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- Re: Topos theory: axiom of choice implies a topos is Boolean
I gather that Goldblatt differs from other texts in that it says very
little about how topoi arise in algebraic geometry and is instead
focussed on the interplay between topos theory and logic. This suits me
since I'm not interested in AG but am learning about topos theory for
applications to the foundations of quantum mechanics, but the author
- Re: It's Pi Day: Whose birthday is not in pi?
And today is Albert Einstein's birthday, so Einstein was a...
Pi-eces!
Leroy
- Why Peano Curve is a curve?
Peano Curve, the limit of a curve sequence, is known as "space-filling curve".
It's easy to understand that the limit filling the square. But why it is not just a square, but also a curve?
It seems that the limit of a curve sequence is not necessary a curve. Think about this curve sequence: f(n): x*x + y*y = 1/n. (A sequence of concentric circles). The limit of f(n) is just a single point (0, 0). Of course the limit is not a curve, and it is not mean a single point and a curve contain the same number of points. Why Peano Curve means a curve and a sequence contain the same number of points?
- Re: Topos theory: axiom of choice implies a topos is Boolean
I think I've figured out how to show that f u j = 1 (I'll omit
subscripts on identity arrows for brevity). Firstly, since f u j = (f u
j_1) n (f u j_2) it suffices to show that 1_d factors through f u j_1
and f u j_2. Now observe that, by the aforementioned fact about
pullbacks of coproducts, the following is a pullback:
- Re: Can you use the word "assigning" to mean "mapping"?
My knowledge of German is hopelessly inadequate
to finding a parallel distinction "auf Deutsch".
But I do hear in "zuordnen" a cognate to the word
"ordinate" which is commonly understood to be
the value along the vertical axis which is
dependent upon the "abscissa" (value along the
horizontal axis) in speaking of Cartesian
- Re: Can you use the word "assigning" to mean "mapping"?
On 14 Mar, 16:03, "Achava Nakhash, the Loving Snake"
As a native UK English speaker, I am ashamed to admit that I have no
idea at all what you mean by "I plan to get a back about some day". My
best theory so far is that you mean "book about it".
But on the topic of the thread, although it can become tedious, I
- Re: Source of term "multiplication" in matrix multiplication
I'm curious as to why it matters. Can you give me a good argument why
knowing the true etymology has any real significance in mathematics? We can
propose several likely reasons that are all logically coherent. Is it really
important to know which one is historically true? We can imagine that any of
- Re: It's Pi Day: Whose birthday is not in pi?
I prefer the continued fraction representation of pi to the decimal
expansion. Since the first three terms of the continued fraction
expansion of pi are 3, 7, 15, then this kind of pi birthday would be
March 7th, 1915 or 2015. Or maybe July 3rd of 1915 or 2015, given the
order of day and month in much of the world vs the US.
- Re: An Ultrafinite Set Theory
If {1,2,3} is your set of natural numbers and 1/3 is your smallest
real number then there is no such thing as 2^2, 2^3, 1/4, 1/8, and
you've got four terms in calculation when you've said that only three
are allowed, ...
Shouldn't it be, according your rules:
Sum(1/2^n) = 1/2
(Actually, you haven't yet shown us how to get the existence of 1/2
- Re: JSH: Biggest mystery, pondering again hostility
My idea rips the prime distribution out of the equation.
THAT is MY point which you seem intent on ignoring or missing over and
over and over again.
So no, it doesn't correlate with ANYTHING you mentioned and the
correlation is a well-defined value when you're talking about a
predicted value and an actual value. Here you seem to not be sure
- Re: Source of term "multiplication" in matrix multiplication
s/matrices/NxN matrices/ (i.e. what you say is only true of square
matrices of a particular size).
Overall, the above sounds like a post-justification rather than a
probably explanation of the term. Ring theory started with
Dedekind in about 1870 and it was not until the early 20th century
that rings were unified by axiomatising the abstract structure
- Re: Can you use the word "assigning" to mean "mapping"?
On Mar 13, 10:36 am, Jose Capco
wrote:
Using "assigning" doesn't strike me as wrong, but I would not have
used it. Using "mapping" is clearly not wrong. Personally, I would
use "taking". Since you are asking about the fine points of English,
and I can only speak accurately for American English, it is incorrect
- Re: I Think Therefore I Am - rebuttal
What Ed Green said is correct. And I will add that even if all of
these various configurations of matter, or chess games never actually
happened, they are all OBSERVABLE.
You cannot observe a chess game between 2 people where 3 people
actually win. That would be an unobservable chess game.
Descartes claims "I think....therefore a,b,c,d,e...". He might as well
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- Re: I Think Therefore I Am - rebuttal
You miss my point, really. The word "logical" perhaps could have been
just as easily been removed from the sentence. Does that make it
clearer? There is no arrangement of matter or information we can make
that was not a feasible arrangement of matter or information, just as
there is no (legal) game of chess that can be played which was not
- Re: According to their plan, the first 2*3.5TeV collisions will be performed the 30-th of March. I’m scared, but can not do anything, - all ways lead to catastrophe. LHC/CERN.
Here is not complete list of your potential killers: 2003 J.-P.
Blaizot, J. Iliopoulos, J. Madsen, G.G. Ross, P. Sonderegger, H.-J.
Specht. 2008 John Ellis, Gian Giudice, Michelangelo Mangano, Igor
Tkachev, and Urs Wiedemann. And of course, Rolf Heuer, director of
CERN, who neglects the opinion of physicists, saying about dangers of
- Re: I Think Therefore I Am - rebuttal
- It's Pi Day: Whose birthday is not in pi?
Hello all,
At least not in the first 200 million digits, that is. David
Andersen's cool applet,
[link]
allows you to search for an arbitrary string of digits in the
database. It we use the convention mm/dd/yyyy, then today is
03142010, and it occurs after the 54th million decimal place.
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- Re: Can you use the word "assigning" to mean "mapping"?
You are wrong; 'assigning' can't be used in that way. You should
realise that your English is less than perfect, too, and take
correction unless you have damn good evidence on your side.
Andrew Usher
- THE FALL OF RIEMANN'S HYPOTHESIS--INVERSE 19 MATHEMATICS
This is to announce that Hope research has the capabilty right now to
to assign primality to any number, and project any prime placement due
to our recent posted disscovery last night of the culmination of a
"well recorded research" that the "weld points" or the "circlage
Points" between the Prime number proportion are at exact 6, and 36
- Re: e^e
Tony wrote in news:fa015042-af9c-4f4d-9271-
e05f5afb3...@t20g2000yqe.googl egroups.com:
An old "West Coast Number Theory" problem, (before 1980,
I think) asks for the existence of a "Humdrum Number"
which was defined as an integer N such that e^(e^N) is
an integer. As far as I know, this remains unresolved.
- Re: e^e
No.
- Re: According to their plan, the first 2*3.5TeV collisions will be performed the 30-th of March. I’m scared, but can not do anything, - all ways lead to catastrophe. LHC/CERN.
Thunder (sound) doesn't exhibit much of a temperature increase
in and of itself. The energy of an average 3 mile-long lightning
strike is one billion to ten billion joules--6.24 x 10^16 TeV, but
spread out over much greater time and space as compared to a 7 TeV
proton-proton collision.
- Re: Some Subgroups of SL(2,Z) of finite index
Yes indeed.
This makes me think as the product of numbers of points in projective
spaces GF(p^(n-i))^i
Thanks a lot for your valuable advice.
- Re: tanx=x
Actually Wikipedia has a pretty nice writeup
of details related to Euler's solution here:
[Basel problem -- Wikipedia]
[link]
regards, chip
- Re: The perpetual calendar
Nope. It's any change. And I go to bed when I'm tired. I get up
when I wake up. IOW, my life isn't run by the clock but others are.
It's extremely annoying to be woken up at 21:30 by chattering neighbors
who don't go to bed while the outside light is on. Closing windows
in the summer is not an option.
- Re: The perpetual calendar
And, finally, somebody is thinking and the news media are reporting it.
It's not last night which is the problem. It's the mornings which
are now dark until 08:00 and, later in the summer, the "nights"
which are lit up until 22:00.
My sister told me it take months for her to get used to the change.
- Re: tanx=x
All roots of sin(z) are 0, +/- pi, +/- 2*pi,... ,
so when we pass to S(u) = sin(z)/z with u = z^2,
the roots are u = pi^2, 4*pi^2, 9*pi^2, etc.
Consider the complex plane if one wishes to
pursue Enrico's point (see upthread) in the
simpler context of sine:
sin(x+iy) = sin(x)*cosh(y) + i cos(x)*sinh(y)
- Re: Outer measure
On Sat, 13 Mar 2010 15:27:31 -0500, "G. A. Edgar"
Took me a minute to see what the definition of w should be...
Let's restrict everything to [0,1]; what happens in the complement
doesn't matter. In particular, B is [0,1] \ A.
Then B also has inner measure 0 and outer measure 1.
So we define
w((E cap A) union (F cap B) = (1/2) (m(E) + m(F)).
- 40 Days
40 days since Groundhog Day on February 2.
- Re: Source of term "multiplication" in matrix multiplication
We can start observing that there is the »natural«
way to »add« matrices, by adding the components.
So, therefore, this is called »addition«.
I assume that the algebraic laws for matrix
multiplication then relate it to matrix addition
in the way multiplication is related to addition
- Re: According to their plan, the first 2*3.5TeV collisions will be performed the 30-th of March. I’m scared, but can not do anything, - all ways lead to catastrophe. LHC/CERN.
The behavior of dangerous condensate, which are bombarded by eV or TeV
particles, is analogues to behavior of another condensate – nucleus,
consisting of protons and antiprotons. Let’s suppose that atmosphere
consists of protons and stable neutrons.
It is theoretically permitted that in the collision of cosmic proton
- Re: Outer measure
On Sat, 13 Mar 2010 15:27:31 -0500, "G. A. Edgar"
Eewps, back to the drawing board...
- Re: tanx=x
I'm pretty sure the tan x = x problem was an American Math Monthly
problem, maybe as long as 30 years ago.
- Re: JSH: Math, logic, pragmatic reality and primes
Maybe "harry" would like to do a word count on that text also.
---
J K Haugland
[link]
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- Circular Curve Path
Here is a link to the KBH Circular Curve Path:
[link]
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- Re: tanx=x
On Fri, 12 Mar 2010 11:50:22 -0800 (PST), Chip Eastham
in this page one use a polynomial's result
for S=1-u/3!+u^/5!+...but S is not a polynomial
because S=sinz/z with z^2=u
and all roots of sinz/z are not pi, 2*pi, 3*pi....
- Re: Can you use the word "assigning" to mean "mapping"?
Of course, supervisors are paid to pick a yoon.
"Mapping" is more professional.
"Assigning" lacks professionalism.
I'd write, "Let f:A -> B be a monomorphism."
To be loquacious, I'd write, "Let f:A -> B be a monomorphism from A to B."
If I were being paid by the word or wanted to small talk, I'd write,
- 19Degrees vs 18.94736842105 degrees" NEW MATHEMATICS OF THE OPEN AND CLOSED HORIZONS BY INVERSE 19 MATHEMATICS
AS A RULE IT IS A RULE OF INVERSE 19 MATHEMATICS that "19 Degrees in
the Open horizons and 18.9473... in the closed horizons" . This is
important because this is why Inverse 19 will challenge the tensors
and use of 8 Pi in Einstiens Equation which did not appreciate -1,
Tensors were done by Riemann who himself did not full;y understand
- Re: CLIMATE-GATE, RELATIVITY-GATE, ENTROPY-GATE
[link]
"Scientists have made a major discovery using the Large Hadron
Collider, the world's largest atom-smasher, a $5 billion feat of
engineering built to re-create conditions in the universe just after
- Re: The perpetual calendar
The reason that some posters mentioned the 28-hour day is that
it can be implemented simply by taking one of the 24-hour days
of the week and divide it into sixths, giving four hours each to the
other six days of the week.
The first website to give this proposal is actually the following
link:
[link]
- What is this figure called? A wedge? #517 Correcting Math
Alright, I confirmed my suspicions that a tetrahedron in 3D is a no-go
as the best tiler
because of obvious inability to form a solid packing with no gaps in
between.
I found this website to show me the densest tetrahedron packing:
--- quoting from wolfram ---
[link]
- Re: RELATIVITY INCOMPATIBLE WITH QUANTUM MECHANICS OR WITH ITSELF?
Philosophers of science giving advice about inconsistent theories (IN
CAPITALS):
[link]
"Internal inconsistency is a defect in a theory that gives grounds for
seeking a better theory. Proving that a theory is inconsistent has the
same import as showing that it has false empirical consequences:
- Re: The perpetual calendar
I think the problem jmfbah has when we fall back is that she feels
tired an hour before bedtime. That's why for her, Year Round
Standard Time is the best.
Cheryl points out how to her, the fall back clock shift isn't as bad
as
the spring forward clock shift. This reminds me of a classic joke
about
how to make springing forward feel more like falling back:
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