A hidden assumption

drkitten said:
Unfortunately, I don't. That paper demonstrates pretty conclusively that you have no idea how transfinite mathematics works and that you've learned to parrot a few symbol strings but have no idea what they actually mean.

I had hoped that you could provide evidence against the obvious conclusion and in support of the idea that you had even a marginal understanding of Cantor's theories.

By your own admission, you have none.



You mean this?



Easily responded to. I don't believe you know what any of the words in that phrase mean, either.
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Here it is again:

Contor's notion of a complete set means that the set of all things of some common property has an exact magnitude(a complete thing) which he called cardinal number.

Now please show how a complete set exists without a complete (exact) cardinal.

If you claim that aleph0 is not an exact (complete) value, then Cantor's transfinite system does not hold.
 
doronshadmi said:
Contor's notion of a complete set means that the set of all things of some common property has an exact magnitude(a complete thing) which he called cardinal number.
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Showing me a set of words that you don't understand a second time will not make you understand them.


Now please show how a complete set exists without a complete (exact) cardinal.
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Domain error.

Once again, you have produced a question that cannot be answered because you are using words in ways incongruent to their meanings.


If you claim that aleph0 is not an exact (complete) value,
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Exact and complete are not synonyms. There is no such thing as a "complete" value, because completeness is a property of sets, not of numbers.
 
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drkitten said:
There is no such thing as a "complete" value, because completeness is a property of sets, not of numbers.
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Value is a general concept which is also related to cardinal numbers, where in the case of cardinal number the value is called magnitude.

The completeness of a set and its magnitude are inseparable (the completeness of a set is measured by the value of its cardinal ( http://en.wikipedia.org/wiki/Cardinal_number )), so please stop your zigzag and show that aleph0 is separable of the set of Natural numbers.

Futhermore, by using Dedekind's notion of 1-to-1 mapping Cantor proved that any unbounded subset of N has the same cardinality as N. It can be done only if |N| is inseparable of N (where N is complete).

If you cannot do that, then your claims do not hold water.
 
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doronshadmi said:
Value is a general concept which is also related to cardinal numbers, where in the case of cardinal number the value is called magnitude.

The completeness of a set and its magnitude are inseparable (the completeness of a set is measured by the value of its cardinal ( http://en.wikipedia.org/wiki/Cardinal_number )), so please stop your zigzag and show that aleph0 is separable of the set of Natural numbers.

Futhermore, by using Dedekind's notion of 1-to-1 mapping Cantor proved that any unbounded subset of N has the same cardinality as N. It can be done only if |N| is inseparable of N (where N is complete).
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More words that you demonstrably don't understand.


If you cannot do that, then your claims do not hold water.
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I should put a laughing dog here. You haven't presented a well-founded conjecture that can be proven or disproven. The words you used are not meaningful in the combination that you use them.

And my claims therefore don't hold water. How rich....
 
drkitten said:
And my claims therefore don't hold water. How rich....
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Hmmm, just out of interest, other than the statement that doron understands very few of the words he uses, what claims did you make, drkitten?
 
jsfisher said:
Hmmm, just out of interest, other than the statement that doron understands very few of the words he uses, what claims did you make, drkitten?
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Well, last night I claimed -- correctly -- that Colonel Mustard did it in the conservatory with the lead pipe. Or maybe in the ballroom with Miss Scarlet; I don't remember exactly. It was late and I had been drinking a bit. I'm afraid that some kittens just can't hold their lighter fluid.

Tonight I'm sticking to wood stain.
 
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drkitten said:
No, thank you. My spoon is broken.
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Yes I know. It is permanently broken all along the dialog.
drkitten said:
You haven't presented a well-founded conjecture that can be proven or disproven.
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I did better than that.

I provided the simplest state that actually enables us to present some well-founded conjecture that can be proven or disproven.

This simplest state is used by you as a hidden assumption of any premise and conclusion.

Please carefully follow:

http://www.internationalskeptics.com/forums/showpost.php?p=3628609&postcount=707

http://www.internationalskeptics.com/forums/showpost.php?p=3630543&postcount=717

http://www.internationalskeptics.com/forums/showpost.php?p=3633592&postcount=723

if you wish to avoid the hidden assumption.
 
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doronshadmi said:
I provided the simplest state that actually enables us to present some well-founded conjecture that can be proven or disproven.
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You claimed that the simplest state is silence ... but you're not showing any evidence of that.
 
nathan said:
So, when you wrote 'The completeness of a researchable thing is exactly its restriction.' you were not describing a researchable thing? Is that what you are now saying?
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A researchable thing cannot be both researchable AND complete.

If you force completeness on a researchable thing you are actually limiting it.

The incompleteness of a researchable thing is actually its natural ability to be developed both from within and from without, without any limitation.

The thing that is naturally not changed under any manipulation is simplicity at its self state, but then it is both invariant and non-researchable and it is the best point of view of any researchable thing, which is naturally a never ending developing thing, that is not restricted by any limitation like a completed development.
 
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doronshadmi said:
Since when you are talkin' to youself (and you are also correct, in ths case)?
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Goodness, I haven't heard that particular comeback since I left the elementary school playground. Is that the best you can do for substantive comment?

I'm afraid, Doron, that it's obvious to anyone with a passing knowledge of the field that you are very badly abusing notation and terminology. That in and of itself is not necessarily bad --- but it's also obvious that you have no idea THAT you are doing it, or in what regard your terminology differs from the standard. You've been urged to produce clear definitions for your concepts since this first page of this thread, and have systematically avoided doing so. When I start holding your feet to the fire about "no, that's not what that word means; no, those words are not synonymous; no, that adjective cannot be applied to that word," you not only fail to correct your terminology to re-express the question, but you get hostile.

Infantilely so, in this case.

Your puerile response is the best possible demonstration I could have hoped for that you really don't understand any of the concepts you're slinging around.
 
doronshadmi said:
Please explain us how (for example) |N| is not related to N.
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What exactly do you mean by "not related"? Are you expecting |N| to be a member of N? It isn't, nor should it be expected to be. Aleph-null isn't a natural number.

Also please explain us why 1+|N|=|N|+1 and why 1+ω≠ω+1?
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"Us" don't need that explained; you are the only one lost at sea. It would be very difficult explaining it to you because you understand neither cardinal nor ordinal numbers. And helping you understand much of anything has proven very difficult because you have your kindergarten perception filters permanently enabled.
 
drkitten said:
Goodness, I haven't heard that particular comeback since I left the elementary school playground. Is that the best you can do for substantive comment?

I'm afraid, Doron, that it's obvious to anyone with a passing knowledge of the field that you are very badly abusing notation and terminology. That in and of itself is not necessarily bad --- but it's also obvious that you have no idea THAT you are doing it, or in what regard your terminology differs from the standard. You've been urged to produce clear definitions for your concepts since this first page of this thread, and have systematically avoided doing so. When I start holding your feet to the fire about "no, that's not what that word means; no, those words are not synonymous; no, that adjective cannot be applied to that word," you not only fail to correct your terminology to re-express the question, but you get hostile.

Infantilely so, in this case.

Your puerile response is the best possible demonstration I could have hoped for that you really don't understand any of the concepts you're slinging around.
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You will do anything in order not to answer to http://www.internationalskeptics.com/forums/showpost.php?p=3635569&postcount=747, isn't it?
 
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