dismiss. Why are you still dodging defining cardinality as you use the term? 
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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 

Yesterday, 06:29 AM  #525 
Penultimate Amazing
Join Date: Mar 2008
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It is valid because of the following reasons:
1) All v in V and all v∪{v} in V are not nonfinite sets, in terms of "von Neumann's treatment of the natural numbers". 2) For all v in V and for all v∪{v} in V, v is a strict cardinality of v, and v∪{v} is strict cardinality of v∪{v}. 3) V does not have strict cardinality since for all v∪{v} in V, v∪{v} < V, which means that V can't be a measurement value of V. 4) Without strict cardinality, V is not a set in terms of ZF(C), and therefore can't be a member of itself, in the first place. 
__________________
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. 

Yesterday, 07:01 AM  #526 
ETcorngods survivor
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Posts: 22,920


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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 

Yesterday, 01:45 PM  #527 
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Originally Posted by jsfisher
Definition 1: A = B iff there is bijection from A to B (where in case of bijection, B can be replaced by A and we get bijection from A to itself). V = { v : (v is not nonfinite member of von Neumann ordinals) } = The set of all natural numbers in terms of sets. v or v∪{v} are not nonfinite sets, where the cardinality of v (notated as v) or the cardinality of v∪{v} (notated as v∪{v}) is defined (by definition 1) by bijection form a given domain to itself. Definition 2: A < B iff (there is injection no surjection from A to B) OR (A=∅ ∧ B~=∅). ∀v ∈ V(v∪{v} ∈ V ∧ v < v∪{v}) by definition 2, which means that the expression A <= B (injection from A to B) is not satisfied from v to v∪{v} in V. Now let's look if A <= B (injection from A to B) can be used in order to establish V. ∀v ∈ V(v∪{v} ∈ V ∧ v∪{v} < V) In simple words: For all v∪{v} in V, v∪{v} is too small in order to be valued as V, which means that V can't be defined as the cardinality of all V members. In other words: A <= B (and definitely V <= V) do not hold water. As for the set of all natural numbers, N is not 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. 

Yesterday, 01:52 PM  #528 
Master Poster
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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; Yesterday at 01:55 PM. Reason: added original post before doronshadmi starts editing it. again. 

Yesterday, 02:29 PM  #529 
ETcorngods survivor
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Great! except your definition doesn't exclude anything that would support your definition for nonfinite set. 'Tis a problem, no?
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Kinda funny, too, you end up with substantially the same definition for cardinality as I, just with more steps. So, what is your definition for nonfinite set? You broke the one you provided before. 
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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 

Yesterday, 03:04 PM  #530 
ETcorngods survivor
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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 

Yesterday, 10:40 PM  #531 
Penultimate Amazing
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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. 

Today, 12:48 AM  #532 
Penultimate Amazing
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I start by using your definition of nonfinite set, here it is:
So not nonfinite set is a finite set by your terms.
Originally Posted by jsfisher
V = { v : (v is not nonfinite member of von Neumann's treatment of the natural numbers) } = The set of all natural numbers in terms of sets. Kinda funny, that you don't understand that your definition of nonfinite set holds, only if N holds. Unlike your relative approach that relies on set A and another set B, I first directly define the cardinality of not nonfinite set by using the same set, as follows: Definition 1: A = B iff there is bijection from A to B (where in case of bijection, B can be replaced by A and we get bijection from A to itself) So first I am focused on what happens inside set V, among its members, and it is done in order to check the validity of V (will be done later). v or v∪{v} are not nonfinite sets, where the cardinality of v (notated as v) or the cardinality of v∪{v} (notated as v∪{v}) is defined (by definition 1) by bijection form a given domain to itself (by direct definition of cardinality). So first v or v∪{v} (which are the not nonfinite members of von Neumann's treatment of the natural numbers) are defined directly. Definition 2: A < B iff (there is injection no surjection from A to B) OR (A=∅ ∧ B~=∅). ∀v ∈ V(v∪{v} ∈ V ∧ v < v∪{v}) by definition 2, which means that the expression A <= B (injection from A to B) is not satisfied from v to v∪{v} in V. Now let's look if A <= B (injection from A to B) can be used in order to establish V. ∀v ∈ V(v∪{v} ∈ V ∧ v∪{v} < V) In simple words: For all v∪{v} in V, v∪{v} is too small in order to be valued as V, which means that V can't be defined as the cardinality of all V members. In other words: A <= B (and definitely V <= V) do not hold water. As for the set of all natural numbers, N is not established. Here it is: Code:
V = { > Bijection according to Definition 1  (order is irrelevant).  0 = ∅,  ↓ Nobijection according to Definition 2 (order is irrelevant).  1 = { ∅ },  ↓ Nobijection according to Definition 2 (order is irrelevant).  2 = { ∅, {∅} },  ↓ Nobijection according to Definition 2 (order is irrelevant).  3 = { ∅, {∅} , {∅, {∅}} },  ↓ Nobijection according to Definition 2 (order is irrelevant).  4 = { ∅, {∅} , {∅, {∅}}, {∅, {∅}, {∅, {∅}}} },  ↓ Nobijection according to Definition 2 (order is irrelevant).  v NoBijection according to Definition 2 (order is irrelevant). ... } Order is not irrelevant since all we is that ∀v ∈ V(v∪{v} ∈ V) Without V, there is no basis to the extension of Cardinality beyond the natural numbers. 
__________________
That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

Today, 03:10 AM  #533 
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Some correction of the previous post:
The sentence at the end of the diagram has to be replaced by: Order is irrelevant since all we care is that ∀v ∈ V(v∪{v} ∈ V) no matter where they are in V. 
__________________
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. 

Today, 04:39 AM  #534 
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Posts: 22,920

Is this your final answer, then? No more changes?
Since your latest definition for "finite set" depends on your definition(s) for cardinality, you'll need to save it until later. The term is undefined until you've adequately defined cardinality.
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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 

Today, 07:00 AM  #535 
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jsfisher, you jumped all over my previous post.
My previous post has to be read in the following order, in order to be understood: 1) First I use your definitions, which define the complement terms "nonfinite" and "finite" (which I write as "not nonfinite") 2) Then I use von Neumann's treatment of the natural numbers, which is right in line with your point, in order to define V not nonfinite members, which are v and v∪{v}. 3) Then I directly define the cardinality for all v in V, by bijection (=) from v to itself. 4) Than I indirectly define the cardinality for all v and v∪{v, by injection nonsurjection (<) from v to v∪{v or from ∅ to ~∅, in V. 5) (3) and (4) are done within V, at this stage. 6) Only than I use (4) in order to show that V is too big in order to be valued as the cardinality of set V, simply because ∀v ∈ V(v∪{v} ∈ V ∧ v < v∪{v} < V). Wrong, jsfisher, in case that you have missed it, I start by using your definition of "finite set". Wrong again jsfisher, at this stage I still use your definition of the term "nonfinite member". Yes I already aware of your religious approach about definitions. It is a "direct approach" since the bijection is done from A to itself, where v is not nonfinite member (still by your definition of nonfinite) of von Neumann's treatment of the natural numbers, which is right in line with your point, isn't it jsfisher? Wrong, definition 1 directly defines the cardinality of a not nonfinite member v (in set V) by bijection from v to itself, where V is not considered at all at this stage. Again, at this stage we argue only about what is inside set V, such that v is not nonfinite member (still by your definition of nonfinite) of von Neumann's treatment of the natural numbers, which is right in line with your point. Wrong again, bijection (=) is from v to itself in V, where injection nonsurjection (<) is from v to v ∪ {v} or form ∅ to ~∅ in V (anything about V is not considered yet, but only about what within it.) ================================================== ======= Now let's look if A <= B (injection from A to B) can be used in order to establish V. ∀v ∈ V(v∪{v} ∈ V ∧ v < v∪{v} < V) In simple words: For all v∪{v} in V, v∪{v} is too small in order to be valued as V, which means that V can't be defined as the cardinality of all V members. In other words: A <= B (and definitely V <= V) do not hold water. As for the set of all natural numbers, N is not established. Here it is: Code:
V = { > Bijection according to Definition 1  (order is irrelevant).  0 = ∅,  ↓ Nobijection according to Definition 2 (order is irrelevant).  1 = { ∅ },  ↓ Nobijection according to Definition 2 (order is irrelevant).  2 = { ∅, {∅} },  ↓ Nobijection according to Definition 2 (order is irrelevant).  3 = { ∅, {∅} , {∅, {∅}} },  ↓ Nobijection according to Definition 2 (order is irrelevant).  4 = { ∅, {∅} , {∅, {∅}}, {∅, {∅}, {∅, {∅}}} },  ↓ Nobijection according to Definition 2 (order is irrelevant).  v NoBijection according to Definition 2 (order is irrelevant). ... } Order is not irrelevant since all we is that ∀v ∈ V(v∪{v} ∈ V) Without V, there is no basis to the extension of Cardinality beyond the natural numbers. ================================================== ======= The trick of V as a weak limit cardinal, is no more no less than an ad hoc artificial trick out of nowhere, which its aim it to save ZF(C) from its big crash, as already given in http://www.internationalskeptics.com...&postcount=523. 
__________________
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. 

Today, 08:24 AM  #536 
ETcorngods survivor
Moderator Join Date: Dec 2005
Posts: 22,920

That definition requires an already existing definition for cardinality. You cannot use mine because you reject it. You can't use yours because you haven't introduced it/them yet. So you cannot use my definition for finite/nonfinite set.
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Definition 1: A = B iff there is bijection from A to B
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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 

Today, 04:42 PM  #537 
Master Poster
Join Date: Nov 2006
Posts: 2,230

There's the right way, the wrong way, and the let'smakethingsmorecomplicatedbyaddingjunkandmakingupthings way.
Guess which way you use doronshadmi? You've already been using finite/nonfinite. You only started using this nonsense term in the last 4 days. Specifically post 503. In fact, jsfisher was trying (that's a recurring theme) to correct you in using the right terms before you "write 'not nonfinite". Finite and nonfinite. They are complimentary. Not finite set and nonfinite set, but just finite and nonfinite. Let's stick with the correct terms. Stop making up words. 
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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. 

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