Deeper than primes - Continuation

[realpaladin]

"Mutually independent" means they need each other to be independent of, therefore, they can not be independent.

Get it?

 

[jsfisher]

"Mutually independent" means they need each other to be independent of, therefore, they can not be independent.

Get it?

Do you really need to ask?

 

[realpaladin]

Do you really need to ask?

Nah... Doron's rambling brings out the worst in me.

 

[doronshadmi]

There are some traditional mathematicians that can't recognize traditional notions (even if there is a clear comparison between standard and non-standard notations of some standard notion (and in this case the notion of base 2 is represented as <0,1>)) unless it is expressed by traditional notations.

 

[realpaladin]

There are some traditional mathematicians that can't recognize traditional notions unless it is expressed by traditional notations.

What of it?

 

[doronshadmi]

"Mutually independent" means they need each other to be independent of, therefore, they can not be independent.

Get it?

So what, there is no hierarchy of dependency between them, and this is the notion of being mutual independent.

The traditional mathematician in this thread claims that P(S) rises from S, but in http://www.internationalskeptics.com/forums/showpost.php?p=8137722&postcount=890 I clearly show that Both P(S) and S (where S is a placeholder of a set) share the same type of form, such that there is an element of that form in P(S), but not in S.

In other words, given S, it is incomplete because not all the possible forms of a given type are its members.

Once again:

Lets improve the last part of http://www.internationalskeptics.com/forums/showpost.php?p=8137722&postcount=890 (also be aware of

a) There is no additional distinct element (there is nothing) between two distinct elements, which are constructed according to the given form.

which follows traditional maths' point of view):

Since (every P(S) of distinct elements of a given form has a power set of distinct elements of that given form) AND (for every given set under placeholder S there is a distinct element of that form, which is an element of P(S) but it is not an element of that set) AND (the largest power set of distinct elements of that form does not exist) then no given set (under placeholder S) with distinct elements of that given form is complete (no matter if k is the cardinality of a finite or non-finite non-empty set under placeholder S).


Get it?

 

[jsfisher]

So what, there is no hierarchy of dependency between them.

Get it?

Yeah! It's not like adverbs and nouns are ever related. They are just words. It doesn't matter how you use them. They have no relationship to each other...at least in Doron's world.

 

[jsfisher]

There are some traditional mathematicians that can't recognize traditional notions (even if there is a clear comparison between standard and non-standard notations of some standard notion (and in this case the notion of base 2 is represented as <0,2>)) unless it is expressed by traditional notations.

Ah! Lost ground on that whole traditional notation lie, so now you shift to the change the subject technique. You leap from exponentiated tuples to powers of 2 and now you attempt to seamlessly equate all that to the previously unmentioned binary notation.

The starting point was still not traditional mathematical notation, so you still lied there. Powers of 2 and binary are not synonymous, so there's another lie. And there's still that gap between power sets and your silly notation. I predict another lie is in the works to attempt to obscure that Doron-failure, too.

 

[doronshadmi]

Each time when the traditional mathematician in this thread can't comprehend a given notion, even if it is translated to the standard notion, he calls it a lie.

Say no more.

 

[dafydd]

Wrong, axioms are mutually independent self evident truths (no empirical (in)formation is needed) of a given axiomatic system.

I made it up and you take it seriously? Sheesh!

 

[jsfisher]

Each time when the traditional mathematician in this thread can't comprehend a given notion, even if it is translated to the standard notion, he calls it a lie.

Say no more.

You are in a rut, Doron, with this same sequence of obfuscation again and again. You need a new shtick. This one's tired.

 

[dafydd]

You are in a rut, Doron, with this same sequence of obfuscation again and again. You need a new shtick. This one's tired.

The thread is becoming very threadbare.

 

[doronshadmi]

Since the posters here did not get the previous version of my argument, let's improve it according to their replies, by doing it in baby steps.

Here it is:

Let's follow the traditional mathematical notion in order to show that given any non-empty set of distinct elements with a given form, no possible set (where S is a placeholder of a given set of that form) is complete, because:

a) There is no additional distinct element (there is nothing) between two distinct elements, which are constructed according to the given form.

b) Given the powerset P(S) of distinct elements of a given form, S is a placeholder for any possible set of distinct elements of that form.

c) The largest powerset P(S) of distinct elements of that form does not exist.


1) <0,1> is the common notation of the forms that is equivalent to base 2 (where the possible notations under this base are 0 and 1, notated as <0,1>).

2) ^ is the power operation.

3) k is the (finite or infinite) cardinality of any given set of the considered distinct forms under placeholder S.

4) <0,1>^k(where k=1 to ∞) expression (which is equivalent to 2^k expression) is used for both S (where S is a placeholder of a given set of the considered form) and P(S), where P(S) is the powerset of any possible set under place holder S, such that the cardinality of P(S) is determined by 2^k(where k=1 to ∞) and the cardinality of any set under placeholder S is determined by k(where k=1 to ∞).

5) P(S) and any possible set with cardinality k (under placeholder S) have the same type of elements, notated by <0,1> symbols.

6) The order of the presentation of P(S) and the sets under placeholder S, is insignificant, and all we care is the shared type of forms among P(S) (which its cardinality is determined by 2^k(where k=1 to ∞)) and the sets under placeholder S (which their cardinality is determined by k(where k=1 to ∞)).

Here is a finite example (k is finite):

By <0,1>^1 (which is equivalent to 2^1)
P(S)=
{0,1}
where the sets (with cardinality k) under placeholder
S=
(
{0} → 1
or
{1} → 0
)

By <0,1>^2 (which is equivalent to 2^2)
P(S)=
{00,01,10,11}
where some possible sets (with cardinality k) under placeholder
S=
(
{
10,
11
} → 00
or
{
10,
00
} → 01
or
{
00,
11
} → 10
or
{
01,
10
} → 11
)

...

Nothing is changed even if k=∞ (in this case the cardinality of P(S) is 2^∞ and the cardinality of any possible set under placeholder S is ∞) because also in this case, given a set under placeholder S with distinct elements of the considered form, there is a distinct element of that form, which is an element of P(S) but it is not an element of the considered set under placeholder S.

Since (the distinct elements of the considered form are elements of powerset P(S)) AND (for every considered set -with cardinality k- under placeholder S, there is a distinct element of that form, which is an element of P(S) but it is not an element of that set) AND (the largest powerset of distinct elements of that form does not exist) then no given set (under placeholder S) with distinct elements of that given form is complete (no matter if any set (with the considered form) under placeholder S, has finite or infinite cardinality k(where k=1 to ∞)).

This post can be simplified by further editing that does not change the result.

 

[realpaladin]

http://www.internationalskeptics.com/forums/showthread.php?t=232772

 

[doronshadmi]

http://www.internationalskeptics.com/forums/showthread.php?t=232772

Irrelevant.

Next time please be honest and simply say that you have to clue of http://www.internationalskeptics.com/forums/showpost.php?p=8140608&postcount=933 subject even if it is given by baby steps.

You simply do not get that there are at least 2^∞ sets (where each set has cardinality ∞) under placeholder S, where each one of them has ∞ members of <0,1> form and no one of them is complete, because there is always a given element of <0,1> form, which is a member of P(S), but it is not a member of anyone of the 2^∞ sets (where, again, each one of them has ∞ members of <0,1> form, and now we realize that no one of them is complete).

This fact is not changed, whether k (of the expression 2^k) is finite or infinite.

 

[Little 10 Toes]

Since the posters here did not get the previous version of my argument, let's improve it according to their replies, by doing it in baby steps.

Here it is:

Let's follow the traditional mathematical notion in order to show that given any non-empty set of distinct elements with a given form, no possible set (where S is a placeholder of a given set of that form) is complete, because:

Wrong. The set can be complete. My set S is the set of positive single digit numbers when written out in English have only 4 letters in them. My set S is (four, five, nine). It is complete. Since you claim that it is incomplete, please provide any missing elements of this set.

 

[jsfisher]

Let's follow the traditional mathematical notion in order to show that given any non-empty set of distinct elements with a given form, no possible set (where S is a placeholder of a given set of that form) is complete,

So many extraneous words. Stripping the preceding of the Doron-ese gibberish and word salad, we are left with: To be shown: no set is complete.

...because:

a) There is no additional distinct element (there is nothing) between two distinct elements, which are constructed according to the given form.

Since "between" is not a set concept, this is irrelevant.

b) Given the powerset P(S) of distinct elements of a given form, S is a placeholder for any possible set of distinct elements of that form.

This is gibberish coupled with Doron's inverted processing. Given a set, S, he could then consider its power set, but not the other way around.

By virtue of being meaningless, this one is also irrelevant.

c) The largest powerset P(S) of distinct elements of that form does not exist.

It is impossible to say if Doron intended this to be a premise or a deduction. Either way, it has no basis and gets chucked into the trash heap with the first two.

1) <0,1> is the common notation of the forms that is equivalent to base 2 (where the possible notations under this base are 0 and 1, notated as <0,1>).

Common to whom? Be that as it may, this is a mighty tortured way to introduce binary numbers.

2) ^ is the power operation.

3) k is the (finite or infinite) cardinality of any given set of the considered distinct forms under placeholder S.

Just saying "Let k = |S|" would have been too easy?

4) <0,1>^k(where k=1 to ∞)...

So, we now abandon the previous meaning assigned to k.

...expression (which is equivalent to 2^k expression)

No, they are not equivalent. The former is being suggested as binary notation (I say suggested because, as always, Doron never completes his thoughts), and the best that can be inferred for <0,1>^4, as an example, is some non-specific 4-character string of 0's and 1's; 2^4, on the other hand, is 16.

...is used for both S (where S is a placeholder of a given set of the considered form) and P(S), where P(S) is the powerset of any possible set under place holder S, such that the cardinality of P(S) is determined by 2^k(where k=1 to ∞) and the cardinality of any set under placeholder S is determined by k(where k=1 to ∞).

Well, this certainly jumps around, doesn't it? It also assumes quite a bit. To this point in the presentation, the relationship between |S| and |P(S)| has not been established. And given the inverted approach Doron insists on abusing, he'll be hard-pressed to establish that |S| is the base-2 log of |P(S)| nor that the arithmetic is meaningful for non-finite sets.

5) P(S) and any possible set with cardinality k (under placeholder S) have the same type of elements, notated by <0,1> symbols.

6) The order of the presentation of P(S) and the sets under placeholder S, is insignificant, and all we care is the shared type of forms among P(S) (which its cardinality is determined by 2^k(where k=1 to ∞)) and the sets under placeholder S (which their cardinality is determined by k(where k=1 to ∞)).

Gibberish. Fortunately, Doron will follow up with an example to increase the muddle:

Here is a finite example (k is finite):

By <0,1>^1 (which is equivalent to 2^1)
P(S)=
{0,1}

Last time anyone other than Doron checked, 2^1 = 2, so no, the alleged equivalence isn't there.

Doron still persists in his ass-backwards P(S) leads to S nonsense, too. Apparently, too, we are to infer that <0,1>^n really means the set of all possible n-character strings of 0's and 1's.

where the sets (with cardinality k) under placeholder
S=
(
{0} → 1
or
{1} → 0
)

This is a rectal extraction. Doron has provided no basis for this. This also contradicts the meaning of <0,1>^n invoked for P(S).

Be that as it may, though, neither possibility for set S leads to the alleged power set, above. So, not only is Doron just scribbling according to some arbitrary, unstated, variable rules, he doesn't even get the right result when he's done.

...<second incompetent example, but one with an even more bizarre process for generating S>...

Nothing is changed even if k=∞

Yes, nothing changes. The whole thing continues to be fantastically wrong.

 

[doronshadmi]

"Equivalent to ..." is not the same as "the same as ..." but our traditional mathematician here does not know that.

He also unable to get that P(S) members and the members of the sets under placeholder S, are of the same form.

As a result he totally misses http://www.internationalskeptics.com/forums/showpost.php?p=8140608&postcount=933.

Say no more.

 

[jsfisher]

"Equivalent to ..." is not the same as "the same as ..." but our traditional mathematician here does not know that.

Perhaps, Doron, you should work on those abysmal reading comprehension skills of yours. No one but you has suggest equivalence means the same as.

Moreover, the equivalence you claimed does not exist. Making things up -- which you so often do -- doesn't make them true.

He also unable to get that P(S) members and the members of the sets under placeholder S, are of the same form.

That would be the form you tried to demonstrate and failed, miserably.

As a result he totally misses http://www.internationalskeptics.com/forums/showpost.php?p=8140608&postcount=933.

Say no more.

Not much more needs to be said. Doron makes an incompetent post. Doron attempts to pass gibberish as intelligence. Doron defends it by blaming everyone else.

Nothing new to see here.

 

[dafydd]

Doron, there is only maths. Try using it sometime.