Re: tommy1729 set axioms

On Tue, 15 Jul 2008 18:41:19 EDT, amy666 <tommy1729@xxxxxxxxxxx>
wrote:

On 15 Jul., 21:40, amy666 <tommy1...@xxxxxxxxxxx>
wrote:
Jessy wrote :

amy666 <tommy1...@xxxxxxxxxxx> writes:

 [] in [[]] AND NOT [] in [[]]

what is the union of [] and NOT [] ?

You're confused about what NOT means here.  NOT
is
the negation that
applies to formulas, i.e., I mean:

  [] in [[]] and NOT ([] in [[]]).

NOT [] is meaningless.

oh i see ...

then i will have a second look on what you wrote.

it still holds.

[] and NOT [] both in [[]].

no problem.


?? You still misinterprete NOT.
Your theory gives two contradictory answers to the
question "Is [] an element of [[]]?", namely "yes"
and "no" at the
same time.
(Provided our interpretation of the brackets you
introduced is right)
"Yes" because in general x is an elment of [x] by
definition
"No" because no x can be an element of the empty set
[] (=[[]] by
Axiom)
by definition of empty set, especially if x=[].



--
Jesse F. Hughes
"If the world weren't rather strange, by now I
should
at least be with
some research group talking about my number
theory
research."
-- James S. Harris learns the world
learns the world is a funny place

regards

tommy1729

regards

tommy1729


sure both yes and no since [] = NOT [].

No. If there were such a thing as "NOT []"
then there'd be no problem with both []
and "NOT []" being an element of the same
set. At least no purely logical problem.

But nobody but you has said anything about
this silly "NOT []" thing. People have pointed
out that your theory proves that "[] is an elemeent
of [[]]" is true and it _also_ proves that the very
same statement is false.

How you choose to define "NOT []" is
irrelevant to that. Your theory proves that
a certain statement is true and it also proves
the same statement is false. That means the
theory is inconsistent, by definition.

David C. Ullrich

"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
.

Relevant Pages

  • Re: tommy1729 set axioms
    ... You still misinterprete NOT. ... Your theory gives two contradictory answers to the ... "No" because no x can be an element of the empty set ... -- James S. Harris learns the world ...
    (sci.math)
  • Re: Some basic set theory questions
    ... that the empty set exists to a proof that the empty set exists. ... Perhaps a reasonably charitable reading of my remarks would ... anyone who's not for some reason worrying about ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
  • In a Bad Mood
    ... I don't know why I'm in such a bad mood, ... I read someone's argument that relativity is contradictory, ... or that Godel was wrong, or that Cantor was a charlatan, ...
    (sci.logic)
  • Re: finite sets and minimal subsets
    ... _Every_ set has a minimal subset, namely the empty set. ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
  • Re: In a Bad Mood
    ... >>I read someone's argument that relativity is contradictory, ... >>or that Godel was wrong, ... would you like me to continue the discussion on the halting ... > from the 1st digit to infinite number of digits. ...
    (sci.logic)
Loading