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Topic: § 534 Finis
Replies: 4   Last Post: Aug 18, 2014 8:28 PM

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Ben Bacarisse

Posts: 1,404
Registered: 7/4/07
Re: § 534 Finis
Posted: Aug 18, 2014 11:53 AM
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mueckenh@rz.fh-augsburg.de writes:

> On Monday, 18 August 2014 05:38:18 UTC+2, Ben Bacarisse wrote:
>>
>> > I use "to list" if all terms of a bijection have to be given because
>> > there is no abbreviating rule.

>
>> So is there no listing of a finite set?
>
> Why not? Of course a finite set (and only a finite set) can be listed
> by writing all its members.


Yes, I must remember that what you give a definition it can't be taken
to define all cases. It seems that "to list" is used as stated, but
also for finite sets and, quite probably, probably for others as well.
I doubt it has any meaning at all. In English, a listing is a bijection
with N. You don't see able to say what "a listing" means in WMglish.

>> > This applies in case of sequences
>> > without finite rule like real numbers without finite description. The
>> > Kolmogorov complexity of such sequences is infinite.

>
>> a sequence of rationals with finite KC can be
>> given, but none for the reals.

>
> Wrong. Consider pi, 2pi, 3pi, ...


Why do you keep editing my words without any indication (this time mid
sentence!)? It's deceitful, and in this case there was a typo in what I
wrote, so there was no need to edit me at all. Let me put it this way:
if we accept your (minor) abuse of notation and describe unending
sequences that can be finitely defined as having finite KC, and unending
sequences that can not be finitely defined as having "infinite KC", then
you are stating that there can be no finite description of the list of
all reals (because at least one, according to you, has infinite KC) but
there is for the list of all rationals (take the S I defined, for
example -- it is an effective procedure for generating the positive
rationals one by one).

Of course, this should surprise no one, since it's standard mathematics,
and all of your mathematics is standard mathematics. You just lob in a
few word bombs in WMglish to get an argument going.

--
Ben.



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