In article <e05a3157-6fb1-4927-92ec-7a10f4a07...@b9g2000prh.googlegroups.com>,
Student of Math  <omar.hosse...@gmail.com> wrote:

   [...]

Where you have used ZF(C) in your proof?

There are STANDARD constructions of R using Q, Q using Z, Z using N,
and N using ZF (no choice needed at any stage), which show that
everything I did can be done in ZF. For example, you can see all of
these constructions (as well as the definitions required) in "Proof
and Fundamentals: A First Course in Abstract Mathematics" by Ethan
D. Bloch, Birkhauser Publ, 2000, Chapter 8 (pp 323-362). You construct
the naturals by using the Axiom of infinity. You construct the
integers as a set of equivalence classes of pairs of natural
numbers. You construct the rationals as a set of equivalence classes
of the set of all pairs (a,b) with a and b integers, b nonzero. Then
you construct the real numbers as pairs (L,R), where L and R are sets
of rationals satisfying certain properties. All is done at the level
of sets.

Now, how about ->your<- alleged argument for the Continuum Hypothesis?

--
=====================================================================> "It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes" by Bill Watterson)
=====================================================================
Arturo Magidin
magidin-at-member-ams-org

Hi,
I think i have found a way to answer to Cantor's Continuum hypothesis
by using this
assumption : [0,1/3^n]={0} when n tends to the infinity.
If this assumption is from ZFC?

Regards,
Omar

On Apr 15, 5:00=A0pm, magi...@math.berkeley.edu (Arturo Magidin) wrote:

Now, how about ->your<- alleged argument for the Continuum Hypothesis?

I want to express it as soon as it possible.

On 14-04-2008 14:58, Student of Math wrote:
perhaps it maybe strang or impossible but, I think I have prove
Continuum Hypothesis
The Continuum Hypothesis can neither be proved nor disproved in ZFC.

What is your idea about this assumption:
There exists the smallest cardinal number |S_1| for which
aleph_0<|S_1| <=2^(aleph_0)

In article <03666749-9a48-4f82-8385-8e039d5a1...@a9g2000prl.googlegroups.com>,
James Dow Allen  <jdallen2...@yahoo.com> wrote:

On Apr 14, 8:59=A0pm, Jos=E9 Carlos Santos <jcsan...@fc.up.pt> wrote:
On 14-04-2008 14:58, Student of Math wrote:
perhaps it maybe strang or impossible but, I think I have prove
Continuum Hypothesis
The Continuum Hypothesis can neither be proved nor disproved in ZFC.
Aren't you assuming ZFC is consistent?
Perhaps Student of Math has disproven that.
James

The consistency of mathematics (ZF or NBG) is equivalent
to the consistency with either AC or not AC added, and
if AC is added, with CH or not CH added.w

If Student of Math has disproven that, we had better
change some of the axiomatization of set theory.
--
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558

On 2008-04-28, Student of Math <omar.hosseiny@gmail.com> wrote:
What is your idea about this assumption:
There exists the smallest cardinal number |S_1| for which
aleph_0<|S_1| <=2^(aleph_0)

That one is true. So how does the proof use that to prove CH?

- Tim

On Apr 14, 8:59=A0pm, Jos=E9 Carlos Santos <jcsan...@fc.up.pt> wrote:
On 14-04-2008 14:58, Student of Math wrote:
perhaps it maybe strang or impossible but, I think I have prove
Continuum Hypothesis
The Continuum Hypothesis can neither be proved nor disproved in ZFC.

Aren't you assuming ZFC is consistent?
Perhaps Student of Math has disproven that.

James

I see no reason why it should be true without the Axiom of Choice.

In article <83c7fc99-9293-4c3b-bed4-0510c8007...@y21g2000hsf.googlegroups.com>,
Student of Math <omar.hosse...@gmail.com> wrote:

it is shameful, my proof was worng completely and, the struggle ended.

Can't say I'm surprised.

sorry for taking your valuable time.

Had you presented your argument (with any caveats you wished) to begin
with instead of all that silly teasing and hedging and huffing, then
everyone's time (yours included) would have been better
served. Instead, you acted like a cheap strip-tease at a bad
vaudeville show.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org