Re: The Smullyan paradox
- From: LauLuna <laureanoluna@xxxxxxxx>
- Date: Sat, 16 Feb 2008 10:08:41 -0800 (PST)
On Feb 16, 2:33 pm, "LordBeotian" <pokips...@xxxxxxxx> wrote:
Smullyan formulated the following paradox:
--
let A and B be two numbers such that A=2B or B=2A
than we can prove that
(*) The difference A-B in case A>B is strictly lower than the difference B-A
in case B>A.
Proof: let's fix x:=A
in case A>B we have B=x/2 and A-B=x/2
in case A<B we have B=2x and B-A=2x
Surely you mean B-A=x.
and obviously 2x>x/2 QED.
This is clearly paradoxical because in the same way we can prove the converse
statement.
---
Now my question is: is (*) a meaningful mathematical statement? It seems to
be so, but if it is so how can it be formulated in (for example) the language
of PA or any other formal language?
.
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- The Smullyan paradox
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