Cont: Deeper than primes - Continuation 2

[Little 10 Toes]

Only examples are given. No definitions.

Try agsin. Let me help.

I define the term "successor" as:

I define the term "maybe succcesor" as:

 

[doronshadmi]

Only examples are given. No definitions.

Wrong.

({Z} IsSuccessorOf Z) OR ({Z} ~IsSuccessorOf Z) is a wff that defines {Z} such that it is not necessarily a successor of Z.

 

[Nonpareil]

Wrong.

({Z} IsSuccessorOf Z) OR ({Z} ~IsSuccessorOf Z) is a wff that defines {Z} such that it is not necessarily a successor of Z.

No, it doesn't. It says, very simply, that {Z} may or may not be the successor of Z.

It does not tell us how we know whether or not {Z} is a successor of Z. That is what we are trying to pry out of you.

 

[Little 10 Toes]

Besides doronshadmi, when asked about successors, you only now started talking about how it might not be a successor after all.

 

[doronshadmi]

It does not tell us how we know whether or not {Z} is a successor of Z. That is what we are trying to pry out of you.

By the result of the relation between {Z} and Z.

(If {Z} IsSuccessorOf Z, then Z is incomplete) OR (If {Z} ~IsSuccessorOf Z, then Z is complete)

Again, straightforward examples are given in:

http://www.internationalskeptics.com/forums/showpost.php?p=11271494&postcount=1388

http://www.internationalskeptics.com/forums/showpost.php?p=11274453&postcount=1427

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Once again, by the standard definition of successor, Successor(Z) = Z u {Z}

By my non-standard definition of successor, Successor(Z) is {Z} only if {Z} is used as a successor of Z (which means that also {Z}~$Z holds).

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As long as you try to understand the relations between {Z} and Z by the standard definition, you have lost it.

 

[Nonpareil]

By the result of the relation between {Z} and Z.

What relation?

(If {Z} IsSuccessorOf Z, then Z is incomplete) OR (If {Z} ~IsSuccessorOf Z, then Z is complete)

That does not explain the definition of "IsSuccessorOf".

Again, straightforward examples are given in:

http://www.internationalskeptics.com/forums/showpost.php?p=11271494&postcount=1388

http://www.internationalskeptics.com/forums/showpost.php?p=11274453&postcount=1427

Neither do those.

Once again, by the standard definition of successor, Successor(Z) = Z u {Z}

Or that.

By my non-standard definition of successor, Successor(Z) is {Z} only if {Z} is used as a successor of Z (which means that also {Z}~$Z holds).

Or that.

As long as you try to understand the relations between {Z} and Z by the standard definition, you have lost it.

You have yet to show that there was anything to find.

 

[doronshadmi]

What relation?

First of all ({Z} IsSuccessorOf Z) OR ({Z} ~IsSuccessorOf Z) is syntactically valid by http://www.internationalskeptics.com/forums/showpost.php?p=11269502&postcount=1344.

Based on this validity, semantics (i.e. what the strings mean (some model)) is given by:

http://www.internationalskeptics.com/forums/showpost.php?p=11274453&postcount=1427

http://www.internationalskeptics.com/forums/showpost.php?p=11271494&postcount=1388

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EDIT:

"(If {Z} IsSuccessorOf Z, then Z is incomplete) OR (If {Z} ~IsSuccessorOf Z, then Z is complete)" uses also semantics.

Please look at https://en.wikipedia.org/wiki/Formation_rule.

 

[Nonpareil]

First of all ({Z} IsSuccessorOf Z) OR ({Z} ~IsSuccessorOf Z) is syntactically valid by http://www.internationalskeptics.com/forums/showpost.php?p=11269502&postcount=1344.

I didn't say it wasn't. It just isn't what anyone is looking for.

That would be, in case you have missed the past three years of discussion, a definition of "successor".

Based on this validity, semantics (i.e. what the strings mean (some model)) is given by:

http://www.internationalskeptics.com/forums/showpost.php?p=11274453&postcount=1427

http://www.internationalskeptics.com/forums/showpost.php?p=11271494&postcount=1388

No, it isn't.

What is the definition of "successor", doron?

 

[jsfisher]

For anyone who has forgotten some earlier great moments in Doronetics, we have also been told that 2 may or may not be a member of the set containing 2 as its only member.

0.25 and 1/4 are different numbers.

A set is the union of its members.

And so on, but never, ever has Doronshadmi successfully defined any of his invented terms.

 

[doronshadmi]

jsfisher claims that ({Z} IsSuccessorOf Z) OR ({Z} ~IsSuccessorOf Z) is a tautology (always true) and therefore useless.

It may looks useless syntactically, but if semantics is also used, one enables to demonstrate models that can be used in order develop an interesting mathematical framework, that dose no follow after the, so called, standard mathematical framework.

 

[doronshadmi]

No, it isn't.

No one force you to think otherwise.

But there are results to your decisions, and in this case you can't realize why sets N or S (as shown in http://www.internationalskeptics.com/forums/showpost.php?p=11274453&postcount=1427) are incomplete.

 

[Little 10 Toes]

Still haven't defined successor.

 

[doronshadmi]

For anyone who has forgotten some earlier great moments in Doronetics, we have also been told that 2 may or may not be a member of the set containing 2 as its only member.

2 is not the same as {2}.

0.25 and 1/4 are different numbers.

If also structural properties are considered.

A set is the union of its members.

A set includes the members (if exist) of unioned sets, where one of the cases is X u X.

And so on, but never, ever has Doronshadmi successfully defined any of his invented terms.

It is true that you successfully follow aftero what I just wrote above.

 

[Nonpareil]

No one force you to think otherwise.

But there are results to your decisions, and in this case you can't realize why sets N or S (as shown in http://www.internationalskeptics.com/forums/showpost.php?p=11274453&postcount=1427) are incomplete.

That would be because you have not defined "successor".

 

[doronshadmi]

Still haven't defined successor.

I believe you that you are unable or don't wish to combine the syntactic and semantic accepts of the considered subject.

 

[doronshadmi]

That would be because you have not defined "successor".

It is defined.

You simply don't wish to combine the syntactic and semantic accepts of the considered subject, in order to realize that it is defined, but that is your choice, and it is perfectly ok with me.

 

[Nonpareil]

It is defined.

No, it's really not.

 

[Little 10 Toes]

No, it's really not.

Have to agree.

 

[doronshadmi]

No, it's really not.

Your reality is the result of your choice not to combine the syntactic and semantic accepts of the considered subject.

 

[Little 10 Toes]

Is there a reason why you can't define successor?