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Cont: Deeper than primes - Continuation 2

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doronshadmi said:
You continue to define the Archimedean Property in terms that do not distinguish between the finite and the infinite.
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It also doesn't distinguish between the possible genders of my offspring. Neither the possible genders of my offspring nor cardinality are relevant to the definition.

If you can prove otherwise, we'd all be delighted to see your proof.
 
jsfisher said:
It also doesn't distinguish between the possible genders of my offspring. Neither the possible genders of my offspring nor cardinality are relevant to the definition.

If you can prove otherwise, we'd all be delighted to see your proof.
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You, again, ignore the fact that you continue to define the Archimedean Property in terms that do not distinguish between the finite and the infinite, by define it also on infinitely many things.
 
doronshadmi said:
At least is not restricted to one and only one thing.
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Then it should be easy for you to give us just one of the possible values. Here are some wrong answers, please answer in the same fashion:

0
-17
Pi
257.889

Your answer is?

My more or less friendly advice is that you drop the Archimedean property ASAP. You saw it mentioned on Wikipedia, and thought you found a promising angle of attack there. You didn't, and you don't understand the concept.
 
doronshadmi said:
You, again, ignore the fact that you continue to define the Archimedean Property in terms that do not distinguish between the finite and the infinite, by define it also on infinitely many things.
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You, again, ignore the fact that cardinality has no relevance to the definition. If you can show otherwise, please do so, but another of your bare assertions doesn't show anything.
 
doronshadmi said:
So x simply marks endless larger things or endless smaller things, no matter what names are given to them.
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So you agree, then, that the reals has no largest element. Why did you argue against it if you now agree with it?
 
jsfisher said:
So you agree, then, that the reals has no largest element. Why did you argue against it if you now agree with it?
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Endless larger or the endless smaller things are not any particular (fixed) value, where largest or smallest values are particular (fixed) values.

So if the reals can't be defined in terms of largest or smallest value, then they are also infinitesimals (for example: endless smaller values that are > 0), but the Archimedean property disallows infinitesimals.

So, please make up your mind.
 
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Hevneren said:
Sorry, but you still haven't answered. If there's no Archimedean property, some x greater than or equal to any natural number must exist. Can you give us an example of such an x?
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Sorry, but you are still missing my answer.

Endless larger or endless smaller things are not restricted to fixed value like your requested x.

EDIT: http://www.internationalskeptics.com/forums/showpost.php?p=11735330&postcount=2631.

EDIT: Also please look at http://www.internationalskeptics.com/forums/showpost.php?p=11735353&postcount=2635.
 
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doronshadmi said:
Endless larger or the endless smaller things are not any particular (fixed) value, where largest or smallest values are particular (fixed) values.
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Ok.

So if the reals can't be defined in terms of largest or smallest value
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Ok.

then they are also infinitesimals
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And you were fine up to here, but this does not follow.

(for example: endless smaller values that are > 0)
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Endlessly smaller values > 0 are not infinitesimals.

but the Archimedean property disallows infinitesimals.
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No, the Archimedean Property doesn't disallow any such thing. Either the thing has the property or not.

Are you that unfamiliar with the definitions of these things?
 
I wish to clarify something.

Given a non-composed endless straight line and a point not on that line, there are endless larger non-composed circles that are smaller than that line, and there are endless smaller non-composed circles that are larger than that point.

Yet pi is a proportion among the endless larger and the endless smaller non-composed circles.

So a fixed value can be related to infinitely many things as long as it is not used to define their amount, their sum are any other fixed value that contradicts their property of being endless larger or endless smaller things.

For more details, search for Nicholas of Cusa.
 
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doronshadmi said:
So what they are?
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Endlessly smaller values would be an endless sequence of smaller and smaller values.

Or did you mean infinitesimals? For that, I'll refer you to the wikipedia entry for Archimedean Property, since it provides a good functional definition for infinitesimal as it relates to the Archimedean Property, and it will also expose you to the definition of, you know, the Archimedean Property.

Two birds with one stone as it were.
 
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