Deeper than primes - Continuation

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jsfisher said:
No, by doing it wrong you get something that isn't a mapping but call it one anyway.
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Edit: By doing it differently than the verbal_symbolic-only way, one enables to get more interesting properties of mathematical objects, and in this case, an interesting property of an infinite set like N (by using Hilert's Hotel argument it is shown that there can be more rooms than visitors even if there is 1-to-1 and onto between the names of the rooms and the names of the visitors. This interesting mathematical fact enables to understand that the whole idea of transfinite cardinality as actual infinity, is not well-defined, which opens the door for further research about actual infinity, which is not at the level of collections (collections are no more than forms of potential infinity)).

jsfisher said:
You alleged different skills don't change definitions, they just assist you in your dilutions. Carry on, though. Maybe after another decade of cranking without result you'll see just how much of your life was wasted on nonsense. I suspect not, though.
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Well jsfisher, all you are doing is to demonstrate your inability to reply in details to http://www.internationalskeptics.com/forums/showpost.php?p=9709255&postcount=2839.

No more, no less.

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

EDIT:

As for functions with no output, let visitor(x) be a function which returns the name of the visitor in a given room of Hilbert's hotel, where x is the number of some room.

If there is no visitor in room 2, then visitor(2) does return any output, which is equivalent to 2 → expression, such that 2 is equivalent to x and → is equivalent to visitor(x).

For example:

1 → 1
2 →
3 → 2
4 → 3
5 → 4
...
 
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Doron, stop using Hilbert 's hotel as a corroboration for your meandering meaning.

I posted a link with a video from an educational programme for 13 year old kids that simply shows you are even clueless about this.

You do a lot of names dropping, names calling and posturing, but there is bupkus academic, rigorous or even correct about your methods.

You are claiming something but fail to specify what.

Every single treatise you post reads like a badly scanned random paragraph from someone else's work.

I am pretty sure nobody in this thread knows :

- What *is* Doron Shadmi's claim?
- How does he prove that it is correct?

The sanatoria are full of people that claim that the rest of the world doesn't get *it*.

Show that you are not someone who should have joined them there and answer the questions.


- What *is* Doron Shadmi's claim?
- How does he prove that it is correct?
 
Well, he has claimed that he doesn't need to define anything. He has used the power of Direct PerceptionTM as proof, wherein he simply believes something with all his might and *poof* it becomes true.

His most current claim is that |N| > |N|, and he's expanded his proof methods to include disregarding any established meaning for mapping with a touch of no understanding of the meaning of "larger than" for infinite sets and coupled it all with his true believe to produce absolute proof.

Can't you follow his dissertation?
 
jsfisher said:
Well, he has claimed that he doesn't need to define anything. He has used the power of Direct PerceptionTM as proof, wherein he simply believes something with all his might and *poof* it becomes true.

His most current claim is that |N| > |N|, and he's expanded his proof methods to include disregarding any established meaning for mapping with a touch of no understanding of the meaning of "larger than" for infinite sets and coupled it all with his true believe to produce absolute proof.

Can't you follow his dissertation?
Click to expand...
jsfisher, please provide some detailed reply to the content of http://www.internationalskeptics.com/forums/showpost.php?p=9709765&postcount=2841 (including to the content of the link).
 
jsfisher said:
Well, he has claimed that he doesn't need to define anything. He has used the power of Direct PerceptionTM as proof, wherein he simply believes something with all his might and *poof* it becomes true.

His most current claim is that |N| > |N|, and he's expanded his proof methods to include disregarding any established meaning for mapping with a touch of no understanding of the meaning of "larger than" for infinite sets and coupled it all with his true believe to produce absolute proof.

Can't you follow his dissertation?
Click to expand...

Ah yes, the kindergarten trick of just making a statement and then relying on others that do have skills to disprove it.

The main reason nobody ever takes him seriously is that he never does it right.

I mean, he never puts up a hypothesis, then follows through with an end-to-end rigorously worked out proof.

It is always of the ilk: prove that frogs can't fly.
And whenever someone makes an effort and proves it, he will add something like 'you just don't get how pixie dust works, do you'.

As for the N mapping, if he would watch that link, and understand it, he would at least have replied as to why that is incorrect.

From the fact that he completely ignores it and continues with his trademark childish 'I know what you are, but what am I?' we can conclude that British education tops Israeli know-how.
 
doronshadmi said:
jsfisher, please provide some detailed reply to the content of http://www.internationalskeptics.com/forums/showpost.php?p=9709765&postcount=2841 (including to the content of the link).
Click to expand...

I already have. The fact you continually repeat your same mistakes, misrepresentations, misinterpretations, personal desires, and innermost confusion without regard to what anyone else posts doesn't mean each and every utterance from you deserves its own individual response.

Your posts of late mostly begin with a misuse of "mapping". When and until you repair that gross faux pas, the rest of your posts are without foundation.
 
realpaladin said:
I mean, he never puts up a hypothesis, then follows through with an end-to-end rigorously worked out proof.
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He probably can't.

Press him for why he truly believes a set is the union of its members. Given a simple counterexample of a set that isn't a union of its members, like, say S = {{A}, {B}}, he has no trouble recognizing the members of S are {A} and {B}, or that then union of {A} and {B} is {A, B}, but he seems completely unable to connect those two facts, that the union of the members of S, those being {A} and {B}, is {A, B}.

Faced with that straight-forward two step hop in reasoning, Doron turns left.
 
jsfisher said:
He probably can't.

Press him for why he truly believes a set is the union of its members. Given a simple counterexample of a set that isn't a union of its members, like, say S = {{A}, {B}}, he has no trouble recognizing the members of S are {A} and {B}, or that then union of {A} and {B} is {A, B}, but he seems completely unable to connect those two facts, that the union of the members of S, those being {A} and {B}, is {A, B}.

Faced with that straight-forward two step hop in reasoning, Doron turns left.
Click to expand...

But we don't get it.

Don't get me wrong, I like kibitzing with Doron ; it's like having a favourite toothache.
 
jsfisher said:
He probably can't.

Press him for why he truly believes a set is the union of its members. Given a simple counterexample of a set that isn't a union of its members, like, say S = {{A}, {B}}, he has no trouble recognizing the members of S are {A} and {B}, or that then union of {A} and {B} is {A, B}, but he seems completely unable to connect those two facts, that the union of the members of S, those being {A} and {B}, is {A, B}.

Faced with that straight-forward two step hop in reasoning, Doron turns left.
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Well jsfisher you probably can't get the simple notion that being a member (or its absence) holds only if it is included in some set, so a set can't be but the union of its members (or their absence in case of {}).

{{A}, {B}} or {A,B} are two different sets, where each one of them is the union of its members.

EDIT:

As for set {A,B} it is also can be defined as the union of the members of set {A} with the members of set {B}.

As for set {{A}, {B}} it is also can be defined as the union of the members of set {{A}} with the members of set {{B}}.
 
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Let me give Doron a clue as to the answer of his 'problem' :

What Shadmi is doing is just adding a few exceptions to a generic formula.

Any sane mathematician or half capable programmer will simply tack on the rules for the exceptions to the generic formula.

Problem solved.
 
jsfisher said:
Had you read and comprehended what was written beyond the first three words of the post you cited, you would have found the answer to your question.
Click to expand...

Beyond the first three words there is no more than a reply of a person that does not wish to discuss in details about what is written in http://www.internationalskeptics.com/forums/showpost.php?p=9709255&postcount=2839 and http://www.internationalskeptics.com/forums/showpost.php?p=9709765&postcount=2841.

We can add this kind of your "detailed reply" to your "detailed reply" that (by using Traditional Mathematics) rigorously shows how a collection of distinct elements (where each element has exactly 0 length) provides an element which has length > 0.
 
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doronshadmi said:
Beyond the first three words there is...
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...another reminder that your misuse of terms doesn't cut it, and that what you presented is not a mapping. Fix that. Only then is there any point to discussing anything that follows it.

Here, for your reference since you seem to have such trouble with very basic things (including reading, but maybe this time will be different):

A map or mapping, M, from A to B is a function where for all X in A, M(X) is in B.

Simple enough?
 
I see Doron conveniently ignores all real answers and resorts to his old tactics of linking back.

Doron, show one thing, just one, that really is groundbreaking.

Up until now you have not.
 
jsfisher said:
...another reminder that your misuse of terms doesn't cut it, and that what you presented is not a mapping. Fix that. Only then is there any point to discussing anything that follows it.

Here, for your reference since you seem to have such trouble with very basic things (including reading, but maybe this time will be different):

A map or mapping, M, from A to B is a function where for all X in A, M(X) is in B.

Simple enough?
Click to expand...

EDIT:

Your definition is too general such that we can't know M(X) possible detailed outputs, where one of the cases can be no output at all. It may be even worse in case that M(X) must return some output according to your definition. According to your previous replies about this subject I think that this is the case.

Here is a better way, which deals with the discussed subject in details.

Let visitor(x) be a function which returns the name of the visitor in a given room of Hilbert's hotel, where x is the number of some room.

If, for example, there is no visitor in room 2, then visitor(2) does not return any output, which is equivalent to 2 → expression, such that 2 is equivalent to x and → is equivalent to the function visitor(x).

visitor(x) is used infinitely many times, without missing even a single room, for example:

1 → 1
2 →
3 → 2
4 → 3
5 → 4
...

By checking the results of function visitor(x), we righteously conclude that there are more rooms than visitors exactly because there is 1-to-1 and onto between the names of the rooms and the names of the visitors and yet there is at least one room without any visitor.

Simple enough?
 
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doronshadmi said:
Your use of M(X) is golbal, so by using your definition we can't know its possible detailed outputs, where one of the cases can be no output at all.

Here is a better way, which deals with the discussed subject in details.

Let visitor(x) be a function which returns the name of the visitor in a given room of Hilbert's hotel, where x is the number of some room.

If there is no visitor in room 2, then visitor(2) does not return any output, which is equivalent to 2 -> expression, such that 2 is equivalent to x and -> is equivalent to the function visitor(x).

visitor(x) is used infinitely many times, without missing even a single room, for example:

1 -> 1
2 ->
3 -> 2
4 -> 3
5 -> 4
...

Simple enough?
Click to expand...

:ld:
 
doronshadmi said:
Your definition is too general such that we can't know M(X) possible detailed outputs, where one of the cases can be no output at all.
Click to expand...

That is not a problem with the definition; it is a problem with your usage. The definition stands correct.
 
realpaladin said:
Correct.
Click to expand...

And at this point, Doron is finding the footing a little unstable. So, we will google his way through the Intertubes trying to find something he can misinterpret and misrepresent as proving his usage was correct all along.

Likely it will involve some obscure computer science monogram that included a passing reference to Hilbert and to the four-color map theorem.
 
jsfisher said:
That is not a problem with the definition; it is a problem with your usage. The definition stands correct.
Click to expand...

EDIT:

The problem is that your understanding of the definition of a function can't handle with the case that the function does not have any output.

In order to help you to get such a case all you have to do is to use the function LookForXmember(z) from P(X) to X where z is some P(X) member that does not have any X member to be mapped with.

This case is notated as z →, where z is, for example, the member of P(X) that (by using |P(X)| > |X| Cantors proof by contradiction) does not have any X member to be mapped with, and → is actually function LookForXmember(z) from P(X) to X that does not return (does not have) any output.

So as you see, mapping of the form x → is mathematically valid.

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

Again, visitor(x) (please see http://www.internationalskeptics.com/forums/showpost.php?p=9711109&postcount=2861) is used infinitely many times, without missing even a single room, for example:

visitor(room 1) returns visitor's name 1
visitor(room 2) returns nothing
visitor(room 3) returns visitor's name 2
visitor(room 4) returns visitor's name 3
visitor(room 5) returns visitor's name 4
...

By checking the results of function visitor(x), we righteously conclude that there are more rooms than visitors exactly because there is 1-to-1 and onto between the names of the rooms and the names of the visitors (no N member is missing in both sides of the mapping) and yet there is at least one room without any visitor, or in other words we have shown that in addition to |N| = |N| case there is also |N| > |N| case, which means that the whole idea of transfinite cardinality (that is related to sets) is not (mathematically) well-defined.

If you still do not get it than think about this:

visitor(room 2) returns nothing

is equivalent to

LookForXmember(z) from P(X) to X that does not return (does not have) any output( as can be seen in |P(X)| > |X| Cantors proof by contradiction)

Simple enough?
 
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doronshadmi said:
The problem is that your understanding of the definition of a function can't handle with the case that the function does not have any output.

In order to help you to get such a case all you have to do is to use the function LookForXmember(z) from P(X) to X where z is some P(X) member that does not have any X member to be mapped with.

This case is notated as z ->, where z is, for example, the member of P(X) that (by using |P(X)| > |X| Cantors proof by contradiction) does not have any X member to be mapped with, and -> is actually function LookForXmember(z) from P(X) to X that does not return (does not have) any output.

So as you see, mapping of the form x -> is mathematically valid.

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

Again, visitor(x) (please see http://www.internationalskeptics.com/forums/showpost.php?p=9711109&postcount=2861) is used infinitely many times, without missing even a single room, for example:

visitor(room 1) returns visitor's name 1
visitor(room 2) returns nothing
visitor(room 3) returns visitor's name 2
visitor(room 4) returns visitor's name 3
visitor(room 5) returns visitor's name 4
...

By checking the results of function visitor(x), we righteously conclude that there are more rooms than visitors exactly because there is 1-to-1 and onto between the names of the rooms and the names of the visitors (no N member is missing in both sides of the mapping) and yet there is at least one room without any visitor.

Simple enough?
Click to expand...

Incorrect.
 
doronshadmi said:
The problem is that your understanding of the definition of a function can't handle with the case that the function does not have any output.
Click to expand...

There is no problem with the definition nor my understanding of it; it is a problem with your usage. The definition stands correct.
 
jsfisher said:
There is no problem with the definition nor my understanding of it; it is a problem with your usage. The definition stands correct.
Click to expand...
jsfisher, you simply refuse to deal with the case of function with input but no output, and the possible mathematical conclusions that are derived form it.

In other words, evasion has been noted.
 
doronshadmi said:
jsfisher, you simply refuse to deal with the case of function with input but no output, and the possible mathematical conclusions that are derived form it.

In other words, evasion has been noted.
Click to expand...

The definitions for mapping and for function are correct as they stand. They are in need of no alteration to satisfy the whim of DoronShadmi. Mathematics does not suffer by its reluctance to behave according to your misconceptions, misunderstandings, personal desires, or fantasies.

What you continually present is not a mapping. Fix that. Only then is there any point to discussing anything that follows it. And again, for your reference:

A map or mapping, M, from A to B is a function where for all X in A, M(X) is in B.​
 
jsfisher said:
A map or mapping, M, from A to B is a function where for all X in A, M(X) is in B.
Click to expand...

Doron makes the mistake of taking the above definition and assuming

X in A, M(X) - > Y where X == Y.
And *then* he raises the roof because he adds an extra dimension outside of the mapping function (in the Hilbert case, temporal) which causes the original context to be invalid.

Then he starts babbling Turbo Pascal...

Doron, if you just add your temporal dimension (ie the customer *left*) to the mapping *function * from the start, you will see that nothing spectacular is happening here.

I will help:
X in A, t for temporal, M(X, t) - > Y, Y in B t
 
The power of the paradox

realpaladin said:
Doron makes the mistake of taking the above definition and assuming

X in A, M(X) - > Y where X == Y.
And *then* he raises the roof because he adds an extra dimension outside of the mapping function (in the Hilbert case, temporal) which causes the original context to be invalid.

Then he starts babbling Turbo Pascal...

Doron, if you just add your temporal dimension (ie the customer *left*) to the mapping *function * from the start, you will see that nothing spectacular is happening here.

I will help:
X in A, t for temporal, M(X, t) - > Y, Y in B t
Click to expand...


Actually, it looks to me like he's heading towards a conclusion that cardinality varies on a case by case basis. He has performed similar feats of illogic before, wherein he "proved" in ways that only Doron can that in Zeno's paradox (using the Achilles vs. hare in a race variation) that Achilles wins, the hare wins, and that neither ever reaches the finish line. It was all very impressive.

Oh, yes, and Turbo Pascal was involved. ;)

ETA: Oh, I almost forgot. Doron's conclusion was that there was no paradox at all since all three outcomes occurred.
 
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jsfisher said:
ETA: Oh, I almost forgot. Doron's conclusion was that there was no paradox at all since all three outcomes occurred.
Click to expand...

Is that where we got the Schroedinger's Cat variation from that we apparently need an observer?

I still wonder if he understood that I meant that nowhere in the Uncertainty Principle formulae an observer is needed and that in fact it meant that an observer actually *causes * the uncertainty...
 
realpaladin said:
Doron makes the mistake of taking the above definition and assuming

X in A, M(X) - > Y where X == Y.
And *then* he raises the roof because he adds an extra dimension outside of the mapping function (in the Hilbert case, temporal) which causes the original context to be invalid.

Then he starts babbling Turbo Pascal...

Doron, if you just add your temporal dimension (ie the customer *left*) to the mapping *function * from the start, you will see that nothing spectacular is happening here.

I will help:
X in A, t for temporal, M(X, t) - > Y, Y in B t
Click to expand...
EDIT:

realpaladin, all you have is to realize that a function with no output is a valid mathematical expression.

If you do this step in your mind you are able to conclude that in case of infinite sets there are at least 3 options in the case of a function from set X into itself:

1) There is 1-to-1 from X into its proper subset (already known).

2) There is 1-to-1 and onto from X into itself (already known).

3) There are more members from X into itself (does not known, yet).

Here it is again, in front of your mind (and no temporal terms are used), where there is an OR condition between these these 3 possibilities.

Again, function visitor(x) from N into itself is used infinitely many times, without missing even a single room (a single N member as an input), for example:

visitor(room 1) returns visitor's name 1
visitor(room 2) returns nothing
visitor(room 3) returns visitor's name 2
visitor(room 4) returns visitor's name 3
visitor(room 5) returns visitor's name 4
...

By checking the results of function visitor(x) (without missing even a single input) we righteously conclude that there are more rooms than visitors exactly because there is 1-to-1 and onto between the names of the rooms and the names of the visitors (no N member is missing in both sides of the mapping, in case of infinite sets) and yet there is at least one room without any visitor (there is at least one case with an input that does not return (does not have) any output (and this case is not temporal), or in other words we have shown that in addition to |N| = |N| case there is also |N| > |N| case, which means that the whole idea of transfinite cardinality (that is related to infinite sets) is not (mathematically) well-defined).

Your "Turbo Pascal" argument does not prevent the possible equivalence between expressions like function visitor(x) and x →.

For example, if there is no visitor in room 2, then visitor(2) does not return any output, which is equivalent to 2 → expression, such that 2 expression is equivalent to x expression and → expression is equivalent to the visitor() expression.
 
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jsfisher said:
Actually, it looks to me like he's heading towards a conclusion that cardinality varies on a case by case basis. He has performed similar feats of illogic before, wherein he "proved" in ways that only Doron can that in Zeno's paradox (using the Achilles vs. hare in a race variation) that Achilles wins, the hare wins, and that neither ever reaches the finish line. It was all very impressive.
Click to expand...
jsfisher you still have troubles with A OR notA --> T.
 
doronshadmi said:
EDIT:

realpaladin, all you have is to realize that a function with no output is a valid mathematical expression.

If you do this step in your mind you are able to conclude that in case of infinite sets there are at least 3 options in the case of a function from set X into itself:

1) There is 1-to-1 from X into its proper subset (already known).

2) There is 1-to-1 and onto from X into itself (already known).

3) There are more members from X into itself (does not known, yet).

Here it is again, in front of your mind (and no temporal terms are used), where there is an OR condition between these these 3 possibilities.

Again, function visitor(x) from N into itself is used infinitely many times, without missing even a single room (a single N member as an input), for example:

visitor(room 1) returns visitor's name 1
visitor(room 2) returns nothing
visitor(room 3) returns visitor's name 2
visitor(room 4) returns visitor's name 3
visitor(room 5) returns visitor's name 4
...

By checking the results of function visitor(x) (without missing even a single input) we righteously conclude that there are more rooms than visitors exactly because there is 1-to-1 and onto between the names of the rooms and the names of the visitors (no N member is missing in both sides of the mapping, in case of infinite sets) and yet there is at least one room without any visitor (there is at least one case with an input that does not return (does not have) any output (and this case is not temporal), or in other words we have shown that in addition to |N| = |N| case there is also |N| > |N| case, which means that the whole idea of transfinite cardinality (that is related to infinite sets) is not (mathematically) well-defined).

Your "Turbo Pascal" argument does not prevent the possible equivalence between expressions like function visitor(x) and x ->.

For example, if there is no visitor in room 2, then visitor(2) does not return any output, which is equivalent to 2 -> expression, such that 2 expression is equivalent to x expression and -> expression is equivalent to the visitor() expression.
Click to expand...

This demonstrates you are horrible at reading comprehension.

Incorrect Doron. Your Word Salad is incorrect.
 
realpaladin said:
This demonstrates you are horrible at reading comprehension.

Incorrect Doron. Your Word Salad is incorrect.
Click to expand...

So you refuse to realize that a function with no output is a valid mathematical expression.

realpaladin, it's a free country, you don't have to.
 
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