Cont: Deeper than primes - Continuation 1/3*9

[doronshadmi]

Also please be aware that if N is one of its base members, then N is of the form (x∪{x}) (a successor) that does not have its largest successor, since ∀ is not a property of N.

More details are seen in http://www.internationalskeptics.com/forums/showpost.php?p=13205791&postcount=280 .

 

[Little 10 Toes]

Let's make it easy since doronshadmi is not understanding the simple items.

Which, if any, of the following items are in N?
1) The War of 1812
2) 10% GDP
3) Oranges
4) The ratio between the circumference of a circle and it's diameter
5) Beethoven's Fifth
6) {... -2, -1, 0, 1, 2, ...}
7) { {∅} ,{ { { {∅} } } } }
8) Double shot of espresso, 3 soy creams, 1 brown sugar, 97 degree, no whip

Please note, since doronshadmi has used N before, I am confirming that I am not talking about the set of natural numbers (also known/written as N or N).

Doronshadmi, do you understand that all of these items can be elements of set N?

 

[jsfisher]

You have been outspoken that there is no largest successor. That means that any set I choose is going to be "~largest successor". That means that any set I choose (including N) is going to be a member of N.

N does not have even one largest successor, this is exactly why N can't be but an infinite set that includes base sets OR successor sets that are not largest successors sets.

You didn't understand my post at all, did you? Your response is just trying to cycle back to your hatred of the universal quantifier without regard to the topic at hand.

You so-called membership function is bogus. About your so-called membership function you wrote:

x is largest successor is the same as x is not a member.

x is ~largest successor is the same as x is a member.

Well, guess what? Your set N is a set, and N is not the largest successor of N. Therefore, by your so-called membership function, N must be a member of N.

 

[jsfisher]

Also please be aware that if N is one of its base members, then N is of the form (x∪{x}) (a successor) that does not have its largest successor, since ∀ is not a property of N.

That's nice, but it has nothing to do with you so-called membership function, M.

If x is largest successor, then M(x) : false.

If x is not largest successor, then M(x) : true.

Clearly, M(N) must be true, so N is a member of N.

 

[doronshadmi]

Clearly, M(N) must be true, so N is a member of N.

N as a member of N is of the form (x∪{x}) (a successor) that does not have its largest successor, since ∀ is not a property of N.

If x is largest successor, then M(x) : false.

If x is not largest successor, then M(x) : true.

Since N is a successor that is not largest successor, then M(N) is indeed true, since ∀ is not a property of N.

 

[jsfisher]

N as a member of N is of the form (x∪{x})

If that's what you want, then you need to include that in your membership function directly. As written every set is a member of N. That's not a very good membership function.

 

[doronshadmi]

As written every set is a member of N. That's not a very good membership function.

Not every set, a successor set that is also largest set is not a member of set N.

So terms like "every set", "all sets", ∀ etc. are not properties of set N.

 

[jsfisher]

Not every set, a successor set that is also largest set is not a member of set N.

Well, since there is no "largest successor set", it is every set. Your N is the set of all sets, or at least that is what your membership function would have us believe.

Your membership function is nonsense. You haven't gotten any closer to defining your set N. Defining N is key to what you think you need to define cardinality, so that sits dead on the vine as well.

You have made no progress on the topic at hand.

 

[doronshadmi]

If that's what you want, then you need to include that in your membership function directly.

It is included directly:

If x is largest successor, then M(x) : false.

If x is not largest successor, then M(x) : true.

Not being largest successor set is:

(successor set AND not largest successor set) OR (base set).

In case of N as a member of N, N is a (successor set AND not largest successor set), which means that "every set", "all sets", ∀ etc. are not properties of set N.

 

[doronshadmi]

Well, since there is no "largest successor set", it is every set. Your N is the set of all sets,

EDIT:
Wrong again, jsfisher, terms like "every set", "all sets", ∀ etc. are not properties of set N, exactly because any one of its successor sets is (successor set AND not largest successor set).

 

[jsfisher]

Not being largest successor set is:

(successor set AND not largest successor set) OR (base set)

...deleted...

I want to rewrite this differently.

 

[jsfisher]

EDIT:
Wrong again, jsfisher, terms like "every set", "all sets", ∀ etc. are not properties of set N, exactly because any one of its successor sets is (successor set AND not largest successor set).

"∀" is not now nor has it ever been a property. You've proven again you don't understand the meaning of basic mathematical concepts. You are in no position to lash out against them. Please stop pretending.

 

[doronshadmi]

EDIT:

"(successor set AND not largest successor set) OR (base set)" is universally true.

No, take for example a finite set of the form (x∪{x}). It has largest successor set, something that N does not have.

"∀" is not now nor has it ever been a property. You've proven again you don't understand the meaning of basic mathematical concepts. You are in no position to lash out against them. Please stop pretending.

Therefore "every set", "all sets", ∀ etc. can't be related to set N, exactly because it is an infinite set.

 

[jsfisher]

It is included directly:

If x is largest successor, then M(x) : false.

If x is not largest successor, then M(x) : true.

Not being largest successor set is:

(successor set AND not largest successor set) OR (base set).

Your most recent set of supporting definitions are these:

Let's put what is needed in one post, in order to define N as a set.

Definition 1: Any given set that is not of the form (x∪{x}), is called a base set.

Definition 2: Any given set that is of the form (x∪{x}), is called a successor set.

Definition 3: Given a successor set in some set, it is called largest successor set iff given a base set in that set, it has at least one successor set that does not have its successor set, in that set.

You never qualified "any given set" to be restricted to being in N. Did you mean to? You never stated how one would determine if this "any given set" is of the form x ∪ {x}. How would you?

As for definition 3, well, it is badly worded and doesn't state what you think it does. What are you trying to say? Whatever you meant by it, it certainly was not this:

Not being largest successor set is:
(successor set AND not largest successor set) OR (base set).​

If nothing else, the thing you are trying to define (largest successor set) appears in the definition.

Remember, too, the goal you are trying to attain for the present is a definition for your set N. Something like:

N = { y : M }​

with a formulation for M acceptable to the set theory axioms. Your so-called definitions are little more than a distraction from the goal.

 

[jsfisher]

Therefore "every set", "all sets", ∀ etc. can't be related to set N, exactly because it is an infinite set.

Not a relation either. Please stop pretending.

 

[doronshadmi]

As for definition 3, well, it is badly worded and doesn't state what you think it does. What are you trying to say? Whatever you meant by it, it certainly was not this:

Not being largest successor set is:
(successor set AND not largest successor set) OR (base set).​

If nothing else, the thing you are trying to define (largest successor set) appears in the definition.

"Not being largest successor" set is not the definition of largest successor set, but it is the use of the term largest set as part of the expression (successor set AND not largest successor set) "after" it is defined.

You are mixing between the use of the term "largest successor set" in some expression ("after" it is defined) and the definition of the term "largest successor set" which is:

Definition 3: Given a successor set in some set, it is called largest successor set iff given a base set in that set, it has at least one successor set that does not have its successor set, in that set.

What is written after the iff does not use the term "largest successor set" in order to define "largest successor set".

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

I agree with you that the expression (successor set AND not largest successor set) is misleading, so let's correct it as follows:


If x is largest successor, then M(x) : false.

If x is not largest successor, then M(x) : true.

Not being largest successor set in N is:

(successor set that has its successor set) OR (base set).

In case of N as a member of N, N is a (successor set that has its successor set), which means that "every set", "all sets", ∀ etc. are not related to set N.

 

[doronshadmi]

You never stated how one would determine if this "any given set" is of the form x ∪ {x}. How would you?

Please demonstrate exactly how one can't determine if a given set is of the form x ∪ {x} or not of the form x ∪ {x}.

 

[doronshadmi]

Not a relation either. Please stop pretending.

Relation is a noun, related is a verb.

I used "related".

If you have a better word of the connection between ∀ and a set, then please say it.

 

[Little 10 Toes]

You never stated how one would determine if this "any given set" is of the form x ∪ {x}. How would you?

Please demonstrate exactly how one can't determine if a given set is of the form x ∪ {x} or not of the form x ∪ {x}.

• Have the common decency to use the quote function properly to refer to the message that you are quoting from. I have done that for you with jsfisher's original message. You're welcome.
• How about you stop shifting the burden. Your claim, your evidence. You show how you would determine "any given set" is of the form x ∪ {x}.

Also:
1) The War of 1812
2) 10% GDP
3) Oranges
4) The ratio between the circumference of a circle and it's diameter
5) Beethoven's Fifth
6) {... -2, -1, 0, 1, 2, ...}
7) { {∅} ,{ { { {∅} } } } }
8) Double shot of espresso, 3 soy creams, 1 brown sugar, 97 degree, no whip

Do you understand that all of these items can be elements of set N?

Since this is the third time that I am asking, I am going to assume that you can't.

 

[jsfisher]

"Not being largest successor" set is not the definition of largest successor set, but it is the use of the term largest set as part of the expression (successor set AND not largest successor set) "after" it is defined.

You said: "Not being largest successor set is...". So, yeah, it is a definition (albeit in the negative).