Cont: Deeper than primes - Continuation 2

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jsfisher said:
Not me, no.
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Yes you, yes.

Because of these restrictions your reasoning can't distinguish between being a primitive and being an optional property of a given primitive.

This inability is the common cause of your misunderstanding of the last issues at hand.
 
Doron, if you have anything that qualifies as mathematics, please highlight that part.

Thanks.
 
Can't even meet a simple request about not providing links to links? Post #1627 refers back to #1605 which does not have the words define or definition being used by you. Is there a reason why you can't cut and paste the direct information? You have been wasting both my time and your time with not just posting the definition.
 
Little 10 Toes said:
Can't even meet a simple request about not providing links to links? Post #1627 refers back to #1605 which does not have the words define or definition being used by you. Is there a reason why you can't cut and paste the direct information? You have been wasting both my time and your time with not just posting the definition.
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Little 10 Toes, the definition of successor known only by using a reasoning, which enables to distinguish between the must-have (called primitive) and its optional (non must-have) properties.

As long as such distinction can't be done by your reasoning, and you insist to use this reasoning, you are simply waste your time in this thread.

http://www.internationalskeptics.com/forums/showpost.php?p=11284084&postcount=1527 very simply demonstrates how your reasoning can't handle with the issue at hand.
 
jsfisher said:
Doron, if you have anything that qualifies as mathematics, please highlight that part.

Thanks.
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jsfisher, if you are able to distinguish between being a primitive and being an optional property of a given primitive, then and only then your reasoning actually enables to value the fruitfulness of this distinction for mathematics.

As it currently stands, your used reasoning simply can't distinguish between being a primitive and being an optional property of a given primitive.

More details about the weakness of your currently used reasoning, are very simply demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=11304307&postcount=1624.
 
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zooterkin said:
How is the set of positive integers incomplete? Which numbers are missing?
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Positive integers (where each one of them is a finite number) that are not in the range of a set, which its size is determined by a given infinite number.

I am not talking about any particular positive integer, but about the fact that any particular positive integer has {positive integer} as its successor, where this mechanism prevents the completeness of the set of infinitely many positive integers.

By the standard definition of successor, Successor(n) = n u {n}

By my non-standard definition of successor, Successor(n) is {n} only if {n} is used as a successor of n (which means that also the option that {n} is not used as a successor of n holds).

Please look at http://www.internationalskeptics.com/forums/showpost.php?p=11257789&postcount=1169 and http://www.internationalskeptics.com/forums/showpost.php?p=11297273&postcount=1593.

http://www.internationalskeptics.com/forums/showpost.php?p=11264137&postcount=1251 (and its links) helps to understand the notion of a collection of infinitely many finite things (where in this case, a finite thing is each step).

Also http://www.internationalskeptics.com/forums/showpost.php?p=11271494&postcount=1388 is very helpful.
 
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zooterkin said:
Which ones are missing? In the set of all natural numbers, which ones are not there?
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doronshadmi said:
Those that are not written down.

EDIT:
In order to understand my answer, you first have to understand the notion of a singleton as a successor (for example http://www.internationalskeptics.com/forums/showpost.php?p=11259142&postcount=1179 , http://www.internationalskeptics.com/forums/showpost.php?p=11259373&postcount=1181 and http://www.internationalskeptics.com/forums/showpost.php?p=11259463&postcount=1185).
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doronshadmi said:
Positive integers (where each one of them is a finite number) that are not in the range of a set, which its size is determined by a given infinite number.

I am not talking about any particular positive integer, but about the fact that any particular positive integer has {positive integer} as its successor, where this mechanism prevents the completeness of the set of infinitely many positive integers.

By the standard definition of successor, Successor(n) = n u {n}

By my non-standard definition of successor, Successor(n) is {n} only if {n} is used as a successor of n (which means that also the option that {n} is not used as a successor of n holds).

Please look at http://www.internationalskeptics.com/forums/showpost.php?p=11257789&postcount=1169 and http://www.internationalskeptics.com/forums/showpost.php?p=11297273&postcount=1593.

http://www.internationalskeptics.com/forums/showpost.php?p=11264137&postcount=1251 (and its links) helps to understand the notion of a collection of infinitely many finite things (where in this case, a finite thing is each step).

Also http://www.internationalskeptics.com/forums/showpost.php?p=11271494&postcount=1388 is very helpful.
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Could you be more specific? Which of the set of natural numbers is not present in the set of natural numbers?
 
doronshadmi said:
I am not talking about any particular positive integer, but about the fact that any particular positive integer has {positive integer} as its successor
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No, it isn't. As you keep telling us, it is or is not the successor, that being an optional property which, and with a wave of our hands we can decide it isn't.

...where this mechanism prevents the completeness of the set of infinitely many positive integers.
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For any integer n, {n} may or may not be one of those doron-successor things, but so what? {n} isn't an integer. Its non-appearance in the set of integers is neither surprising nor relevant.
 
doronshadmi said:
I say that being a successor is an optional property of being a set, where also being incomplete is an optional property of being a set.

In both cases the must-have (non-optional property) is being a set.

Once again, Little 10 Toes, your current used reasoning simply can't deal even with http://www.internationalskeptics.com/forums/showpost.php?p=11295089&postcount=1586, and this is far from being good.
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And yet you still can't define this optional property.

Please define sucessor. And by the way, I was asking this question before you started claiming "primitive", and before you started claiming it was optional.
 
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