mm-59
===
Check my math! I've derived a differential equation for
strings starting from Stokes> Theorem to show that energy is
conserved along a world-sheet. These diff> eq's involve
connection coef?ients. And I'm not really sure what it all>
means yet. I would appreciate it if some who are more skilled
in the art> would take a look at this and comment. The math
can be found at:
http://www.sirus.com/users/mjake/diffeq.htmlSee link in
original post.What does it mean that ? Does this mean that
the surface is a geodesic?And what does it mean that ? Does
this mean that there is no force in thedirection of time? If
F is still an arbitrary ?ld, then does this meanthat the
string must be traveling in a frame where the time component
iszero?
===
I just started Complex variables and applications
by Churchill, et al. Iam ?ed by something already. In
Churchill, they say that anaccumulation point is...a point z0
... of a set S if each neighborhood if z0 contains at leastone
point of S distinct from z0. Why is it different from R? To
wit,every neighborhood of x0 has an in?ite number of points
of, say, E.TIA,Lurch
===
They are equivilent. Let me see if I
can explain it on the internet. Ifthis helps let me knowyou
can just think of R for simplicity, although I don't think my
argumentwill use this fact.let's say we want to check if x0 is
an accumulation point of some set S.I want to show that:Every
open neighborhood contains at least one point of S distinct
from x0is equivelent toEvery open neighborhood contains
in?itely many points of SSuppose every open neighborhood
contains at least one point of S distinctfrom x0. Fix an open
neighborhood. (just pick any one) Pick one of thepoints
distinct from x0, call it x1. (again, pick one). Now, clearly
thereexists an open neighborhood of x0 that doesn't contain
x1. For example, if|x0 - x1| = a, then take the a/2
neighborhood of x0 (this is just sayingthat x1 is some
distance away from x0 since it is a different point, so ifwe
take a neighborhood that only goes out half as far, x1 is not
in thatneighborhood).Now, this smaller neighborhood must
contain a point of S. call it x2. nowtake an even smaller
neighborhood that doesn't contain x2. this evensmaller
neighborhood doesn't contain x1 or x2, but it does contain
somepoint of S distinct from x0. So we can keep repeating
this forever. Inother words, for any n, however large n is,
there is some x_n in S.I hope that made sense. To recap, if
you keep taking smaller neighborhoods,you keep ?ding points.
So if every neighborhood contains one point, everyneighborhood
must contain in?itely many points, since each
neighborhoodalso contains every smaller neighborhood.This
might not be very rigorous, but hopefully it will get you
started.Obviously, if every neighborhood contains in?itely
many points, itcontains at least one point.Justin Van
WinkleSuppose----- Original Message ----- > ...a point z0 ...
of a set S if each neighborhood if z0 contains at least> one
point of S distinct from z0. Why is it different from R? To
wit,> every neighborhood of x0 has an in?ite number of
points of, say, E. TIA, Lurch
===
Lurch> They are equivilent.
Let me see if I can explain it on the internet. If> this
helps let me know you can just think of R for simplicity,
although I don't think my argument> will use this fact. 
let's
say we want to check if x0 is an accumulation point of some
set S. I want to show that:> Every open neighborhood contains
at least one point of S distinct from x0> is equivelent to>
Every open neighborhood contains in?itely many points of S
Suppose every open neighborhood contains at least one point
of S distinct> from x0. Fix an open neighborhood. (just pick
any one) Pick one of the> points distinct from x0, call it
x1. (again, pick one). Now, clearlythere> exists an open
neighborhood of x0 that doesn't contain x1. For example,if>
|x0 - x1| = a, then take the a/2 neighborhood of x0 (this is
just saying> that x1 is some distance away from x0 since it
is a different point, so if> we take a neighborhood that only
goes out half as far, x1 is not in that> neighborhood). Now,
this smaller neighborhood must contain a point of S. call it
x2.now> take an even smaller neighborhood that doesn't
contain x2. this even> smaller neighborhood doesn't contain
x1 or x2, but it does contain some> point of S distinct from
x0. So we can keep repeating this forever. In> other words,
for any n, however large n is, there is some x_n in S. I hope
that made sense. To recap, if you keep taking
smallerneighborhoods,> you keep ?ding points. So if every
neighborhood contains one point,every> neighborhood must
contain in?itely many points, since each neighborhood> also
contains every smaller neighborhood. This might not be very
rigorous, but hopefully it will get you started. Obviously,
if every neighborhood contains in?itely many points, it>
contains at least one point. Justin Van Winkle> Suppose>
----- Original Message ----- >I just started Complex
variables and applications by Churchill, et al.> I> am
?ed by something already. In Churchill, they say that
an> accumulation point is> ...a point z0 ... of a set S if
each neighborhood if z0 contains atleast> one point of S
distinct from z0. Why is it different from R? To wit,> every
neighborhood of x0 has an in?ite number of points of, say,
E.>TIA,>Lurch>
===
Charlie Johnson> I just started Complex
variables and applications by Churchill, et al.I> am ?ed
by something already. In Churchill, they say that an>
accumulation point is> ...a point z0 ... of a set S if each
neighborhood if z0 contains at least> one point of S distinct
from z0. Why is it different from R? To wit,> every
neighborhood of x0 has an in?ite number of points of, say,
E.It is equivalent.It is always equivalent in a metric
space.-- Maxi
===
How is it equivalent? If one has the usual
metric in R and C, thenaccording to the books I am reading,
they are different. C requiring onlyone point and R requiring
in?ite amount of points. (The metric in C isabs(z-z0) < e and
the metric in R being the usual: abs(x - x0) < e.)Lurch>
Charlie Johnson > I just started Complex variables and
applications by Churchill, et al.> I> am ?ed by
something already. In Churchill, they say that an>
accumulation point is> ...a point z0 ... of a set S if each
neighborhood if z0 contains atleast> one point of S distinct
from z0. Why is it different from R? To wit,> every
neighborhood of x0 has an in?ite number of points of, say,
E. It is equivalent.> It is always equivalent in a metric
space. -- > Maxi
===
> How is it equivalent? If one has the
usual metric in R and C, then> according to the books I am
reading, they are different. C requiring only> one point and
R requiring in?ite amount of points. (The metric in C is>
abs(z-z0) < e and the metric in R being the usual: abs(x -
x0) < e.)If every neighbourhood of z0 contains one point of E
distict from z0, thenby considering the open balls centered in
z0 of radius 1/n you see thatthere is in?itely many
(otherwise there would be none in some of thesedisks for n
suf?iently large).-- Maxi
===
I don't quite get it yet, but I
will work on it.Lurch> How is it equivalent? If one has the
usual metric in R and C, then> according to the books I am
reading, they are different. C requiringonly> one point and R
requiring in?ite amount of points. (The metric in Cis>
abs(z-z0) < e and the metric in R being the usual: abs(x -
x0) < e.)> If every neighbourhood of z0 contains one point of
E distict from z0, then> by considering the open balls
centered in z0 of radius 1/n you see that> there is in?itely
many (otherwise there would be none in some of these> disks
for n suf?iently large). -- > Maxi
===
Im having trouble
understanding some questions. Some help would beappreciated.
I have read the book, but dont follow it.Problem
1F={B->A,A->C}1. the non-trivial dependencies are: B->A,
A->C, B->Cis that right? I was wondering if it was a trick
question.2. Find a non-empty instance of R that satis?d
every FD in F, botnot A->Bany idea what that question MEANS.
Does it want a real example? Imconfused.3. Find an instance
of R that satis?s every FD in F, bot not A-> B. again does
this mean an example? Im confused.
===
I understand that it is
possible to express the number of ways ofhaving k bishops on
an n*n board such that they are not attacking eachother as a
combinatorial formula and i have been trying to derive
theformula without any l, can anyone help me out ?
===
It
might be helpful to separate the board into two pieces
according to thecolors of the squares, then translate the
diagonals into rows and columns, soyou can use familiar
coordinate methods. An inductive proof might work.| I
understand that it is possible to express the number of ways
of| having k bishops on an n*n board such that they are not
attacking each| other as a combinatorial formula and i have
been trying to derive the| formula without any l, can
anyone help me out ?
===
> I understand that it is possible to
express the number of ways of> having k bishops on an n*n
board such that they are not attacking each> other as a
combinatorial formula and i have been trying to derive the>
formula without any l, can anyone help me out ?Is this
right?.. Each bishop has a coordinate (r,c) (row, column).
For allthe bishops, the r's are different to each other, and
the c's are differentto each other.So for k bishops the total
amount of possible coordinates is how manydifferent ways you
can take k r's out of 8, times how many different waysyou can
take k c's out of 8. And that should be enough for you.. If
it'sright..I think so.-- Quaternion
===
> I understand that
it is possible to express the number of ways of> having k
bishops on an n*n board such that they are not attacking
each> other as a combinatorial formula and i have been trying
to derive the> formula without any l, can anyone help me
out ?> Is this right?.. Each bishop has a coordinate (r,c)
(row, column). For all> the bishops, the r's are different to
each other, and the c's are different> to each other.No,
bishops attack on diagonals, not rows & columns. OP; have you
tried starting small? n = 2, n = 3, see whether there are any
patterns? Or try searching Sloane's On-Line Encyclopedia of
Integer Sequences for the word bishop?--
===
> I understand
that it is possible to express the number of ways of> having
k bishops on an n*n board such that they are not attacking
each> other as a combinatorial formula and i have been
trying to derive the> formula without any l, can anyone
help me out ?Is this right?.. Each bishop has a coordinate
(r,c) (row, column). For all>the bishops, the r's are
different to each other, and the c's are different>to each
other.>So for k bishops the total amount of possible
coordinates is how many>different ways you can take k r's out
of 8, times how many different ways>you can take k c's out of
8. And that should be enough for you.. If it's>right..I think
so.Thats a little too simplistic, as you can see
fromhttp://acm.uva.es/p/v102/10237.html with 6 bishops on an
8*8 boardthere are 5599888 ways and with 5 bishops on a 30*30
board there are3127859642656 ways.
===
> I understand that
it is possible to express the number of ways of> having k
bishops on an n*n board such that they are not attacking
each> other as a combinatorial formula and i have been
trying to derive the> formula without any l, can anyone
help me out ?>Is this right?.. Each bishop has a coordinate
(r,c) (row, column). For all>the bishops, the r's are
different to each other, and the c's are>different to each
other.>So for k bishops the total amount of possible
coordinates is how many>different ways you can take k r's
out of 8, times how many different ways>you can take k c's
out of 8. And that should be enough for you.. If
it's>right..I think so.> Thats a little too simplistic, as
you can see from> http://acm.uva.es/p/v102/10237.html with 6
bishops on an 8*8 board> there are 5599888 ways and with 5
bishops on a 30*30 board there are> 3127859642656 ways.Yes I
thought bishops were towers for some reason..Different
languages-- Quaternion
===
> I understand that it is
possible to express the number of ways of> having k bishops
on an n*n board such that they are not attacking each> other
Why would bishops attack one another? Oh--over homosexuality
perhaps?> as a combinatorial formula and i have been trying
to derive the> formula without any l, can anyone help me
out ?-- G.C.
===
It is very good that I heard Andrei Linde
speak last night at UC Berkeley as my updated version
ofhttp://qedcorp.com/APS/EmergentGravity.doc shows. Also a
rather large crowd showed up to hearmy talk right in the
middle of the talk before mine.Linde explained that he does
not believe most of the current textbook presentations of
in?ary cosmology.The essence of his talk is in my 2
equations II.9 and II.10 in the new version of
http://qedcorp.com/APS/EmergentGravity.docThe key is the
friction term in II.9 which is a linearization of my II.8
near the bottom of a local minimum in the effective potential
of the vacuum coherence ?ld in the FRW large scale limit
assuming homogeneity.The friction term that is the root cause
of chaotic in? with slow descent at large order parameter
followed by oscillatory reheating to make the post-in?ary
Big Bang is quite simply the effect of the connection ?ld for
parallel transport in the second application of the covariant
time derivative to the scalar ?ld. Of course Linde has no
micro-dynamics for the emergence of the scalar ?ld as I do
nor does he derive Einstein's gravity together with the
uni?d exotic vacuum dark energy/matter ?ld in a two-way
bootstrap of the never-ending spontaneous self-organizing
parallel universes splitting off into baby universes in the
sense of Andrei Sakharov's metric elasticity a special case
of P.W. Anderson's More is different.Steve Carlip gave a
interesting talk on topology change in WKB approx to quantum
gravity with a possibleexplanation of why space is
homogeneous on large scale consistent with in?.
===
Given
two nx1 column matrices (vectors) X=(x1 x2 ... xn)^T and Z=(z1
z2 ... zn)^T, all elements real numbers (T=transpose):1) Is
there a simple matrix operation to create the nx1
matrix(x1*z1 x2*z2 ... xn*zn)^T from X and Z? I am referring
to a mathematical operation like inner product, rather than
an algorithm or computer program.2) Is there a way using
matrix operations to produce the column vector (exp(x1)
exp(x2) ... exp(xn))^T (exp=exponential function) from X?3)
Related to (2), is there a way using matrix operations to
produce the nxn diagonal matrix D(x1 0 0 ... 0)(0 x2 0 ...
0)( ... )(0 0 0 ... xn)from X? And conversely, given D as
above, to write X in terms of D using matrix operations?
===
>
Given two nx1 column matrices (vectors) X=(x1 x2 ... xn)^T and
Z=(z1 z2 > ... zn)^T, all elements real numbers
(T=transpose):> 1) Is there a simple matrix operation to
create the nx1 matrix> (x1*z1 x2*z2 ... xn*zn)^T from X and
Z? I am referring to a mathematical > operation like inner
product, rather than an algorithm or computer program.let Em
be the square matrix (eij) such that emm = 1 and eij =
0otherwise.consider Em.Z.X, m = 1, 2, 3, ..., n> 2) Is there
a way using matrix operations to produce the column vector >
(exp(x1) exp(x2) ... exp(xn))^T (exp=exponential function)
from X?assuming exp(A) = Sum A^n/(n!) over n = 0, 1, 2, ...,
in?ityyou can obtain the jth entry of the sought
vector:exp(A)ej,where A is the diagonal matrix aii = xi, aij
= 0 for i not equal to j,and ej is the jth elementary
vector.> 3) Related to (2), is there a way using matrix
operations to produce the > nxn diagonal matrix D> (x1 0 0
... 0)> (0 x2 0 ... 0)> ( ... )> (0 0 0 ... xn)> from X?
And conversely, given D as above, to write X in terms of D
using > matrix operations?consider X.ejform a linear
combo.
===
theorem to matrix transformations. The textbook
that I am using hasexamples of using the inverse function
theorem for ordinary R(n)->R(m)functions but not for matrix
transformations such as S(X)=X^3, where X isin Mat(3,3) for
example. Here is the problem that I need to solve and
mysolution. I would greatly appreciate if someone could go
over my reasoningand point out any ?hat I have and
explain to me how to solveProblem: A = [ 0 1 0 ] [ 0 0 1 ] [
1 0 0 ]Note that A^3 = I (identity matrix). Is there a cont.
differentiablefunction g such that g(I)=A and (g(A))^3=A in
the neighborhood of I? My Solution:Let f: X -> X^3 (X is a
matrix)then f(g(x)) = [g(x)]^3 = xif X = If(g(I)) = INow use
the chain rule for the derivative of f(g(I)):[D(fog)(X)] =
[Df(g(X))][Dg(X)] (by de?ition)Let X = I:[D(fog)(I)] =
[Df(g(I))][Dg(I)] = [Df(A)][Dg(I)] (since g(I)=A)Finding
[Df(A)] is a bit tricky. I used the general de?ition of
thederivative to show that[Df(A)]H = 3A^2H + 3AH^2since lim
{(1/H) * (f(A+H) - f(A) - (3A^2H + 3AH^2))} = 0. Now I let H
= Iso that [Df(A)]I = 3A^2 + 3AI then went on to show that
the determinant of this matrix (using A fromthe problem) = 54
(is nonzero).
===
Since we're discussing the axiom of
foundation (in the textbooks I've seen, it's called 
the axiom
of regularity), does anyone know what the intuitive
justi?ation for this axiom is? I mean, all the other axioms
seem pretty natural to me, even the infamous axiom of choice.
But where in world did they come up with the axiom of
regularity?Have a tolerable existence. Eli
===
>Since we're
discussing the axiom of foundation (in the textbooks I've
seen, >it's called the axiom of regularity), does anyone know
what the intuitive >justi?ation for this axiom is? I mean,
all the other axioms seem pretty >natural to me, even the
infamous axiom of choice. But where in world did >they come
up with the axiom of regularity?It was to avoid having a set
x which is its only element,and more complicated versions of
this. It is easy to seethat both it and its negation are
consistent.-- This address is for information only. I do not
claim that these viewsare those of the Statistics Department
or of Purdue University.Herman Rubin, Department of
Statistics, Purdue University
===
The foundation axiom rules
out situations that you might call membershiploops. For
example, if A1 in A2 in A3 in A1, then {A1,A2,A3} has a
nonemptyintersection with each of its elements.| Since we're
discussing the axiom of foundation (in the textbooks I've
seen,| it's called the axiom of regularity), does anyone know
what the intuitive| justi?ation for this axiom is? I mean,
all the other axioms seem pretty| natural to me, even the
infamous axiom of choice. But where in world did| they come
up with the axiom of regularity?|| Have a tolerable
existence. Eli
===
> Since we're discussing the axiom of
foundation (in the textbooks I've seen, > it's called 
the
axiom of regularity), does anyone know what the intuitive >
justi?ation for this axiom is? I mean, all the other axioms
seem pretty > natural to me, even the infamous axiom of
choice. But where in world did > they come up with the axiom
of regularity?It is not assumed because of some intuitive
justi?ation, but becauseit doesn't interfere with ordinary
mathematics (sets of the kindprohibited by the axiom aren't
ever needed) and it simpli?s modeltheory by a jillion
times.Thomas
===
|Since we're discussing the axiom of
foundation (in the textbooks I've seen, |it's called 
the
axiom of regularity), does anyone know what the intuitive
|justi?ation for this axiom is? I mean, all the other axioms
seem pretty |natural to me, even the infamous axiom of choice.
But where in world did |they come up with the axiom of
regularity?i think the answer is that (in the presence of the
usual other axioms)it's equivalent to the statement every set
belongs to some level ofthe cumulative hierarchy, which is a
powerful statement because itallows you to prove theorems
applying to all the sets in the universe,by trans?ite
induction with respect to the level of the
cumulativehierarchy to which they belong (the levels of the
hierarchy beingindexed by ordinal numbers).the cumulative
hierarchy starts out with the empty set as the bottomlevel,
then the power set of the empty set as the next level, and
soforth on upwards. at limit ordinals you take the union of
the levelsbelow.speaking as a non-specialist in set theory,
what most bugged me aboutthe axiom of foundation when i was
?st trying to learn axiomatic settheory (after already
learning ?st-order logic) was that on the onehand it sounds
like it's trying to prevent weird loops and weirdin?ite
regresses of membership chains, while on the other hand
themeans by which it's trying to prevent it (namely the
expressive powerof axioms of ?st-order logic) is notoriously
ineffectual at actuallypreventing the existence of models with
in?ite regresses. but inretrospect i guess the idea is
supposed to be that that shouldn'treally bother me any more
than the similar fact that ?st-order peanologic is trying to
prevent the same kind of in?ite regresses, andessentially
fails to do so, for essentially the same reason. inboth cases
you still end up with a powerful means of proving
theoremswithin the theory by some kind of induction even
though some of themodels of the theory contain in?ite
regresses which naively seemto violate the spirit of the
inductive principles.--
===
>Since we're discussing the axiom
of foundation (in the textbooks I've seen, >it's 
called the
axiom of regularity), does anyone know what the intuitive
>justi?ation for this axiom is? I mean, all the other axioms
seem pretty >natural to me, even the infamous axiom of choice.
But where in world did >they come up with the axiom of
regularity?>The Axiom of Foundation is not really necessary -
exactly 99.93% (:-)) of mathematics can be done without it. In
fact, it even limits our universe of discourse when we accept
it. However, it is there to make things nice. Without it, it
is consistent to have pathologies such as a set which is an
element of itself, two distinct sets each of which is a
member of the other, and a sequence x of distinct sets such
that x_(n+1) is an element of x_n.The axiom also allows an
ice-cream cone construction of the class of sets. With the
axiom, there is a sequence R through the ordinals such that a
< b implies R(a) is a subset of R(b) and the universe of sets
is the well-founded sets, viz., theunion of all these sets.
(In particular, R(0) = 0 and R(a+1) = P(R(a)).) This
structure allows certain proofs in set theory; for example,
the well-founded sets provide a model for ZF.I get most of
this from Kunen.One more question: If we didn't mind invoking
the axiom of foundation, wouldn't {a, {a,b}} suf?e as a
de?ition of the ordered pair (a,b)? Seems to me the answer
is yes.-- Stephen J. Herschkorn
herschko@rutcor.rutgers.edu
===
> One more question: If we
didn't mind invoking the axiom of> foundation, 
wouldn't {a,
{a,b}} suf?e as a de?ition of the> ordered pair (a,b)?
Seems to me the answer is yes.Sure, but what makes {a, {a,b}}
better than {{a}, {a,b}}? The key isto prove that (a,b) =
(c,d) => a=c & b=d. With your proposedde?ition, the proof is
a royal pain, and the resulting thingiesaren't really any
simpler.Thomas
===
>One more question: If we didn't mind
invoking the axiom of>foundation, wouldn't {a, {a,b}} suf?e
as a de?ition of the>ordered pair (a,b)? Seems to me the
answer is yes.>Sure, but what makes {a, {a,b}} better
than {{a}, {a,b}}? The key is>to prove that (a,b) = (c,d) =>
a=c & b=d. With your proposed>de?ition, the proof is a royal
pain, and the resulting thingies>aren't really any
simpler.>Doesn't seem to like the necessary implication is
more dif?ult than with the usual de?ition.. If {a,{a,b}} =
{c,{c,d}}, suppose a = {c,d} and c = {a,b}. Then a is an
element of c, which is an element of a. This is not possible
with foundation. By contradiction, a = c and {a,b} = {c,d},
whence b = d.I would say that my de?ition is in a sense
simpler, since it requires the construction of one fewer set,
or the representation requires two fewer characters. Seems to
me that the real objection is that invokes foundation
unnecessarily. (Note that Halmos doesn't even mention
foundation in NST.)Also, once an ordered pair is well-de?ed,
one needs never refer to the de?ition again.-- Stephen J.
Herschkorn herschko@rutcor.rutgers.edu
===
> Doesn't seem to
like the necessary implication is more dif?ult than> with
the usual de?ition.. If {a,{a,b}} = {c,{c,d}}, suppose a =>
{c,d} and c = {a,b}. Then a is an element of c, which is an>
element of a. This is not possible with foundation. By>
contradiction, a = c and {a,b} = {c,d}, whence b = d.I
suppose so. (You also need to prove that {a,{a,b}} is
necessarily adoubleton, which is also a quick deduction from
Foundation.)> I would say that my de?ition is in a sense
simpler, since it> requires the construction of one fewer
set, or the representation> requires two fewer characters.
Seems to me that the real objection is> that invokes
foundation unnecessarily. (Note that Halmos doesn't even>
mention foundation in NST.)Ok, I suppose I grant your point
then. I'd only add that I think thisobjection is a very
important one. As noted before, Foundation isn'tadded because
of some intuitive con?ence, but rather because it isknown to
be harmless, and it's a big help in model theory.So that
means that one must be able to develop ordinary
mathematicswithout using it (or else it wouldn't be so
harmless, it would beimportant), and since you need to show
that, once you've done it, itis no longer interesting to show
that you could have used it here orthere along the way.So
invoking Foundation unnecessarily is a bad thing, but in a
verydifferent way from (say) invoking Choice unnecessarily.
ThomasX-Cise: tanbanso@iinet.net.auX-CompuServe-Customer:
YesX-Coriate: admin@interspeed.co.nzX-Ecrate:
tanandtanlawyers.comX-Punge: Micro$oft
===
at 06:35 PM,
Elaine Jackson <elainejackson7355@home.com> said:>The whole
problem is just that you're misquoting the axiom.No he is
not.>You say: Every nonempty B contains a y >with (B
intersect y) = empty.Not only him. Everybody who uses GBN or
ZF says so as well.>I say: Every nonempty B contains a y for
which >there is no z with z in y and z in B.In what context
do you say it?>My axiomWhat set theory is your axiom a part
of? What are the other axioms?>but it allows for the
possibility that there exist>citrus fruits that are not
sets.Then it's not part of the same set theory, it is your
responsibilityto give the complete set of axioms that you are
using.>Citrus fruits that have no elements, but aren't
the>empty set, are technically called individuals. No. There
are sets theories that have individuals without having
toabandon extentionality. Again, if you wish to be taken
seriously youwill need to state what set theory it is that
you are using.-- Shmuel (Seymour J.) Metz, SysProg and
JOATnot reply to spamtrap@library.lspace.org
===
| at 06:35
PM, Elaine Jackson <elainejackson7355@home.com> said:||>The
whole problem is just that you're misquoting the axiom.||No
he is not.||>You say: Every nonempty B contains a y |>with (B
intersect y) = empty.||Not only him. Everybody who uses GBN or
ZF says so as well.In a careful presentation, it would be
usual to write it out in termsof epsilon and =, and not
de?ed terms like intersect which technicallyare not part of
the language of ZFC.I did a web search, and I see that on
Mathworld the axiom is given as aform of the axiom scheme of
epsilon-induction, which again does not involvereferring
directly to intersections.|>I say: Every nonempty B contains
a y for which |>there is no z with z in y and z in B.||In
what context do you say it?The point here is that speaking of
intersections presupposes that theobjects in question are
sets, whereas set theories with urelementstypically consider
epsilon to be a relationship on the whole domain,including
both urelements and sets. So saying there doesn't exist a
zsuch that z in y and z in B allows for the possibility that
y or Bis an urelement (like a piece of fruit). Thus the same
statement ofthe foundation axiom would suf?e for a set
theory with urelementsof this kind.|>My axiom||What set
theory is your axiom a part of? What are the other axioms?ZFU
would be a familiar example of this kind of set theory.|>but
it allows for the possibility that there exist|>citrus fruits
that are not sets.||Then it's not part of the same set theory,
it is your responsibility|to give the complete set of axioms
that you are using.Seymour Metz is being overly formal
again.|>Citrus fruits that have no elements, but aren't
the|>empty set, are technically called individuals. ||No.But
they are.|There are sets theories that have individuals
without having to|abandon extentionality.She didn't say this
was the only sense in which the term was used. True,another
way to model urelements/atoms/individuals is to have them
bearthe epsilon relation to themselves. But that requires
either abandoningor adjusting the foundation axiom.|Again, if
you wish to be taken seriously you|will need to state what set
theory it is that you are using.The context was adequate.Keith
RamsayOk, I'm trying to work on my homework and am st on
4.9 #10 of VectorAnalysis by Davis. The question states By
means of Stokes' theorem, ?d S F*dR around theellipse
x^2+y^2=1, z=y, where F=xi+(x+y)j+(x+y+z)k.I got the curl of
F and that equalled i-j+k but I'm not really sure how to
dothe rest of the problem. Any help would be appreciated.
I've wasted a lot oftime and gotten almost nowhere.
===
I
forgot to mention that the answer is in the back of the
book:+-2pi depending upon the direction of integration.I just
can't ?ure out how to get that.
===
I'm reading about
topological groups and I am having trouble with the de?ition
of such a group. What exactly are the open sets?Any help would
be appreciated.X-Cise:
tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate:
admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge:
Micro$oft
===
at 08:02 PM, Arthur <rpall@altern.org>
said:>I'm reading about topological groups and I am having
trouble with the> de?ition of such a group. What exactly are
the open sets?That's like asking what the open sets are in a
topological space. Partof specifying a topological group is
specifying a topology; the opensets of a topological group
are the open sets of its topology.-- Shmuel (Seymour J.)
Metz, SysProg and JOATnot reply to
spamtrap@library.lspace.org
===
> I'm reading about
topological groups and I am having trouble with the>
de?ition of such a group. What exactly are the open
sets?>Hey,You can't talk about the open sets since a group is
said topological if? is continuous ( (x,y)-> x+y and
x->x^(-1)are continuous); sometimes it isalso required to be
Hausdorff. But considering a group (G,+) you can putdifferent
topologies on G so that G is a topological group (provided
that Gis continuous (and sometimes, Hausdorff)). We're not
de?ining a specialtopology here.--Julien
Santini,France.
===
> I'm reading about topological groups
and I am having trouble with the> de?ition of such a group.
What exactly are the open sets?> Hey,> You can't talk
about the open sets since a group is said topological> iff it
is continuous ( (x,y)-> x+y and x->x^(-1)are continuous);>
sometimes it is also required to be Hausdorff. But
considering a group> (G,+) you can put different topologies
on G so that G is a topological> group (provided that G is
continuous (and sometimes, Hausdorff)).> We're not de?ining
a special topology here.> --> Julien Santini,> France.>
I see.Arthur
===
Jack & Jonathan,The *Roots of Consciousness*
by Jeffrey Mishlove on the web does NOT includemy 40 page
appendix paper, Consciousness: a Hyperspace View.
Jeffreywanted to include it but there was some dif?ulty with
the complexity ofthe ?ures -- if I remember correctly. Of
course, it had never been in pdfform, since the web (& home
computers) were in a very primitive state in1993. This paper
has the most detailed account of what I now call ADEXtheory
-- the application of the A-D-E Coxeter graphs to
mathematics,physics, and other ?lds such as consciousness
theory. This appendix paperwas written in 1989, and published
in 1993. A short summary and update ofthis paper (with more
ADEX examples) was titled, A Mathematical Strategyfor a
Theory of Consciousness. It was written in 1994 and published
in thebook, *Toward a Science of Consciousness: the First
Tucson Discussions andDebates* (edited by Stuart R. Hameroff,
Alfred W. Kaszniak, and Alwyn C.Scott), MIT Press, 1996.People
have told me that my papers are hard to read without much
moremathematical knowledge than they possess. Jeffrey tells
me that Russianscientists have less trouble with the math
since their mathematical trainingis more advanced than that
of American psychologists and biologists.Actually much of the
mathematics of ADEX theory is of very recent vintage,but the
key area of mathematics is quite old -- group theory (both
?itegroups and Lie groups and relationships between them).
Our understanding ofthese relationships depends on both
algebra and geometry -- especiallyhyperspace geometry --
including differential geometry and
algebraicgeometry.Physicists who study general relativity
know some differential geometry, butthey have not studied the
more recently developed algebraic geometry -- andvery few
physicist (or mathematicians) have seen the great utility of
theA-D-E Coxeter graphs which have been used to classify more
than 20mathematical objects. The advantage of having these
classi?ations, is thatthe A-D-E graphs provide the
relationships between all these mathematicalobjects. I will
mention a few of these objects -- the study and applicationof
which I call ADEX theory: 1. Finite re?n groups (Coxeter
groups also called Weyl groups) 2. Hyperspace polytopes and
thus crystallographic lattices 3. Coxeter arrangements
(mirrors in re?n space) 4. Lie algebras and Lie groups
(& also Kac-Moody Lie algebras) 5. Thom-Arnold catastrophe
bundles (useful for Jack's version of Bohm) [BTW: Thom
claimed (1975) that it models the mind-body
relationship][Yes, this is the aspect I want to ?ut with
you.] 6. McKay groups (?ite subgroups of SU(2) -- unit length
quaternions) 7. Gravitational Instantons (closely related to
Penrose twistors) 8. 2-d Conformal ?ld theories (which live
on hyperspace strings)[Jack: It is interesting that O(2)
macro-quantum order parameter in ordinary space has string
defects e.g. Hagen Kleinert also books on soft condensed
matter physics and cosmic strings. Then introduce extra space
dimensions including fermi dimensions for supersymmetry to get
higher dim branes from the macro-quantum order parameters
perhaps with higher O(N) internal symmetry, hyper-complex
matrix order parameters over hyper-complex generalized
space-time manifolds.My model in
http://qedcorp.com/APS/EmergentGravity.doc is only the low
energy tail of that. BTW new version shows how to go from my
BIT FROM IT Landau-Ginburg eq to Andrei Linde's speci?
equations for chaotic APS-AAPT. I had discovered the friction
term from my equations a year ago not realizing their crucial
role in Linde's theory of the continuous creation of the
parallel universes.] 9. Error-correcting codes (related to
Jack's IT <--> BIT idea)That too. The mind ?ld must have
error correcting codes built into it.] 10. Quantizing
lattices (analog to digital transforms)As the motto for
Plato's academy said, Let no one enter here withoutgeometry.
Today, this geometry must include hyperspace geometry --
whichdates back to the 19th century.BTW: *Roots of
Consciousness* is mentioned at the end of John McKay's
veryshort paper, A Rapid Introduction to ADE Theory. The URL
for this paperis: http://math.ucr.edu/home/baez/ADE.htmlThis
is on John Baez's very extensive website, and from the above
URL youcan access 4 much longer (tutorial) papers by John
Baez on the ADE relatedmathematics.Nuff
said!Saul-Paul----------It's mainly metaphor and not useful
given today's advances.
===
> ....> This shows that our
modern area formula (pi)(r^2) or (pi)(d^2)/4 ....> Ken ,>
Is this really a modern formula for circle's area?.... What I
meant was modern _notation_ for the formula. I'm sorry ifthat
wasn't clear. Ken Pledger.
===
I noticed that continued
fraction expansion for sqrt( (n^2 - n + 2)^2 / 4 - n )was
quite interesting, as soon as n is very great (if n is
small,the property is still true, but not easy to see).Take
n=2^67; then, you can notice that starting from the 4-th term
in the expansion, you will ?d blocks starting with a great
value, and a few very small terms just after. What is
interesting is that a formula f(n,i) can be built that
returns rationals equal to the rational built from the i-th
block. Here is an example: for n=2^67 The 38-th block is
[22801,14,1,1,5,15,1,1,3,3,1,2,1,1,1,18,...] (length is 33).
Considering this block is the continued fraction of a
rational, we have the 38-th rational, being: 238...709 /
?onacci(38+2)^2Now, I found the formula that gives rational
equal to the successiveblocks: ?(n-epsilon) /
(?o(i+1)*?o(i+2)) ) [Times] ( ((-1)^i [Times]
?o(i+1)[Times](n-?o(i+2)-1)[Times]?o(i+2)-1) mod
(?o(i+2)^2)) / (?o(i+2)^2)Now, just put epsilon=0, and you
will see the formula is very good.BUT... The integer part is
sometimes greater (diff=1) than the realvalue; the rest of
the block is ?e.Thus, I think that an epsilon value should
be put in the formula.It looks like epsilon depends on both n
and i.It means that ?n / (?o(i+1)*?o(i+2)) )is almost
the right value for the successive big values in theinitial
continued fraction expansion, but not quite exact.Could
someone ? the formula ?PS - may my formula be simpli?d (for
instance, is it possible to remove the (-1)^i
?)Cordially,
===
> Is there a book similar to Berkeley
Problems in Mathematics, but> geared more towards the
undergraduate, and perhaps more ?ding> stuff rather than
proving stuff? I would hope the problems would be> of the
same relative dif?ulty to an undergraduate as the BPM book>
would be to a graduate. You may ?d some of what you want in
D.K. Faddeev & I.S. Sominskiiold-fashioned, but has a lot of
good problems. Ken Pledger.
===
Some of you may have noticed
frenetic activity from posters trying toconvince you that
there's nothing sinister about mathematicians doingtheir best
to downply my ?d of a way to count prime numbers
byintegrating a partial difference equation, but what's the
bottom line?Does what I found work or not?It does. End of
story, so mathematicians should acknowledge it. I?'s not
important they can just put it in some math text somewhere,or
in some journal and drive on.No big deal.But they're ?hting
to totally ignore it. Translation: Sinisterattempt by
academic types to hide something really important.Otherwise,
why go to so much effort to ?ht me, when a simple way toshut
me up on the issue is just record it somewhere? And it is
aFIRST in human history, so use your common sense.The loser
academic world is ?hting me over something that works. End
of story.These posters trying to convince you otherwise are
just insulting yourbasic intelligence.James HarrisMy math
discoveries, found for
pro?http://mathforpro?.blogspot.com/
===
> Some of you may
have noticed frenetic activity from posters trying to>
convince you that there's nothing sinister about
mathematicians doing> their best to downply my ?d [...]And
again you ?d it perfectly acceptable to hurl insults at
millions-- while reserving to play the indignant sensitive
little ?whensomeone hands you a tiny fraction of your
insults back.> of a way to count prime numbers by>
integrating a partial difference equation, but what's the
bottom line?You have yet to present any kind of way to count
prime numbers thatactually has anything to do with
integration at all.> Does what I found work or not?> It has
been conclusively proven that it doesn't.I presented the
implementation of the exact literal lines you postedhere and
you yourself could not ?d anything wrong with it.If you had
a quarrel with the implementation, you could even simplyhave
posted your own little fortran or basic or c-routine. No
bigdeal. But of course you can't.It does not work. That is
all there is to it.I have given you thebene? of the doubt
long enough to implementexactly what you posted here to see
for myself whether you're on tosomething or not. 
That's
called ?science': I go and examine theevidence myself.And I
have seen with my own eyes that you don't have anything
herethat counts primes. And further *lies* of yours to the
contrary willnot sway someone who's actually examined the
evidence himself.> It does. End of story, so mathematicians
should acknowledge it. Ah: you say so and thus it is so. ?Tis
a simple world you live in.So why does this go for you but not
for everybody else on the planet?Because there's a lot of
people out there that say you stuff doesn'twork. And contrary
to you they have evidence for their claim.> But they're
?hting to totally ignore it. Translation: Sinister> attempt
by academic types to hide something really important.Ask
yourself: how does this line distinguish you from
everyrun-of-the-mill dime-a-dozen psychotic crackpots with a
new theory ofeverything to sell, without a shred of evidence
to present and withdemonstrated lack of grasp of what they're
talking about?> Otherwise, why go to so much effort to ?ht
me, when a simple way to> shut me up on the issue is just
record it somewhere?Nobody is going to any particular effort
?hting you.Nobody is going to record anything anywhere
because there's nothing torecord here.> These posters trying
to convince you otherwise are just insulting your> basic
intelligence.Just to clarify for to odd reader out there: I
am not trying toconvince you of anything at all. (Contrary to
Mr. Harris.) Go and seefor yourself, as I did. You'll see for
yourself.
===
> Some of you may have noticed frenetic activity
from posters trying to> convince you that there's nothing
sinister about mathematicians doing> their best to downply my
?d of a way to count prime numbers by> integrating a partial
difference equation, but what's the bottom line?What you are
posting is, as usual, complete nonsense. To everyone except
you it is obvious that your supposed ?d of a way to count
prime numbers by integrating a partial difference equation is
complete and utter garbage. Pointing out that complete and
utter garbage is complete and utter garbage is not sinister,
it is the obvious thing to do. So the reason why people post
that you are wrong is just plain because you are wrong.
Nothing sinister about that.
===
> Some of you may have
noticed frenetic activity from posters trying to> convince
you that there's nothing sinister about mathematicians doing>
their best to downply my ?d of a way to count prime numbers
by> integrating a partial difference equation, but what's the
bottom line?Your work does *not* involve the integration of a
partial differenceequation. Integration is used to ?d
anti-derivatives. Differenceequations are solved using the
sum calculus. Nowhere in the exposition ofyour ?d do you
ever integrate any equation whatsoever, much less apartial
difference equation.--There are two things you must never
attempt to prove: the unprovable --and the
obvious.--Democracy: The triumph of popularity over
principle.--http://www.crbond.com
===
||> Some of you may have
noticed frenetic activity from posters trying to|> convince
you that there's nothing sinister about mathematicians
doing|> their best to downply my ?d of a way to count prime
numbers by|> integrating a partial difference equation, but
what's the bottom line?||Your work does *not* involve the
integration of a partial difference|equation. Integration is
used to ?d anti-derivatives. Difference|equations are solved
using the sum calculus. Nowhere in the exposition of|your ?d
do you ever integrate any equation whatsoever, much less
a|partial difference equation.you're ly herman rubin 
isn't
reading these threads.--
===
>Some of you may have noticed
frenetic activity from posters trying to>convince you that
there's nothing sinister about mathematicians doing>their
best to downply my ?d of a way to count prime numbers
by>integrating a partial difference equation, but what's the
bottom line?Does what I found work or not?It does. End of
story, so mathematicians should acknowledge it. If>it's not
important they can just put it in some math text
somewhere,>or in some journal and drive on.No big deal.But
they're ?hting to totally ignore it. Translation:
Sinister>attempt by academic types to hide something really
important.Fascinating. If people were raving about how
important it wasof course that would prove it was important.
In fact people areignoring it, and curiously that also proves
it's important.Do you really think anyone's buying
this?>Otherwise, why go to so much effort to ?ht me, when a
simple way to>shut me up on the issue is just record it
somewhere? Huh? First, nobody's going to any trouble - what
looks to you likepeople going to a lot of trouble is just
people having a bit ofgood-natured fun with the village
idiot. And second, all yourstuff _is_ recorded, right there
on Google. (You're going to ?dthat fact embarassing if you
ever sober up...)> And it is a>FIRST in human history, so use
your common sense.The loser academic world is ?hting me over
something that works. End of story.These posters trying to
convince you otherwise are just insulting your>basic
intelligence.Uh, right. Our common sense tells us that when
people on sci.math,you harass in person _all_ ?d your work
of no interest the onlypossible explanation is that they all
realize it's tremendouslyimportant, and every single one of
them is quick enough to realizehe needs to lie about his
opinion before once saying oh my godthat's incredible even
once.That's not common sense as we know it, Jim.>James
HarrisMy math discoveries, found for
pro?>http://mathforpro?.blogspot.com/David C. Ullrich
===
>
> Some of you may have noticed frenetic activity from posters
trying to> convince you that there's nothing sinister about
[snip]> My math discoveries, found for
pro?[snip]http://www.crank.net/harris.html It's not every
braying jackass that gets a whole page at crank.net-- Uncle
Alhttp://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for
children and most mammals)Quis custodiet ipsos custodes? The
Net!
===
James Harris> Some of you may have noticed frenetic
activity from posters trying to> convince you that there's
nothing sinister about mathematicians doing> their best to
downply my ?d of a way to count prime numbers by>
integrating a partial difference equation, but what's the
bottom line? Does what I found work or not?He's talking about
this one:For newbies: www.crank.net/harris.htmlFor
harrisologists:
mathdb.math.cuhk.edu.hk/forum/e_show.php?msg=705
===
James I
believe that the people responsible for covering up the
Roswellincident are the same people responsible for
suppressing your worldchanging ideas about algebraic
integers, and your prime counting function.I would be careful
about what you say of the government. You may end upspeaking
with Mulder and Scully.Lurch> Some of you may have noticed
frenetic activity from posters trying to> convince you that
there's nothing sinister about mathematicians doing> their
best to downply my ?d of a way to count prime numbers by>
integrating a partial difference equation, but what's the
bottom line? Does what I found work or not? It does. End of
story, so mathematicians should acknowledge it. If> it's not
important they can just put it in some math text somewhere,>
or in some journal and drive on. No big deal. But they're
?hting to totally ignore it. Translation: Sinister> attempt
by academic types to hide something really important.
Otherwise, why go to so much effort to ?ht me, when a simple
way to> shut me up on the issue is just record it somewhere?
And it is a> FIRST in human history, so use your common
sense. The loser academic world is ?hting me over something
that works. End of story. These posters trying to convince
you otherwise are just insulting your> basic intelligence.>
James Harris My math discoveries, found for pro?>
http://mathforpro?.blogspot.com/
===
And that are my
dogs!Mulder and Scully are two lovely dogs, Amstaffs of
course. They love Harrisas I do. I and them would like Harris
to be honest about his work andcommit to failure. Or
else!!!!What I really want is that Harris fully gave his work
a scrutiny whichincluded all the corrections from the
bistanders and helping hands. Then hecan conclude and put
forward his proof.One last question to Harris:What is the
difference between algebraic numbers, algebraic
integers,numbers, integers and complex numbers?Karl-Olav
Nyberg
===
> One last question to Harris: What is the
difference between algebraic numbers, algebraic integers,>
numbers, integers and complex numbers?LH
===
What is the
difference between algebraic numbers, algebraic integers,>
numbers, integers and complex numbers?I believe you might
have to wade through JSHs Object Oriented Mathematicsand the
brilliance that that has yet to shine on all of us losers
before youcan even ask the self-proclaimed highest ranking
number theorist in theworld.In fact, Mr. Harris ego is
growing at a super-exponential rate and soon noone in
sci/math will be able to contain his NPD!
===
> Some of you
may have noticed frenetic activity from posters trying to>
convince you that there's nothing sinister about
mathematicians doing> their best to downply my ?d of a way
to count prime numbers by> integrating a partial difference
equation, but what's the bottom line?> Does what I found
work or not?>Now that is an interesting question, isn't it!
pssst, hey Harris... your stuff doesn't work.... but 
don't
tell anybody...
===
> Some of you may have noticed frenetic
activity from posters trying to> convince you that there's
nothing sinister about mathematicians doing> their best to
downply my ?d of a way to count prime numbers by>
integrating a partial difference equation, but what's the
bottom line?> Does what I found work or not?> Now that
is an interesting question, isn't it! > pssst, hey Harris...
your stuff doesn't work.... but don't tell 
anybody...And Sam
Wormley, surprise, surprise, is making a false statement as
it*does* work, but I'm not terribly surprised by his immature
behavior.After all, I found this partial difference equation,
which integratesover a certain range to give a count of prime
numbers!!!Here's the equation:dS(x,y) = [p(x/y, y-1) - p(y-1,
sqrt(y-1))][ p(y, sqrt(y)) -p(y-1,sqrt(y-1))],Here are the
instructions for the integration:S(x,1) = 0.And p(x, y) =
?) - S(x, y) - 1, and you get S as the sum of dSfrom
dS(x,2) to dS(x,y).Now for someone like Sam Wormley it
probably doesn't seem fair thatI'm here posting on 
Usenet
stealing thunder from everyone else, buthey, blame the
mathematicians.The bottom line on my work is that it DOES
work.Now then, do any of you know *how* it works?Maybe some
poster will reply to this post to explain it to you, buthow
do you trust them?And what about the story--my story--of the
discovery?What was I thinking? What motivated me to look in
this area? What'sthe story?If mathematicians hadn't 
decided
to break faith with you and the restof the world, probably
there'd be a book, some popular work,explaining the story.But
how can you get that story if mathematicians are playing
theiracademic games?Bottom line: What I have works.So what if
I sell my story and get rich. That's how capitalism works.
These mathematicians are worse than communists, as how do you
explaintheir behavior?I *am* the American Dream, ?hting for
what should be mine, having toget past weak-minded academics
who are ?hting to block my success. But I shall
prevail!!!I'm sure some hate that I'm in it for the 
money.
But why screw overthe world, why screw *you* over by blocking
the story of my success?What's their motivation?James HarrisMy
math discoveries, found for
pro?http://mathforpro?.blogspot.com/
===
>If mathematicians
hadn't decided to break faith with you and the rest>of the
world, probably there'd be a book, some popular
work,>explaining the story.But how can you get that story if
mathematicians are playing their>academic games?Bottom line:
What I have works.So what if I sell my story and get rich.
Psst, James, there is a very small market for stories about
mathematics.Better ?d some way to work in spies and the CIA,
and pretty girl agents,and such like. And sex. Sex always
sells, even when the sex scenes areseparated by boring
mathematical explanations. People just skip those.-- Wolf
Kirchmeir, Blind River ON CanadaNature does not deal in
rewards or punishments, but only in consequences.(Robert
Ingersoll)
===
>If mathematicians hadn't decided to break
faith with you and the rest>of the world, probably there'd be
a book, some popular work,>explaining the story.>But how can
you get that story if mathematicians are playing
their>academic games?>Bottom line: What I have works.>So
what if I sell my story and get rich. > Psst, James, there
is a very small market for stories about mathematics.> Better
?d some way to work in spies and the CIA, and pretty girl
agents,> and such like. And sex. Sex always sells, even when
the sex scenes are> separated by boring mathematical
explanations. People just skip those.A very small market in
today's world can be worth millions of dollarsUS.The bottom
line is that what I have works, people expectmathematicians
to report on discoveries, but they are not doing
theirjobs.It's easy to check using Google. Go search on
partial differenceequation which can verify for you that they
are real. Then search onprime counting or counting primes to
see if ANYONE besides me hasever used a partial difference
equation to count prime numbers.For those wondering what they
might do to help, I think that maybeknows what might
happen?James HarrisMy math discoveries, found for
pro?http://mathforpro?.blogspot.com/
===
>A very small
market in today's world can be worth millions of
dollars>US.IMO, you need to brush up on your arithmetic,
too.-- Wolf Kirchmeir, Blind River ON CanadaNature does not
deal in rewards or punishments, but only in
consequences.(Robert Ingersoll)
===
> For those wondering what
they might do to help, I think that maybe> knows what might
happen?Dear Time Magazine,Here is what can happen with
education gone bad, a person with delusions ofgrandeur, fame
and fortune. This individual believes he is one of
thegreatest number theorists and analytical researchers of
ALL TIME!Can you perhaps run a story on NPD (you have a
real-live case here)?Here is a clinical de?ition of
NPD:<http://www.behavenet.com/capsules/disorders/
narcissisticpd.htm>Diagnostic criteria for 301.81
Narcissistic Personality Disorder (cautionarystatement)A
pervasive pattern of grandiosity (in fantasy or behavior),