sci.logic Google Group

Re: Relative Boundedness

jonescard...@aol.com (John Jones) — Wed, 07 янв 2009 11:52:11 UT

A set S is an assembly, a collection. That is, where each element is
distinguishable but not sequenced. But that's only the first step. The
next step will be to create a series from this preparatory step.
You can't say a is a sequence without showing what a sequence is. And
defining an nth place on that sequence in terms of a value, entirely

Re: The modern mathematical concept of infinity is indefensible

han.debru...@dto.tudelft.nl (Han de Bruijn) — Wed, 07 янв 2009 11:26:53 UT

You've never summarized the "axioms of math" in your book "Complex made
Simple" and _yet_ it _is_ mathematics all over the place. Right ?
Mathematics is mathematics, based on axiom systems or not. And what the
OP does _is_ mathematics, whether you like it or not. Axiom systems aid
in understanding, perhaps, but cannot replace it.

Re: The modern mathematical concept of infinity is indefensible

dullr...@sprynet.com (David C. Ullrich) — Wed, 07 янв 2009 11:22:09 UT

On Tue, 6 Jan 2009 18:08:49 -0800 (PST), Albrecht <albst...@gmx.de>
wrote:
That follows _if_ "number" means "natural number". In fact
that's not what it means in this context.
The actual content of your post, stripping the assertions
based on misunderstanding that words mean what we say
they mean, boils down to the fact that there are infinitely

Re: The modern mathematical concept of infinity is indefensible

dullr...@sprynet.com (David C. Ullrich) — Wed, 07 янв 2009 11:19:48 UT

He's not a finitist working in that theory, or if
he is there's no evidence of it in his post. He's
_asserting_ that Infinity is _false_. More than
that, he's claiming to _prove_ that Infinity is
false.
Nothing ironic about it.
David C. Ullrich
"Understanding Godel isn't about following his formal proof.

Re: The modern mathematical concept of infinity is indefensible

dullr...@sprynet.com (David C. Ullrich) — Wed, 07 янв 2009 11:15:11 UT

There you go yet again, defending something utterly
other than what the guy said.
ZF-Infinity+-Infinity is logical theory that has
certain well-defined axioms. In the OP there was
nothing about what follows from this axiom or
that axiom, the OP _stated_ that [blah blah]
was "indefensible". He "proved" this, and his

Re: Relative Boundedness

dullr...@sprynet.com (David C. Ullrich) — Wed, 07 янв 2009 11:09:15 UT

On Tue, 06 Jan 2009 15:10:56 +0000, John Jones <jonescard...@aol.com>
wrote:
It seems pointless to ask for definitions of "the limit of A in B"
and "A's representation in B".
Instead I'll just ask this: Are you under the impression that
this stuff you're writing has something to do with mathematics?

Re: Choice sequence lessons.

kram...@aol.com (Keith Ramsay) — Wed, 07 янв 2009 09:03:58 UT

On Dec 31 2008, 6:43 am, Bill Taylor <w.tay...@math.canterbury.ac.n z>
wrote:
Terminology like "locatable real" adds to the confusion. People say
things similar to this when they're talking about constructive
mathematics, more often "constructible real" or "constructive real",
and it does confuse them; this is not a hypothetical case.

Re: The modern mathematical concept of infinity is indefensible

lwal...@lausd.net — Wed, 07 янв 2009 08:45:13 UT

ZF-Infinity+~Infinity is neither sound nor valid?
Since Infinity is independent of the other axioms
of ZF, if ZF-Infinity is unsound and invalid, then
ZF itself is also unsound and invalid.

Re: The modern mathematical concept of infinity is indefensible

lwal...@lausd.net — Wed, 07 янв 2009 08:42:22 UT

I don't find it idiotic. Just because Albrecht is a
finitist working in a theory like ZF-Infinity
(possibly +~Infinity), it doesn't mean that he is
an idiot. Of course, I would not be surprised to
find that many adherents of ZFC consider most
finitists to be idiots.
So ironically, right after he calls Albrecht's

Re: The modern mathematical concept of infinity is indefensible

lwal...@lausd.net — Wed, 07 янв 2009 08:35:30 UT

But Albrecht never disputed this fact. I admit that some
so-called "cranks," such as WM, do believe in a largest
natural, but there's no evidence in this post that
Albrecht is one of them. As far as I can tell, Albrecht
accepts every theorem of PA.
Clearly Albrecht _doesn't_ accept the idea of Infinity.

Re: The modern mathematical concept of infinity is indefensible

nom...@invalid (Herbert Newman) — Wed, 07 янв 2009 08:19:22 UT

What an incredibly silly "argument".
Right. No NATURAL number is able "to denote the number of the natural
numbers". But since the number of natural numbers isn't a NATURAL number,
we can hardly "conclude" the nonexistence of this number from that. :-)
Though again A's "argument" has been shown to be neither sound, nor valid.

Re: The modern mathematical concept of infinity is indefensible

nom...@invalid (Herbert Newman) — Wed, 07 янв 2009 08:02:16 UT

This one caught my attention, since it is especially silly:
Since that latter is (more or less) a "tautology", it "proves" nothing.
(The argument has the same logical form as the following one:
The sun CAN'T be a star, SINCE 1 = 1.)
Actually, the claim
Since ~(#N > #N), P
can be "reduced" to the claim

Re: Choice sequence lessons.

kram...@aol.com (Keith Ramsay) — Wed, 07 янв 2009 07:03:19 UT

On Dec 31 2008, 6:29 am, Bill Taylor <w.tay...@math.canterbury.ac.n z>
wrote:
And how would you know?
I once tried to make a complete list of mathematical acquaintances,
and now and then I realize that I've left somebody out. It's true that
I haven't met as many mathematicians lately as I used to.
Figuring that it might be *you* who needs to study is the

Re: Foundations of Constructive Mathematics

jussila.er...@gmail.com (erkkijussila) — Wed, 07 янв 2009 06:44:41 UT

The task will be facilitated, if you separate generalization and
existence from each other in quantification. I have handled this
problem widely in my book Calculus of Logic (ISBN 978-952-92-3761-6).
Generalization is treated on pages 43-53. There is no difficulty to
generalize x and y. Generally there is no difficulty to show existence

#115 Chapter 5, Reals of Dedekind were not an Algebraically Closed Field; new book 2nd edition: New True Mathematics

plutonium.archime...@gmail.com — Wed, 07 янв 2009 05:51:32 UT

I appreciate Lwal in taking the time to teach Tribble, but in the case
of the number
1/3, I must point out where the AP-Reals stand out as different from
the Reals that
both Tribble and Lwal and every book written on mathematics stands.
Lwal implies from his paragraph that the Reals of Dedekind Cut have a