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Old Today, 05:30 AM   #561
doronshadmi
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Originally Posted by jsfisher View Post
I skipped any treatment of the natural numbers because I don't need any. You are the one insisting it be there, I have shown it isn't required.



Yes, that is what I wrote and what you already quoted. Repeating it was unnecessary.



No, N is defined by the previous expression.



Restating it again does not add value. And you made an error in the process. Be that as it may, though, I am confident you have no idea how the expression actually achieves the goal. You recognize the individual "words" by you don't comprehend their collective meaning.



Yep, proof you don't comprehend their collective meaning.





Oh? Are you unfamiliar with the phrase, vacuously true? F : ∅ → X is an injective map from the empty set to any set X. A function F is an injective map from the not necessarily distinct sets A to B iff:
∀a∈A (∃b∈B (F(a) = b ∧ ∀c∈A (F(a) = F(c) ⇒ a = c)))
Nothing there forbids A or B from being empty.
You have missed my correction in http://www.internationalskeptics.com...&postcount=559 and replied to an irrelevant post.
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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 Today, 05:56 AM   #562
jsfisher
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Originally Posted by doronshadmi View Post
You have missed my correction in http://www.internationalskeptics.com...&postcount=559 and replied to an irrelevant post.

If you need to make extensive corrections to a post (i.e., other than slight typos), then make a new post. Also, be kind enough to highlight the important corrections you think you are making.
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Old Today, 06:05 AM   #563
doronshadmi
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Originally Posted by jsfisher View Post
If you need to make extensive corrections to a post (i.e., other than slight typos), then make a new post. Also, be kind enough to highlight the important corrections you think you are making.
http://www.internationalskeptics.com...&postcount=559 is a new post, where you replied to the older one.
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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; Today at 06:11 AM.
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Old Today, 06:15 AM   #564
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Originally Posted by doronshadmi View Post
It is a new post, where you replied to the older one.
No, it was not a new post. It was an substantial edit to an existing post.

And I replied to the version of the post in place at the time I hit the Quote button. It is rude for you to dismiss my post in its entirety, too. If it comments on mistakes of yours that have been corrected, point out in response to my post how your mistakes were corrected. If it comments on things you thought were correct in the first place, comment on that.

I await the mitigation to your rudeness.
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Old Today, 06:30 AM   #565
doronshadmi
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Originally Posted by jsfisher View Post
No, it was not a new post. It was an substantial edit to an existing post.

And I replied to the version of the post in place at the time I hit the Quote button. It is rude for you to dismiss my post in its entirety, too. If it comments on mistakes of yours that have been corrected, point out in response to my post how your mistakes were corrected. If it comments on things you thought were correct in the first place, comment on that.

I await the mitigation to your rudeness.
jsfisher your post was created almost two hours after my new post was created.

So next time please refresh your screen before you reply.

Please reply to http://www.internationalskeptics.com...&postcount=559.
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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; Today at 06:32 AM.
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Old Today, 06:44 AM   #566
doronshadmi
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Originally Posted by jsfisher
I skipped any treatment of the natural numbers because I don't need any.
You can't skip on these sets, as shown in http://www.internationalskeptics.com...&postcount=559.
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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; Today at 06:45 AM.
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Old Today, 07:33 AM   #567
doronshadmi
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The relevant details are as follows:

jsfisher, in order to establish the minimal set satisfying the requirements of the Axiom of Infinity, one first has to show that all the natural numbers (which are defined by von Neumann's treatment of the natural numbers in terms of sets) are actually establish a set that satisfying the requirements of the Axiom of Infinity.

So at the first stage the following definitions are restricted only to all the members of this minimal set, such that the initial member is the empty set (v=∅) and the rest of the members are defined as v⋃{v}, which are all finite sets:

Definition 1: |v| = |v| iff there is bijection from v to v.

Definition 2: |v| < |v⋃{v}| iff (there is an injective non-surjective function from v to v⋃{v}) OR (injective function from v to v⋃{v} that is based on empty function) (in case that v=)

Definitions 1 and 2 look trivial at first glance, but these are the functions among the finite sets, which define all the natural numbers by von Neumann's treatment.

Since v ∈ V(v∪{v} ∈ V ∧ |v∪{v}| can't be but < |V|) |V| is not established, simply because it can't be defined as the cardinality of all V members, which are all the finite sets by von Neumann's treatment of all the natural numbers.
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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; Today at 07:43 AM.
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Old Today, 08:11 AM   #568
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Just a reminder:

Originally Posted by jsfisher View Post
No, it was not a new post. It was an substantial edit to an existing post.

And I replied to the version of the post in place at the time I hit the Quote button. It is rude for you to dismiss my post in its entirety, too. If it comments on mistakes of yours that have been corrected, point out in response to my post how your mistakes were corrected. If it comments on things you thought were correct in the first place, comment on that.

I await the mitigation to your rudeness.
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