Prev: On May 24 2009, 12:20 pm, Martin Musatov >marty.musa...@gmail.com< wrote: < Martin Musatov wrote: < < WM wrote: < < < On 24 Mai, 09:17, lwal...@lausd.net wrote: < < < < On May 23, 2:14 am, WM <mueck...@rz.fh-augsburg.de> wrote: < < < < < < On 23:
Next: Mathematical-Induction unioned with Indirect Infinitude of Primes template #679 Correcting Math
From: porky_pig_jr on 15 Jul 2010 01:11
On Jul 15, 12:03 am, "sci.math" <marty.musa...(a)gmail.com> wrote:
> On May 24 2009, 12:20 pm, Martin Musatov <marty.musa...(a)gmail.com<
> wrote:< Martin Musatov wrote:
> < < WM wrote:
>
> < < < On 24 Mai, 09:17, lwal...(a)lausd.net wrote:
> < < < < On May 23, 2:14 am, WM <mueck...(a)rz.fh-augsburg.de< wrote:
> <
> < < < < < On 23 Mai, 03:45, "Dik T. Winter" <Dik.Win...(a)cwi.nl< wrote:
> < < < < < < I have still not found a definition of "potential
> infinity" that is valid
> < < < < < < within ZF.
> < < < < < The definition of potential infinity would avoid that
> obvious
> < < < < < contradiction. I do not know whether it would make ZF free
> of
> < < < < < contradictions. But that is not my concern. I need that
> axiom only for
> < < < < < arithmetics where the natural numbers already are known.
> <
> < < < More precisely, I don't need any axiom at all. Natural numbers
> are
> < < < there whether or not someone takes the trouble to "formalize"
> them.
> < < < But it will help you (Dik) to understand potential infinity.
> <
> < < < < Once again, this thread is quickly approaching that thousand
> post
> < < < < mark yet again, which means that Google users such as WM and
> < < < < myself will be leaving the thread soon.
> <
> < < < So it is.
> <
> < < < < I noticed how earlier, a standard set theorist (I forgot which
> one)
> < < < < made a crack about how since WM is an ultrafinitist and
> Google's
> < < < < maximum thread length is a thousand,
> <
> < < < This is so since the thread "A consideration concerning the
> diagonal
> < < < argument of G. Cantor", started by albrecht here in sci.logic in
> Jan.
> < < < reached 9244 posts in Oct. 2008.
> <
> < < < < this means WM must
> < < < < believe that 1001 is the largest number. Debates about Google
> and
> < < < < other ways to access Usenet aside, I doubt that there's a link
> < < < < between ultrafinitism and Google use. (Phil Carmody might have
> < < < < found a link between being a so-called "crank"/"idiot" and
> Google,
> < < < < but not all "cranks" are ultrafinitists. In particular, I'm
> not an
> < < < < ultrafinitist -- I freely admit that the number 1002 exists,
> and WM's
> < < < < upper bound far exceeds this number.)
> <
> < < < Please note: There is no upper bound. There is no largest
> natural
> < < < number.
> <
> < < < < Since I'll be leaving the thread soon, let me at least comment
> on
> < < < < WM's latest attempt to work with Potential Infinity:
> <
> < < < < < Axiom Of Potential Infinity: For every natural number there
> is a set
> < < < < < that contains this number together with all smaller natural
> numbers,
> < < < < < and for every set of natural numbers there is a natural
> number that is
> < < < < < larger than every number of the set.
> <
> < < < < I see nothing wrong with this axiom, or trying to replace the
> usual
> < < < < Axiom of Infinity (which WM calls the Axiom of _Actual_
> Infinity in
> < < < < order to distinguish it from his new axiom) of ZF with this
> axiom, to
> < < < < obtain the new theory ZF-(Actual) Infinity+WM's Potential
> Infinity. It
> < < < < has no affect on the Axiom of Extensionality, unlike WM's
> previous
> < < < < attempts to define Potential Infinity, so the standard set
> theorists
> < < < < can't use Extensionality as an excuse to ignore this axiom.
> <
> < < < < We might even try to write the axiom in the language of ZF. We
> try:
> <
> < < < < AneN (Ex (AmeN (m<=n -< mex))) & Ay (EneN (AmeN (mey -< m<n)))
> <
> < < < < But there's one problem -- the set N, of course, is not
> supposed to
> < < < < exist in WM's theory, so how can we even mention N in this
> axiom,
> < < < < when we can only talk about that which _exists_?
> <
> < < < N exists just as a potentially infinite set, AneN means for all
> < < < natural numbers that you can think of, specify, name, identify,
> < < < write, ... briefly: For all that are there.
> <
> < < < < Perhaps, instead of a set N, we can define the one-place
> predicate
> < < < < N(x), intended to agree with the standard definition of
> natural number
> < < < < (so that N(x) <-< x is a natural number). Then the axiom
> becomes:
> <
> < < < < An (N(n) -< Ex (Am ((N(m) & m<=n) -< mex))) & Ay (En (N(n) &
> Am ((N(m)
> < < < < & mey) -< m<n)))
> <
> < < < < (As an aside, what's interesting about WM's axiom is that if
> we
> < < < < replace the word "natural" with "ordinal," then the resulting
> < < < < formula is actually a theorem of ZF, and serves as a
> definition
> < < < < of successor and limit ordinals.)
> <
> < < < Is it? "For every set of ordinals, there is an ordinal larger
> than the
> < < < ordinals of that set."
> < < < This means that you can pick every set of ordinals. Doesn't it
> imply
> < < < the existence of the set of all ordinals? Or do you presuppose
> that
> < < < you can pick every set of ordinals because the set of all
> ordinals is
> < < < anyhow excluded?
> <
> < < < However: If so, then you see that set theory does not improve
> the
> < < < situation.
> < < < In potential infinity the set N is never understood as a set
> that
> < < < cannot be increased.
> < < < In set theory, N is a set that cannot be increased, but on the
> next
> < < < level the set of all ordinals, as a set that cannot be
> increased, must
> < < < be excluded.
> <
> < < < This always reminds me on the problem of initial creation. The
> world
> < < < could not create itself. So God is introduced. But the question
> who
> < < < created God is forbidden.
> < < <Jesus is Lord. Amen!
> < < < If we use the above complete set N (that cannot be increased by
> any
> < < < element), then we are forced to introduce larger ordinals. But
> then we
> < < < are not allowed to use the set of all these ordinals. So we
> haven't
> < < < won anything but have left the solid grounds of science and have
> < < < invented a highly questionable hypothesis. That is why I find
> that
> < < < mathematics has evolved to what better would be called math.
> <
> < < < Regards, MM
> <
> < There is only one thing the preceding chaos proves and proved
> < definitively and that is the fact that P==NP. "Only a foold would
> < insist on an impossibility to which there is no gain." Martin
> Michael
> < Musatov %P-Complete:

:-)
From: I.N. Galidakis on 17 Jul 2010 21:47
porky_pig_jr(a)my-deja.com wrote:
> :-)

Brave, yet lame attempt at cheap humor by the resident anonymous newsgroup
clown.

Keep it up "Porky".
--
I.

From: Don Stockbauer on 17 Jul 2010 23:59
On Jul 17, 8:47 pm, "I.N. Galidakis" <morph...(a)olympus.mons> wrote:

To Pee or To Not Pee: this is the question.


"10-4 back door, face the penis to the urinal and let 'er roar."
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