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Cont: Deeper than primes - Continuation 2

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doronshadmi said:
Next ;) question please.
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Flippancy does not a definition make.

You get predicate calculus plus "set" as a concept, "is a member of" as a relation, and whatever else is provided by the axioms other than the Axiom of Infinity (e.g. set union and set equality). Nothing else.

How is "is a successor of" defined?
 
jsfisher said:
Flippancy does not a definition make.

You get predicate calculus plus "set" as a concept, "is a member of" as a relation, and whatever else is provided by the axioms other than the Axiom of Infinity (e.g. set union and set equality). Nothing else.

How is "is a successor of" defined?
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As a relation, exactly as "is a member of" is a relation.
 
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doronshadmi said:
As a relation, exactly as "is a member of" is a relation.
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Yes, it was obviously a relation. Are you being deliberately obtuse? Now, how is that relation defined?

Here, I'll help get you started: "for all X, for all Y, X is a successor of Y if and only if...."
 
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doronshadmi said:
I agree, it is not the standard axiom of infinity that keeps silence about {y} as a successor of y.

It is ok with me Nonpareil, you do not have to agree with my version of the axiom of infinity (http://www.internationalskeptics.com/forums/showpost.php?p=11263283&postcount=1235) that does not keep silence about {y} as a successor of y.
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No one has to. Particularly as you are failing to properly define it and the results you wish to get from it are also poorly defined, as well as nonsensical.
 
jsfisher said:
Here, I'll help get you started: "for all X, for all Y, X is a successor of Y if and only if...."
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Since you are using the term "all" you are using a hidden assumption that contradicts the notion of being X a successor of Y (the existence of permanently next element).

In order to understand better my notion of what is a successor, please try to define the set of all singleton sets.

The same mechanism that "externally" prevents the completeness of such set, prevents "internally" the completeness of an inductive set (where the set of natural numbers is some particular case of an inductive set).
 
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doronshadmi said:
Since you are using the term "all" you are using a hidden assumption that contradicts the notion of being X a successor of Y (the existence of permanently next element).

In order to understand better my notion of what is a successor, please try to define the set of all singleton sets.

The same mechanism that "externally" prevents the completeness of such set, prevents "internally" the completeness of an inductive set (where the set of natural numbers is some particular case of an inductive set).
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No, sorry. Not what was asked.

Answer the question. If your idea is coherent, you should be capable of it.
 
Nonpareil said:
No, sorry. Not what was asked.

Answer the question. If your idea is coherent, you should be capable of it.
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Have you heard about the word "Please"? (for example: "Please answer the question").

Such basic aggressive attitude of you along the following discussion, may harm your ability to understand what I wish to express.

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Please explain, in details, why, exactly, http://www.internationalskeptics.com/forums/showpost.php?p=11264035&postcount=1249 does not capable of it (where "it" is my idea)?

Also please define the set of all steps of
avatar32474_45.gif



Also look at this two avatars:
Code: 
[IMG]http://www.internationalskeptics.com/forums/customavatars/avatar32474_45.gif[/IMG]

     [IMG]http://www.internationalskeptics.com/forums/customavatars/avatar32474_45.gif[/IMG]

According to my infinity number system, the infinite number of steps of the upper avatar is 1... and the infinite number of steps of the lower avatar is (let's say) 1...+4

Both sets of steps are infinite, yet the set of steps of the lower avatar is bigger by 4 if compared to the set of steps of the upper avatar.

This is how my system of infinite numbers works and http://www.internationalskeptics.com/forums/showpost.php?p=11259463&postcount=1185 is some concrete example of it.
 
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jsfisher said:
...attempt to shift the burden snipped...
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http://www.internationalskeptics.com/forums/showpost.php?p=11264296&postcount=1253

EDIT:

Also see this (at the beginning of page two of http://www.bu.edu/linguistics/UG/course/lx502/_docs/lx502-basic set theory.pdf):

"I offer no definition of what a set is beyond the intuitive notion described above. Instead, I am going
to show you what can be done with sets. This is a typical approach to Set Theory, i.e., sets are treated as
primitives of the theory and are not definable in more basic terms."

It is also known that sets are defined by their members, so also "is a member of" is a primitive that is not definable in more basic terms.

So is the case about "is a successor of", it is a primitive that is not definable in more basic terms.

By understating this primitive notion, http://www.internationalskeptics.com/forums/showpost.php?p=11263283&postcount=1235 is wff.
 
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doronshadmi said:
Have you heard about the word "Please"? (for example: "Please answer the question").

Such basic aggressive attitude of you along the following discussion, may harm your ability to understand what I wish to express.
Click to expand...

Give us the definition or go away, doron. Don't try to waste our time with stupid tone-policing games.
 
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