- Re: A local ring problem
In article ,
Of course, this is implicitly assuming at least a weak version of the
Axiom of Choice, to warrant the existence of a maximal ideal
containing the given ideal. But this can be done without assuming that
every proper ideal is contained in a maximum ideal: pick a in I and b
- Re: some problem connected with prove homogeneous inequalities
i didn't note that you were asking about number of variables (I though
that you are asking about constants A,B,...), for given number n,
there are n variables, becouse I want to have term x_1*x_2*...*x_n.
- Re: -- Wrong limits do not commute
...
> > > Limits that do not commute are NUMERICALLY UNSTABLE.
> > >
> > > See ? No offending terminology anymore.
> >
> > Many limits are numerically unstable. And that is not only iterated
> > limits.
>
> Sure. But the latter are it in some special way. Because it's not so
> much the outcome but rather the _process_ that leads to "instability".
- Re: some problem connected with prove homogeneous inequalities
Yes, of course. I've forgotten to mention it :(
I don't think about it, however it could be computed in some
combinatorial way, and I think that it isn't difficult. However, I'm
interesting not in it, but how to compute the bounds of the set S (for
n=2 we have the intersection of two half planes: y>=+-2x.
- Re: A consideration concerning the diagonal argument of G. Cantor
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
...
> > > 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
> > In article ...
> > 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
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?
- Re: a conjecture !
On Sun, 05 Oct 2008 18:49:28 EDT, amy666
wrote:
You answer my question first.
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
- Re: Elementary Theory of Numbers
A typo? Try:
(1 + xn)(1 + x) = 1 + x(n + 1) + x + x^2.n
- Re: Pontryagin duality (again)
On Mon, 06 Oct 2008 13:06:26 +0100, Timothy Murphy
wrote:
If you really think that what's reasonable and accurate
has some bearing on what is or is not accepted usage
that would explain a lot.
You're actually saying that it's "reasonable and accurate"
to use the term "Lie algebra" to mean something _other_
- Re: A consideration concerning the diagonal argument of G. Cantor
It's not believing. I have seen and I can show that actual infinity is
nonsense.
It is bizarre behaviour to keep on believing what has been proved
wrong.
Regards, WM
- Re: -- Wrong limits do not commute
...
> > It appears that HdB's "stable" merely =A0means the (x,y)->(oo,oo) limit
> > exists.
>
> Obviously. A Numerical Approximation f(X,Y) , _if it exists_, is for
> the iterated limits:
Do not confuse numerical mathematics with pure mathematics.
> lim lim f(x,y) -> f(X,Y) ; lim lim f(x,y) -> f(X,Y)
- Re: -- Wrong limits do not commute
What do you not understand? To fix ideas, consider the equality of an iterated limit of the form
lim_{x->0} lim_{y->0} f(x, y)= lim_{y->0} lim_{x->0} f(x, y)
Geometrically, it means that starting at some point near (0, 0), and going first parallel to the x-axis then parallel to the y-axis, is the same (as far as taking the limit) as first going parallel to the y-axis then going parallel to the x-axis. Needless to say, I am not being rigorous here, just trying to convey the idea. I can do that if you want me to, at the cost of considerable obfuscation.
- Re: tomic polynomial: CONJECTURE 3
Tomic polynomials by definition do not have roots of unity
as zeros - except -1,+1 if I read the definition correctly.
- Re: Pontryagin duality (again)
On Sun, 05 Oct 2008 19:58:24 +0100, Timothy Murphy
wrote:
I never _used_ that phrase, I _mentioned_ it as an example
to illustrate what's wrong with "in Banach algebra:.
And you understand that very well.
Another hint: what you're accomplishing here is
something that I doubt you _want_ to accomplish.
- Re: AREA
On Sun, 05 Oct 2008 12:02:24 EDT, amy666
wrote:
Sorry, guy. For most of this thread the things you said made
no sense, because you were talking about things that simply
don't exist. When you mentioned the M-L star it seemed possible
that that's what you really meant to be talking about all the time.
- Re: Virgil disproves Cantor (Was: Re: Yet another disproof of the
...
> > > So now, by Virgil's statement, we have a bijection from the members of
> > > the list to the digits positions. Then the list is just as countable
> > > as the sequences it lists. QDE
> >
> > Yes, by definition every list is countable. What is the problem with
> > that?
> > What Cantor's proof *is* is that also every list of reals is incomplete.
- Re: Why "meta diagonals" are irrelevant
That is irrelevant for the question whether R can be given as a
countable set of lists, i.e., has cardinal number aleph_0.
is irrelevant for the question whether R has cardinal number aleph_0 *
aleph_0 = aleph_0.
Regards, WM
- Re: A consideration concerning the diagonal argument of G. Cantor
Sic.
The N/U EF has too few properties, although they are far-reaching, that
they are difficult to understand, given that generally they are minimal
default properties in small numeric systems, for example with the domain
naturals and range reals. Because they are minimal default properties
(eg, "1", the multiplicative identity, or "0", the additive identity)
- Re: Yet another disproof of the diagonal argument
On Oct 6, 2:31 pm, Denis Feldmann
****************************** ****************************** ****
Not simply trolling: LV is spitting pearls of stupidity in some of his
last posts in this thread that only JHS in his good old times could
have matched. Read, for one, the next marvel when he answered to
- Re: A consideration concerning the diagonal argument of G. Cantor
...
> > That is just what I said. The only treatment that failed to consider
> > that point was Cantor's own of 1892.
...
> "In the paper entitled 'On a property of a set [Inbegriff] of all real
> algebraic numbers' (Journ. Math. Bd. 77, S. 258), there appeared, probably
> for the first time, a proof of the proposition that there is an infinite
- Deterministic vs Nondeterministic Turing machines.
... first of all, is there any generally accepted definition of non-
deterministic Turing Machines? At least I have found almost nothing
usable, including wiki-articles. So I will state my question in the
following form:
Is it true, that there exists ‘probabilistic’-TM, which could not be
simulated with deterministic-TM at all?
- Re: A consideration concerning the diagonal argument of G. Cantor
...
> > >I know that this point is very relevant to Cantor's conclusion. Every
> > >modern textbook excludes replacement of 9 by 0 or so.
> >
> > Give an example of any treatment of Cantor's theorem in a textbook
> > that fails to take into account that multiple decimal representations
> > can represent the same real. There are no such treatements.
- Re: -- Wrong limits do not commute
No.
As far as I recall this is the second time you ask me that type of question. Is there any particular reason why do you want to know who I am? Are you a stalker?
Regards,
G. Rodrigues
- Re: A consideration concerning the diagonal argument of G. Cantor
...
> > In his original paper on the diagonal proof Cantor did for that not
> > consider numbers at all. And indeed, the sequence
> > {m, w, w, w, w, ...}
> > is different from
> > {w, m, m, m, m, ...}
>
> as 1.000... is different from 0.111...?
They *are* different if you only look at the sequence of digits. They
- Re: A consideration concerning the diagonal argument of G. Cantor
...
> > > and the replacement rule 0 --> 1 which yields an anti-diagonal that is
> > > in the sequence, as /every/ initial segment can be found in the list.
> >
> > Every *finite* initial segment is in the list.
>
> How do you get from finity to infinity in a static (not dynamic) set?
Not.
> If the anti-diagonal, has aleph_0 digits, then there is at least one
- Re: Yet another disproof of the diagonal argument
David C. Ullrich a écrit :
Otoh, it is really funny that you dont realize LV is simply trolling,
and you answer as if he was really , in earnest, not understanding that
"apples fall up" needs an explanation of the same order than "6 x 9 =42
(base ten)" *must* be explained by , for instance, a programming bug in
- Re: Yet another disproof of the diagonal argument
Nothing. That's the point.
- Re: Scaling in Modular Inverse problem with very large integers
The notation *is* clear. b^(-k) is clearly 1/(b^k) mod n. WTP?????
- Re: Pontryagin duality (again)
I believe my expression is (slightly) more accurate.
The theorem is a deduction from the axioms for a Lie algebra.
and does therefore hold for all Lie algebras.
But there might (in theory) be other cases where the axioms,
and therefore the result, holds,
eg in some category other than that of finite dimensional
- Re: Pontryagin duality (again)
The comment was correct.
It was not helpful because I already had the information.
Does it matter?
- Re: about CNF converting
"newbie" ha scritto nel messaggio
obviously non deterministic polynomial I mean
Regards
- about CNF converting
Hi all,
did somebody know if is possible to use a non
deterministic algorithm in order to convert
every boolean propositional formula into
an equivalent CNF formula?
Thanks a lot
Regards
- Re: Out-of-print math books: An Update
On Mon, 6 Oct 2008 01:50:23 -0700 (PDT), outofprintmath
Using Firefox (2.0.0.17), it crashes my poor old Win98SE system.
Poor and old it may be, but that system is pretty stable in most
respects. Loading this page, it runs completely out of system
resources, bad things happen, and I have to reboot. Not always,
- Re: field generated by the set of roots of unity
I (still) don't understand what precisely the generalised
polynomials in W_n[x] are.
To simplify notation a bit let K be a cyclotomic field and let
O be the ring of integers of K.
Sticking to the theory of semi-group rings (which my be the
wrong approach here) you seem to consider maps
f: O --> K
having finite support.
- Re: JSH: Google problems, start of debate against series
On Sun, 5 Oct 2008 20:30:38 -0700 (PDT), JSH
Exactly. Spot on. There you have one of the central problems of
psychiatry (in its widest sense) in a ... nutshell. How (if at
all) should you conceptualise delusional (or presumably delusional)
states, such as yours (or other mental states, such as mine, which
- Dedekind-MacNeille completion
Let S be an (partially) ordered set. For A subset S, let
above A = set of upper bounds of A.
below A = set of lower bounds of A.
The Dedekind-MacNeille completion of S is
M = { below above A | A subset S }
If S is a Boolean algebra, then M is a Boolean algebra.
In particular, when A subset S, what set B is there for which
- Re: A consideration concerning the diagonal argument of G. Cantor
WM says...
Look, if you don't believe in "actual infinity", then why are
you talking about it? That's bizarre behavior.
If you want to talk about what you believe, then don't bring
up "actual infinity". If you want to talk about standard set
theory, then use the axioms of standard set theory. Your
arguments are an incoherent mishmash of statements that
- Polyhedron
I am trying to visualize what looks like a particular polyhedron(?), but I am
having a bout of stupidity and cannot figure something simple about it.
I am describing the shape, section-wise:
Consider the unit circle on the xy-plane. Put vertexes at exp(2*k*Pi/8*i), k \in
{0,1,...,7}
Rotate the unit circle around the x-axis by Pi/4.
- Re: A consideration concerning the diagonal argument of G. Cantor
WM says...
You reject set theory. You reject the notion of a "completed
infinity". But you think you can prove that a list has an
entry twith aleph_0 - 1 digits. Do you really think that
makes any sense, or do you know that you are speaking
nonsense?
If you want to prove something about *your* beliefs, then
- Re: vitali sets
vitali set - consider the equivalence classes with equivalence
relation x - y = rational.(on real line). Assuming AC,there is a set
which contains exactly one element from each equivalence class. That
is the vitali set.
Bernstein set - A set which intersects with every perfect set but
contains no perfect set is called a bernstein set.
- Re: Topology with hausdorff, quotient map.
Where is Q ?
Of course. R/~ is a partition of R.
What matters ?
q(r) = Q for r in Q.
q(i) = i + Q for i in Q^c.
q^{-1}(Q) = Q
q^{-1}(i + Q) = i + Q.
so, q(U) = R/~.
- Re: Bit-permutation function and Cantor Dust?
I wrote:
Another way of looking at this is that the middle-halves set
consists of those coefficient pairs (r,s) such that every
digit in the base-4 expansion of r and s is either 0 or 3.
Thus each digit position can be written as (3r_i, 3s_i) where
r_i and s_i are in {0,1}.
When mapped by the inverse transform
- New mathematics / physical sciences positions at http://jobs.phds.org, Oct 06, 2008
There are new job listings at [link]
------------------------------ ------------------------------ --------
Title: Quantitative Trading and Statistical Research Analyst
Employer: RACKSON ASSET MANAGEMENT LLC
Location: New York, NY, United States
Posted: Oct 04
We are looking for a highly quantitative individual to help us
- Re: -- rational distances
If S = B((0,n),1/k), then r = n + 1/k and p = (0,n + 1/k).
Thus I can make B with as large of a radius as I want and
bd S with as much curvature as I want. By your reasoning
even in this case, for example when n = 10^10 and k = 10^-100,
V is still just the horizontal ray from p. Why is this so?
That if bd S and B are tangent, then V is the exterior normal
- Re: Topology with hausdorff, quotient map.
If U open subset R, then inverse of U/~ = \/{ u + Q | u in U }
= U + Q = \/{ q + U | q in Q } = union of open sets. Hm, = R.
Thus U/~ is open.
If x/~ in open { v/~ | v in some set A },
then q^-1(V) = \/{ v + Q | v in A } = A + Q is open, thus = R.
Hence the nonnul open sets of R/~ are
{ { v/~ : v in A } | int A nonnul }
- Re: Out-of-print math books: An Update
All votings are optional and independent from each other. There might
be many reasons, why you don't need a book. You can promote your
reason for or against a book by posting a comment below the
corresponding voting. Comments are optional, but they might help to
promote your vote.
If several items are defined in one voting at one time, no further
- Re: Entropy
If you have 32 objects (32 equally probable alternatives),
you need for their indexing by a binary decision tree
160 digits 0 and 1 (00000, 00001, ... till 11111).
The number necessary for one object is 160/32 = 5.
Construction of large binary decision tree were tedious, and therefore
it is replaced by binary logarithm.
- Re: borel cantelli application
On Oct 5, 11:04 pm, Robert Israel
Thanks for your help Dr. Israel. I was trying to show that the Prob(|
X_n/Y_n - 1| > 1/2 infinitely often) is true for any 1/n but used the
same subscript 'n' and ran into some trouble. After realizing it
should just be a fixed constant k, everything worked out fine. I
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