Deeper than primes

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jsfisher said:
While Doron is off googling to find things he can misinterpret into a post, permit me to say this has been a productive week. Doron, as he shared his wisdom, provided the following additional insights of doronetics:

  • An interval, [X,Y) for example, is a real number.
  • A collection with cardinality > 1 is equivalent to a collection of all distinct elements is equivalent to an interval.
  • If you have A < C, then you cannot have A < B < C.
  • For any real number Y, the immediate predecessor of Y is Y.

This brings my list up to an even 20. Did I miss any from this week?
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This list clearly shows that jsfisher cannot understand any of my arguments.

Here are the relevant examples for this case:
jsfisher said:
Why are you changing the subject to "immediate predecessors"? The proof was whether {X : X<Y} had a largest element.
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Again, your proof has nothing to do with the construction [X,Y] because you force on it Transitivity (a,b,c construction (A < B < C)).
jsfisher said:
If you have A < C, then you cannot have A < B < C.
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[X,Y] is exactly a,b construction (A< B), but your notinless game with symbols can't get it.
 
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[X,Y] is exactly a,b construction (A< B), but your notionless game with symbols can't get it.

In a,b construction like [X,Y] it is clear that X is not the immediate predecessor of Y.

Actually any explicit X is not the immediate predecessor of Y, but this is a technical problem, because we cannot write down the all members of [X,Y].

All we can do is to write down only two particular cases of the form a,b , where a is not the immediate predecessor of b.
 
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Ok, let's go back to the original proof. Keep in mind it was a proof that the set of reals, {X : X<Y} has no largest element. Here it is, again, up to the point Doron suddenly objects:

jsfisher said:
Assume the set {X : X<Y} does have a largest element, Z.

For Z to be an element of the set, Z < Y.
Let h be any element of the interval (Z,Y).
By the construction of h, Z < h < Y.
Click to expand...

At this point, Doron goes off on some rant about circular reasoning, forced transitivity, and violations of deductive reasoning. Now, since there were no objections to any of the preceding steps, we can assume it is the step I've hi-lighted that is the problem.

Doron, a few simple questions:

If h is an element of the interval (Z,Y), can we not conclude h < Y?
If h is an element of the interval (Z,Y), can we not conclude Z < h?
 
doronshadmi said:
You have missed the determination that OMPT.pdf can be understood only by reading all of it, in order to understand any part of it.
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So your notions against 'serial' and 'step by step only thinking' can only be 'understood' by your 'step by step' and 'serial thinking' on 'understanding'. As always your notions simply fail when applied to themselves, so mush so that you require them not to be applied to themselves and that is your determination which no one here is missing
 
jsfisher said:
While Doron is off googling to find things he can misinterpret into a post, permit me to say this has been a productive week. Doron, as he shared his wisdom, provided the following additional insights of doronetics:

  • An interval, [X,Y) for example, is a real number.
  • A collection with cardinality > 1 is equivalent to a collection of all distinct elements is equivalent to an interval.
  • If you have A < C, then you cannot have A < B < C.
  • For any real number Y, the immediate predecessor of Y is Y.

This brings my list up to an even 20. Did I miss any from this week?
Click to expand...


Let’s not forget…

  • The point Y is no longer a point when Doron chooses to call it a ‘side’.
  • To understand Doron’s notions against ‘serial’ or ‘step by step only thinking’ you can only follow Doron’s self asserted ‘serial’ or ‘step by step only thinking’ about understanding his notions.
 
jsfisher said:
Doron, a few simple questions:

If h is an element of the interval (Z,Y), can we not conclude h < Y?
If h is an element of the interval (Z,Y), can we not conclude Z < h?
Click to expand...

This question is irrelevant to [X,Y] case because [X,Y] case is based of a,b construction.

By a,b construction X of [X,Y] case is not the immediate predecessor of Y.

Here is some analogy that may help you to understand my claim.

We know that no infinitely many red photons can cause the photoelectric effect, simply because no red photon has the required energy.

Now think about h < Y or Z < Y as two finite cases (red photons), where no finite case (a red photon) can be used to conclude something about [X,Y] non-finite case.

This inability to conclude something about the non-finite, by using infinitely many finite cases, is a fundamental problem of the mathematical science if the term all is used on a non-finite collection, because no finite case alone has the quality of a non-finite collection of all distinct members.

Furthermore, the notion of transfinite cardinal is based on the idea that its value is greater than any finite cardinal, so if Standard Math agrees with this notion, it must agree with the notion that no finite a,c case (for example h<Y or Z<Y) can conclude (has the quality to conclude) something about the non-finite a,c case (for example [X,Y] , which is the non-finite interval of the all members between distinct X and distinct Y).

Moreover, Standard Math also accepts the notion that since all irrational R members are non-countable, then even if there is some hypothetic way to symbolize non-finite irrational R members, still this set of symbols will have a cardinality of aleph0, and most of the irrationa R members will not be symbolized.

In other words, Y of the non-finite interval [X,Y] (of the all members between distinct X and distinct Y) must have an immediate predecessor by Standard Math, even if it cannot be proved or disproved by it.

Again:

We are in the same state of Godel's incompleteness theorems, where things must be true but cannot be proved or disproved within the deductive framework that deals with the non-finite.
 
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doronshadmi said:
This question is irrelevant to [X,Y] case because [X,Y] case is based of a,b construction.
Click to expand...

Ok, but I didn't ask about the "[X,Y] case".

By a,b construction X of [X,Y] case is not the immediate predecessor of Y.
Click to expand...

Ok, but we were not talking about immediate predecessors.

Here is some analogy that may help you to understand my claim....
Click to expand...

We were not talking about your claim either (plus your track record with analogies isn't so sterling).

Are you totally unable to follow a discussion, or are you just dead-set on high-jacking any discussion that comes along?

Please answer the two questions from my post you quoted, but then ignored.
 
jsfisher said:
Ok, but I didn't ask about the "[X,Y] case".
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Since we are talking ONLY about the intermmediate predecessor of Y of the non-finite [X,Y] interval (a,b construction) of all members between X and Y, then any question that is not related to [X,Y] is irrelevant.

Are you totally unable to follow a discussion?


Please ask relevent questions.
 
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The Man said:
As always your notions simply fail when applied to themselves, so mush so that you require them not to be applied to themselves ...
Click to expand...

No, your notions fail to get OM, and as a result you can't conclude any meaningful thing about it.
 
doronshadmi said:
Since we are talking ONLY about the intermmediate predecessor of Y of the non-finite [X,Y] interval (a,b construction) of all members between X and Y, then any question that is not related to [X,Y] is irrelevant.

Are you totally unable to follow a discussion?


Please ask relevent questions.
Click to expand...

Talking ONLY about immediate predecessors? Nonsense.

The most recent topic of discussion was my proof that the set {X : X < Y} has no greatest element. You objected to the proof with all sorts of fabulous claims.

If you'd now like to accept the proof as written, that would be great, and we can return to your immediate predecessor discussion. However, I doubt you would concede the point. So, let's return to my proof, up to but not including the point of your objection:

jsfisher said:
Assume the set {X : X<Y} does have a largest element, Z.

For Z to be an element of the set, Z < Y.
Let h be any element of the interval (Z,Y).
Click to expand...

Are we fine up to here, or do we need to step back further? If things are good up until this point, please answer the following two questions:

  1. If h is an element of the interval (Z,Y), can we not conclude h < Y?
  2. If h is an element of the interval (Z,Y), can we not conclude Z < h?
 
doronshadmi said:
No, your notions fail to get OM, and as a result you can't conclude any meaningful thing about it.
Click to expand...


What you mean like here…


doronshadmi said:
This question is irrelevant to [X,Y] case because [X,Y] case is based of a,b construction.

By a,b construction X of [X,Y] case is not the immediate predecessor of Y.

Here is some analogy that may help you to understand my claim.

We know that no infinitely many red photons can cause the photoelectric effect, simply because no red photon has the required energy.

Now think about h < Y or Z < Y as two finite cases (red photons), where no finite case (a red photon) can be used to conclude something about [X,Y] non-finite case.

This inability to conclude something about the non-finite, by using infinitely many finite cases, is a fundamental problem of the mathematical science if the term all is used on a non-finite collection, because no finite case alone has the quality of a non-finite collection of all distinct members.

Furthermore, the notion of transfinite cardinal is based on the idea that its value is greater than any finite cardinal, so if Standard Math agrees with this notion, it must agree with the notion that no finite a,c case (for example h<Y or Z<Y) can conclude (has the quality to conclude) something about the non-finite a,c case (for example [X,Y] , which is the non-finite interval of the all members between distinct X and distinct Y).

Moreover, Standard Math also accepts the notion that since all irrational R members are non-countable, then even if there is some hypothetic way to symbolize non-finite irrational R members, still this set of symbols will have a cardinality of aleph0, and most of the irrationa R members will not be symbolized.

In other words, Y of the non-finite interval [X,Y] (of the all members between distinct X and distinct Y) must have an immediate predecessor by Standard Math, even if it cannot be proved or disproved by it.

Again:

We are in the same state of Godel's incompleteness theorems, where things must be true but cannot be proved or disproved within the deductive framework that deals with the non-finite.
Click to expand...

Where you claim “This inability to conclude something about the non-finite, by using infinitely many finite cases..” then proceed to assert your ‘conclusion’ about ‘the non-finite by using infinitely many finite cases’. Concluding that you ‘can not conclude’ is still a conclusion Doron. Although, typical of your notions, it is a contradictory conclusion. Looks like “can’t conclude any meaningful thing about it” is the Doron catch phrase of the day. Oh and in case you missed it, we can conclude something about the infinite “by using infinitely many finite cases” namely that the number of finite cases used is, well, infinite.
 
Interesting aside:

The work function for cesium is 1.95 eV. That divided Planck's constant is 471 THz. This can also be expressed as 636 nm, not that that matters, of course.

Does anyone else find this interesting?
 
The Man said:
What you mean like here…




Where you claim “This inability to conclude something about the non-finite, by using infinitely many finite cases..” then proceed to assert your ‘conclusion’ about ‘the non-finite by using infinitely many finite cases’. Concluding that you ‘can not conclude’ is still a conclusion Doron. Although, typical of your notions, it is a contradictory conclusion. Looks like “can’t conclude any meaningful thing about it” is the Doron catch phrase of the day. Oh and in case you missed it, we can conclude something about the infinite “by using infinitely many finite cases” namely that the number of finite cases used is, well, infinite.
Click to expand...

No.

Actual infinity existence is beyond the collection's existence.

Since you force actual infinity on the level of the collection's existence, you naturally get a contradiction.

But this is your invalid framework, not mine.
 
jsfisher said:
Talking ONLY about immediate predecessors? Nonsense.

The most recent topic of discussion was my proof that the set {X : X < Y} has no greatest element. You objected to the proof with all sorts of fabulous claims.

If you'd now like to accept the proof as written, that would be great, and we can return to your immediate predecessor discussion. However, I doubt you would concede the point. So, let's return to my proof, up to but not including the point of your objection:



Are we fine up to here, or do we need to step back further? If things are good up until this point, please answer the following two questions:

  1. If h is an element of the interval (Z,Y), can we not conclude h < Y?
  2. If h is an element of the interval (Z,Y), can we not conclude Z < h?
Click to expand...

You do not get it jsfisher, so let me help you.

Your failure is right at the first assumption, where you assume that a finite case of [X,Y] can be used in order to conclude something about the non-finite case of [X,Y].

Your inability to distinguish between the finite and the non-finite case of [X,Y] is the reason of why you don't get my red photon analogy.

Furthermore, you do not understand the difference between the finite collection, the non-finite collection and actual infinity, which its magnitude of existence is greater than any non-finite collection, exactly as the magnitude of existence of a non-finite collection is greater than the magnitude of existence of any finite collection.

Jsfisher, your current community of mathematicians have no clue with what they deal with.
 
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doronshadmi said:
You do not get it jsfisher, so let me help you.

Your failure is right at the first assumption, where you assume that a finite case of [X,Y] can be used in order to conclude something about the non-finite case of [X,Y].
Click to expand...

The fact that none of what you wrote about appears in what I have written suggests the failure is solidly yours. Maybe you can find an adult education course to help you improve those reading comprehension skills.
 
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