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Topic: ? 534 Finis
Replies: 3   Last Post: Aug 13, 2014 7:07 PM

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Ben Bacarisse

Posts: 1,573
Registered: 7/4/07
Re: ? 534 Finis
Posted: Aug 13, 2014 3:45 PM
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mueckenh@rz.fh-augsburg.de writes:

> On Wednesday, 13 August 2014 02:39:54 UTC+2, Ben Bacarisse wrote:
>>
>> > There is no finished infinity.
>
>> You've said this a gazillion times. What you won't say is what this
>> means.

>
> It means that a list of all algebraic numbers can be constructed and
> used to prove the existence of a transcendental number.
>

>> Obviously I knew you'd ignore my question
>
> Obviously you ignore this answer every time I give it. Why?


Not only do you not answer it, you don't even dare let the question
stand! You've cut it out, and if that means replying to half a
sentence, then so be it! I am sure there was a time when you had some
sense of academic integrity; when you would never have mangled quotes in
this shameful way, just to avoid a question your find troubling; when
you would have engaged with your critics rather than walking away. Try
to remember those days, when you reply here.

>> | Given, say, a bijection between N and the finite string over the Latin
>> | alphabet, can you write some formula that is true for this bijection in
>> | the wrong theory that is set theory, but true in WMaths? (Or vice

[edit: I used true in both places. It's clear, I hope, that I meant
true in one and false in the other.]
>> | versa, of course.) Maybe it is, in fact, the formula above?
>
> Simply take the list of all algebraic numbers. In set theory by
> diagonalization a transcendental can be obtained. In mathematics this
> is wrong.


So, no, you can't write a formula that is true for this bijection in set
theory and false WMaths[1]. Why not try a simpler one: a
formula that's false for f(x) = x + 1 (f: Z->Z) in set theory but true
in WMaths?

exists x c Z: not(x c image(f))

looks like a candidate because you have stated that it's only true "for
finite sets and in a wrong theory" but you steadfastly refuse to say
that it's true in WMaths. Why is that? Too daft even for you?

<snip>
--
Ben.



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