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Bill Dubuque
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 Posted: Mon Jul 14, 2008 8:02 pm Post subject: Re: #580 All Possible Digit Arrangements destroys the old va |
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plutonium.archimedes@gmail.com wrote:
[quote]Bill Dubuque <wgd@nestle.csail.mit.edu> wrote:
plutonium.archimedes@gmail.com wrote:
Where Natural Numbers = AP-adics ..
Archie, before I can comment you need to answer the following
questions about your ring of AP-adics, henceforth called AP.
1) Is the hypothesized ring AP a (totally) ordered ring, i.e.
does AP have a subset P of "positives", closed under + and *,
with every elt either positive (in P), negative (in -P) or 0 ?
2) Are the positive elements P well-ordered, i.e. does every
nonempty subset of P have a least element?
Lurkers please refrain from commenting until AP responds.
Well, Bill, the reason I wanted you to give a Euclid Infinitude of
Primes proof, both Integers, which is an ill-defined set [...]
[/quote]
I didn>t see an answer to my questions. Could you please plainly
answer either true or false to the above questions. It would help
if you could do so concisely, e.g. something like:
1) is ____
2) is ____
--Bill Dubuque |
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| Posted: Mon Jul 14, 2008 8:37 pm Post subject: #585 Geometry is superior to Algebra and dictates what numbe |
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lwal...@lausd.net wrote:
[quote]On Jul 14, 8:02�am, Bill Dubuque <w...@nestle.csail.mit.edu> wrote:
plutonium.archime...@gmail.com wrote:
Bill Dubuque <w...@nestle.csail.mit.edu> wrote:
1) �Is the hypothesized ring �AP �a (totally) ordered ring, i.e.
� � does AP have a subset P of "positives", closed under + and *,
� � with every elt either positive (in P), negative (in -P) or 0 ?
2) �Are the positive elements P well-ordered, i.e. does every
� � nonempty subset of P have a least element?
Lurkers please refrain from commenting until AP responds.
Well, Bill, the reason I wanted you to give a Euclid Infinitude of
Primes proof, both Integers, which is an ill-defined set [...]
I didn>t see an answer to my questions. Could you please plainly
answer either true or false to the above questions. It would help
if you could do so concisely, e.g. something like:
1) is ____
2) is ____
Archimedes Plutonium gives a partial answer to this
question in another thread, post #581:
The way I have set up the AP-adics is that they form the intrinsic
numbers that lie one the surface of
a ellipsoid (set of all positive AP-adics) and lie on the surface of
a pseudosphere (set of all negative
AP-adics).
So there definitely exist positive and negative AP-adics.
[/quote]
Euclidean Geometry can be thought of as a box with the zero point in
the middle
and the Cartesian coordinate system radiating outwards from the zero
point.
Every point in this Euclidean Space covered by a number which is an
All Possible
Digit Arrangement of infinite rightward string, both positive and
negative signed.
So Euclidean Space is a network where the points are numbers but where
there
are always holes between numbers
Here is all possible digit arrangements of two digits to the two place
value:
00 01
10 11
So there are 4 numbers in that category and no more (no more to
concoct a phony
Cantor diagonal). Notice also that in that category you cannot have
"absolute continuity"
for there is a hole between 00 and 01 or between 00 and 10.
Likewise do the same for All the Reals which would be a matrix that
would be infinite cardinality
and not just a 4 cardinality. And these Reals would be all possible
digit arrangements and would
have a hole between any two Reals. Cantor diagonal does not work here
either.
Now, if we pluck out of the All Reals those that are negative signed
such as (-) 0.3333....3333
and flipped them around we have (-) 3333.....33333 which is a negative
AP-adic.
The collection of all the negative signed Reals when flipped around
form the negative AP-adics
and form a Hyperbolic geometry that is the pseudosphere.
Now if we take all the positive Reals such as for example
0.6666....6666 and flip them around
would be 6666....66666 a positive AP-adics and would form Elliptic
geometry with the tacking on
of two imaginary numbers for the North and South Pole.
So the Reals are All Possible Digit Arrangements of infinite rightward
strings, both positive and negative
signed. They form Euclidean geometry
We can pluck out all the positive Reals, flip them over to make
infinite leftward strings and they form
Elliptic geometry
We can pluck out all the negative Reals, flip them over and they form
Hyperbolic geometry.
So algebra never enters the picture in this program. This program is
all about Geometry and what numbers
are intrinsic to geometry.
After we have all the numbers and geometry settled, can we go back and
then reflect on what Algebra
exists for the AP-adics and what exists for the Reals, since both of
them started from
All Possible Digit Arrangements. That means most of the Algebra of the
past century is flawed and phony.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies |
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Bill Dubuque
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| Posted: Tue Jul 15, 2008 10:47 am Post subject: Re: #584 how modern day Galois Algebra theory is a pool of p |
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plutonium.archimedes@gmail.com wrote:
[quote]Bill Dubuque <wgd@nestle.csail.mit.edu> wrote:
plutonium.archimedes@gmail.com wrote:
Bill Dubuque <wgd@nestle.csail.mit.edu> wrote:
plutonium.archimedes@gmail.com wrote:
Where Natural Numbers = AP-adics ..
Archie, before I can comment you need to answer the following
questions about your ring of AP-adics, henceforth called AP.
1) Is the hypothesized ring AP a (totally) ordered ring, i.e.
does AP have a subset P of "positives", closed under + and *,
with every elt either positive (in P), negative (in -P) or 0 ?
2) Are the positive elements P well-ordered, i.e. does every
nonempty subset of P have a least element?
Lurkers please refrain from commenting until AP responds.
Well, Bill, the reason I wanted you to give a Euclid Infinitude
of Primes proof, both Integers, which is an ill-defined set [...]
I didn>t see an answer to my questions. Could you please plainly
answer either true or false to the above questions. It would help
if you could do so concisely, e.g. something like:
1) is ____
2) is ____
No, I gave you answers. Euclidean geometry is composed of Elliptic geom
unioned with Hyperbolic geom [...]
[/quote]
Archie, I can only help you if you answer my questions concisely
by filling in the blanks above with either "true" or "false".
--Bill Dubuque |
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Ravi
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Grayvyard Mushruumz
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| Posted: Sun Oct 12, 2008 4:04 pm Post subject: Optical Disk Copies Must Be Gifts. |
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The mystic chords of memory... will yet swell the chorus of the Union
when again touched, as surely they will be, by the better angels of
our nature.
--Abraham Lincoln
<a href="http://ecn.ab.ca/~brewhaha/font/Saffron_Karaoke_Duet.wmv"
[quote]Manuscript Education.</a
[/quote]
I don>t think any teacher would argue against paired stimuli being
useful. What might not hav occurred to the average teacher is that he
is a more important and demanding stimulus than any video. That video
is no longer a duet. And it>s not as dark as it began. It>s a quartet
of Choral Dance, and the main demand I make regarding copyright is for
intact distribution.
Beyond the alphabet song that children will undoubtedly learn from
Sesame Street, it>s in a manuscript font very much like the standard
with just a bit of ornamentation, and it attaches different vowels to
consonants. Hopefully, that makes it easier to see how many options
exist for mixing and matching letters. It>s also in colour to
highlight phonetic relations that are usually reserved for University
students studying linguistics. Finally, it>s in a different order, and
for that same latter purpose of letting children know which consonants
can be confused, especially in noisy conditions.
Only the nasals are led by vowels, and that is because I find it
awkward to lead a word with ng. I had the choice of making one
exception or an exception for the whole group. That same group
contains the schwa only because I wanted a limit of five members per
group. That makes some of my graphics neater. Recently, I noticed that
aI is a dipthong, so I spelled it with the oE digraph, because I think
that was the orijinal purpose of that digraph in fonts.
To a music teacher, if there is someone besides myself willing to
teach this work to the point of a-cappella rendition, I also hav six
duets on my web page: SA TB SB TA ST and BA (Front, back, left-
diagonal, right-diagonal, left, right in one usual way of placing
singers; hard parts in the middle). I plan to render them with
instruments other than sine waves. I hope you will not be too
surprised to find that my tuning is not entirely on western octaves,
even if my opening chord can be found on a piano. GCGE (going up, also
identifiable as
2,3,4,5, or a fifth, a perfect fourth, and then a major fourth).
Lyrics are a tricky business in two places of my song. "Xah" is not
"ksah" (extend), "kshah" (Luxury), "gzhah" (Luxurious), or
"gz" (example); it>s a Welsh, Celtic, and Jerman sound in "Loch" as
the Scots say it; a glottal hiss. Qay is not a collision with the
standard name for our letter Kay; it>s a voiced glottal hiss or growl
that you might hear from Spaniards pronouncing an English awr. Dhose
are the only two sounds in the entire work that are not English.
_______
<a href="http://ecn.ab.ca/~brewhaha/">BrewJay>s Babble Bin</a> |
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