sci.logic Google Group

Re: Is Cardinality a FOL concept?

2008-10-06T14:52:28Z

just clarification
FOL_= is first order logic with identity
FOL is more about predicates than about sets so it is more
Nothing is P
Ax ~Px
Only one thing is P
Ex (Px & Ay (Py ->(x=y)))
there are two P's
Ex Ey (((Px & Py) & ~(x=y)) & Az(Pz -> ((z=x) v (z=y)))
and for three Ps it becomes a very long sentence

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T14:47:08Z

georgie says...
It's easy enough to prove the following facts about the sequence:
1. No entry is greater than or equal to 1.
2. If x is any real strictly smaller than 1, then there is an
entry that is greater than x.
The second fact is interesting, but irrelevant to the claim that
no entry is equal to 1.

Re: Out-of-print math books: An Update

2008-10-06T14:47:05Z

In article <y8zy712nwoz....@nestle.csail. mit.edu>,
While I don't consider myself a partisan of either side, the main advantage I
see of paper media is that it is much more likely to last 500 years once it's
on the shelf, even if nobody is interested in it.
In an ideal world, all electronic documents are upgraded whenever the de

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T14:40:54Z

WM says...
What you are doing is making up a theory of infinity, and then showing
that your made-up theory is nonsense. Yes, that's true. You invented a
nonsensical theory. But your invented theory is *not* the theory described
by ZF. It is not Cantor's theory of infinity.
If a 7 year old makes a mistake doing subtraction, does that show that

Hilbert & Bernays project

2008-10-06T14:38:09Z

Where is this [link] going? The
aim is laudable but when will the target be hit?

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T14:35:09Z

The diagonal argument is false, aleph_0 and with it ZF is
inconsistent.
Regards, WM

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T14:33:08Z

He talked about real numbers and intervals of real numbers in that
paper.
Regards, WM

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T14:31:29Z

That is unimportant if real numbers are in question.
But it talks about real numbers and intervals of real numbers.
No. The diagonal elements can only get m or w.
Regards, WM

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T14:13:40Z

1
11
111
...
You can't see that there is no diagonal with X elements unless there
is at least one line with X elements? Sorry, then we are discussing in
different worlds.
Regards, WM

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T13:59:01Z

Take a set of aleph_0 elements and remove one element. That is aleph_0
- 1.
Therefore an anti- diagonal with aleph_0 digits 1 requires at least
one line with as many digits 1.
Another one is: The set consists of aleph_0 countable sets.
See above.
Regards, WM

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T13:54:32Z

I can't change that. It is as it is. Nevertheless we can act "as if"
in arithmetic.
For every 1 of the anti-diagonal there must exist an entry with a
string of 1's reaching to that position.
It depends on the precision of your calculator.
No. I recognized the practical limitations of calculating.
Regards, WM

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T13:32:47Z

If we assume that aleph_0 exists, then we get a contradiction. Yes, it
makes sense to assume, but not to believe in aleph_0.
After all you write here, I can guess what you believe, but there is
not one word about sober science.
> then
Have you ever seen a mathematical proof? One of the most elemntary

Re: Yet another disproof of the diagonal argument

2008-10-06T13:22:27Z

...
> > > The position of an object in a list is not only an integer, it is a
> > > natural number.
> >
> > Bullshit: Then try and give the "natural" position of 1.3 in [0,1].
>
> Pardon, that should read 1/3: try and give the "natural" position of
> 1/3 -that is, 0.(01) in binary- in [0,1].

Re: Yet another disproof of the diagonal argument

2008-10-06T13:21:26Z

> > In article <b9d3f44b-3d52-4048-96ea-bc888 4ff2...@25g2000hsk.googlegroup s.=
...
> > No. But a proof by induction shows only that something is true for all
> > *finite* n, not for some infinite number. So while what you state may
> > be true for all finite lists it is still not necessarily true for an

Re: A consideration concerning the diagonal argument of G. Cantor

2008-10-06T13:27:15Z

Gee, how big does that sequence get? Does it get as big as 1/2 + 1/4 +
1/8 +... = 1? If not, where exactly does it fall short? Why does
that sequence fall short only when we talk about this topic?