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Topic: § 534 Finis
Replies: 8   Last Post: Aug 18, 2014 2:40 AM

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Ben Bacarisse

Posts: 1,522
Registered: 7/4/07
Re: § 534 Finis
Posted: Aug 16, 2014 5:55 PM
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mueckenh@rz.fh-augsburg.de writes:

> On Saturday, 16 August 2014 21:49:10 UTC+2, Ben Bacarisse wrote:
>> mueckenh@rz.fh-augsburg.de writes:
>>

>> > On Friday, 15 August 2014 22:32:19 UTC+2, Ben Bacarisse wrote:
>> >
>> >

>> >> > What do you understand by my "misunderstanding"?
>> >>
>> >> Exactly what you said: that the sequence of cardinalities should have
>> >> limit 0 if set theory was right.

>> >
>> > In fact, if the set limit was the set at omega.

>
>> You'd need to define the WMglish term "the set at omega". I explained
>> how set sequence limits can be defined in the little paper I wrote and
>> there is no "set at omega" involved.

>
> You mean that paper that has been considered nonsense by everybody who
> read it?


Yes, that's the one. Do you think the definition of a set sequence
limit is wrong? I'd be happy to correct any errors. After all, the
definition relies on numerical limits that you are well versed in using.
Did you find the examples I gave unclear?

>> You are free to reject these
>> limits, or to label them with any WMglish adjective you like, but you
>> can't choose what set theory says about it's own definitions.
>>

> Set theory names the final set of all naturals omega.

Don't try to change the subject by saying something else wrong in the
hope that I'll chase down another rabbit hole. Set theory says that the
limit of the set sequence s_n is {} and that the limit of the |s_n| is oo.
You find this puzzling for some reason. Your claim: "the sequence of
cardinalities should have limit 0 if set theory was right" shows a
misunderstanding of what set theory says.

<snip>
>> > What are the infinitely many elements that the cardinality measures?
>>
>> The limit does not measure anything, because there is no "final set" for
>> it to measure. That is the core of you misunderstanding.

>
> It is also Cantor's misunderstanding.


You are the historian, so I won't argue. If you know that Cantor
thought that the limit of the cardinalities of a set sequence should
measure, in some sense, the cardinality of the limit set, then he did
indeed share your misunderstanding.

<snip>
--
Ben.



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