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Topic: Only for mathematicians!
Replies: 3   Last Post: Aug 18, 2014 7:27 PM

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Ben Bacarisse

Posts: 1,404
Registered: 7/4/07
Re: Only for mathematicians!
Posted: Aug 17, 2014 11:40 PM
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mueckenh@rz.fh-augsburg.de writes:

> On Saturday, 16 August 2014 21:49:03 UTC+2, Ben Bacarisse wrote:
>
>

>> | can you show a formula of set theory involving your bijection f form Z
>> | to Z (f(x) = x + 1) which is false in set theory and true with the
>> | correct "interpretation of infinity"? (Or vice versa of course.)

>
> It is not easy to find a difference between a bijection that is
> claimed an actually infinite set and a potentially infinite bijection
> between two equal sets. That's the reason why set theory could exist
> for such a long time! The striking argument was always the
> countability of |N "by definition" and in the potential sense.


I thought not.

> Therefore I have applied two different sets. If actual infinity is
> assumed, then one of the sets gets exhausted before the other. This is
> a result of mathematics, but onlz if infinitz is actual. Otherwise we
> have the bijection going on and on. But such a set would never supply
> an anti-diagonal or a complete list of all algebraics. It is this
> subtle switching infinities that has gone unnoticed for such a long
> time.


Same mathematics, different words.

--
Ben.



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