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Re: ? 534 Finis
Posted:
Aug 13, 2014 3:45 PM


mueckenh@rz.fhaugsburg.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.



