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Topic: Only for mathematicians!
Replies: 24   Last Post: Aug 22, 2014 6:20 PM

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Ben Bacarisse

Posts: 1,316
Registered: 7/4/07
Re: Only for mathematicians!
Posted: Aug 18, 2014 4:50 PM
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mueckenh@rz.fh-augsburg.de writes:

> On Monday, 18 August 2014 05:40:22 UTC+2, Ben Bacarisse wrote:
>> mueckenh@rz.fh-augsburg.de writes:
>>

>> > The striking argument was always the
>> > countability of |N "by definition" and in the potential sense.


This time the hard bit you snipped was my asking:

| 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.)

and it was your admission that you can not provide such a thing the
prompted me to say:

>> I thought not.
>>

> Most mathematicians don't even know that "finished infinity" is more
> than a joke.


Some, like you, appear not to be able to define it without more
undefined words. Maybe you can show a formula, involving some infinite
set, that is true in set theory with its "finished infinities" and false
otherwise (or vise versa of course)? You can't do for bijections
between sets, but maybe you can for just a set.

>> > It is this
>> > subtle switching infinities that has gone unnoticed for such a long
>> > time.

>>
>> Same mathematics, different words.

>
> No. But difficult to see the difference, without my proof.


A formula, provably true in one and false in another, would be a start.
The only proof I've see is of a formula that is true in set theory.
presumably it's true in your world too. So far, all the same
mathematics, despite the dramatic words.

--
Ben.



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