Re: A CHALLANGE TO CANTORIANS

On Aug 20, 2:15 pm, tommy1729 <tommy1...@xxxxxxxxx> wrote:
lwalke3 wrote:

On Aug 19, 7:48 am, David C. Ullrich
<ullr...@xxxxxxxxxxxxxxxx> wrote:
hint : 2^1729 is only finite and 2^aleph_0 is
aleph_1

What? Exactly how do you prove that 2^alph_0 =
aleph_1?

Again, even when you pretend to be "challenging"
us,
the things you say are simply oozing ignorance.

The confusion here is that many people, including
the
OP,
are misinformed as to the definition of aleph.
They
assume that the definition is:

aleph_0 = card(N)
aleph_(n+1) = 2^card(aleph_n)

This has nothing to do with being a crank. I've
seen
many
books and websites (not graduate-level set theory
texts,
of course, but books geared towards a wider
audience)
that define aleph this way. Indeed, the following
website
is devoted to such confusion:

http://www.ii.com/math/ch/#confusion

Notice that, since such people think that aleph_1
is
defined to be c, they state ~CH as being the
existence
of a cardinal between aleph_0 and aleph_1!

So what the OP is really saying is:

hint : 2^1729 is only finite and 2^aleph_0 is c

or even more to the point:

hint : 2^1729 is only finite and 2^aleph_0 >
aleph_0

since his argument is concerning the nonexistence
of
a kappa such that 2^kappa = aleph_0. Similarly,
the
OP interprets Prof. Ullrich's reply as:

What? Exactly how do you prove that 2^aleph_0 =
c?

Notice that the Ghost in the Machine mentioned the
beth numbers, which are defined the way many
people
think the aleph numbers are. Thus one can replace
all
of the OP's alephs by beths in order to understand
what he is really saying.

So I don't fault the OP for assuming that aleph_1
is
defined as 2^aleph_0, since he mostly likely read
the
definition in a book. There are other things the
OP
writes which may make him be labeled a "crank,"
but
this isn't one of them.

you say there is a lot of information wrong about
cantor

well i got my information double checked with a
university , because i knew people would dispute my
definitions...

so that would imply even universities give a wrong
interpretation of cantor ??

so if 2^aleph_0 is not >= aleph_1 ; then what is it
?

ALSO NOTE THAT

aleph_1 = C is not in my original post !!!

it was replied by others

so I AM NOT CONFUSED ABOUT THAT

well thanks for defending me in the sence of not
calling me a crank ...

but then again , i am not confused at all ...

(if all sources for cantor math are wrong , then
maybe all of math is learned wrong ? :p )

greets
tommy1729

btw professor ullrich ??????

he has NEVER HEARD OF 2^aleph_0 >= aleph_1

i had to explain to him

integral x dx = x^2/2 + C

( C is not the continuum here :p)

and he does not know the zeta function has its critical zero's even without continuation !!

he does not know a function NEEDS zero's.

do i need to GO ON ???

and he is rude too

never heard of "ullrichism" here before ? :-)

i would like to see a math competition between

David C. Ullrich VS Robert Israel

0 - 99 im betting ...

and David would probably say the questions where not clear enough :p

Why are you dragging my name into this?

It may be true, as Han de Bruijn wrote in another thread, that I
"seldom get involved with foundational issues": I'd think of it more
as "seldom post to flame-fests". Let me make it clear, though, that
1) I'm firmly on the side of the "mainstream school".
2) I very rarely disagree with David Ullrich on issues of substance in
mathematics.


Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada


.

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