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I am going to get back to the symmetry in proof method of Euclid
Infinitude of Primes, and even
expose some questions on the Euclid number "multiply the lot and add
1" for I sense that this
number is really zero add 1 or 1. Why? because primes such as
100000…..000001 devour
other primes in multiply the lot add 1.

But this diversion is far more important for it involves the
definition of prime, multiplication and
division. When I was doing the first edition of this book in Sept
2007, I let myself be swayed
wrongly. This sometimes happens to the best of us in a science since
what we are doing is
brand new, new discoveries, and so with our new discoveries we are not
quite sure of things
and when some one of the old school voices doubts and skepticism we
tend to fall back
into the old wrong way of doing things.

So when I defined "primeness" in AP-adics and said that
99999….9999997 was the world’s
largest prime number and that the number of primes between
99999…999900 and 99999….9999
was almost equal to the number of primes between 0 and 100, that I was
easily taken aback
when Dik Winter wrongly asserted 9999….999997 was divisible by 7.

I do not know why I did not stand my ground more fiercely and why I so
easily succumbed
to the muddleheadedness.

- — -

> Good try but not true.

> The definition as setup in what I am going to rename as AP-adics so as
> to not confuse with P-adics (as Wikipedia teaches me to call them
> something different).

> Anyway the definition of multiplication and division uses a radix if
> there is a remainder. And the final answer is a Cauchy Sequence over
> all
> the piecewise divisions. So if the radix disappears and never again
> shows up then the number is composite, but if the radix continually
> shows up, even though one or two piecewise divisions is even, means
> the
> final answer is composite.

> 7 into 97 is 13.8
> 7 into 997 is 142.4
> 7 into 9997 is 1428.1
> 7 into 99997 is 14285.2
> 7 into 999997 is 142856.7
> 7 into 9999997 is 1428571
> 7 into 99999997 is 14285713.9
> and the fractional radix repeats in a block

> So the Cauchy sequence of the above never eliminates the radix, does
> it,
> so it is Prime not composite.

> Just because you can find one smooth even division every periodically
> in
> the sequence does not make it overall Composite. To be overall
> Composite
> then the Cauchy Sequence stops yielding a radix answer.

Okay, it may not be a Cauchy Sequence but something else in which I
defined multiply, divide
and primeness above.

But the idea is all there. The idea that to be prime means the radix
never disappears. A prime
number such as 11 has only one division in which the radix disappears
in division by 11. The
prime number 9999….99997 has many divisions in which the radix
disappears, but the definition
as I set it up, qualifies a number as prime if the number makes all
future divisions of its radix
disappear.

The number 0000….0000011 is prime because of this
11 into 0000…000011
11 into 011 is 1
11 into 0011 is 1
11 into 00011 is 1
no more radix remainder

The number 9999….999998 is composite because all radixes disappear
when dividing by 2
2 into 98 is 49
2 into 998 is 499
2 into 9998 is 4999
no more radix

The number 9999….99997 when dividing by 7 never makes all the
radixes disappear and thus
is prime.

My definition of how to multiply, how to divide and what is prime
versus composite is superior to the
old mathematics definitions and ways of doing things. So superior that
my definition includes "primeness
in Reals".

My definition, now says that 0.99999….. is no longer equal to 1 but
is different from 1.0 by a number
that is 0.0000….000001

So we have primeness on the Reals from 0 to 1. And this primeness on
Reals is a mirror image
symmetry of the primeness of the Counting Numbers from 0 to
9999….99999

Now is there anything in mathematics that forces us to accept the
above as the definitions? Forces
us whether we like it or not? And the answer is a yes, as I set up
this entire program with the
conjoining of Elliptic geometry to Hyperbolic geometry that the union
of the two forms Euclidean
Geometry. So my definitions conjoin those geometries.

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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Can anyone tell me why there is no ‘set of agents’ expressly defined
in the models of epistemic logics (ELs)? And why is there no
agent-assignment protocol defined in their semantics? Take for example
propositional ELs that use agent-indexed operators, such as in Fagin
et al [1] which uses knowledge operators K_1, … , K_n where each K_i
denotes the knowledge of agent i. The wikipedia entry uses Fagin’s
system. [2] Another example of a propositional EL is at [3].

Yet in each of those cases (and no exception that I can find), while
there is acknowledged to be a ‘set of agents’ (as there must be), the
models are <S, pi, K_1, … , K_n> in the case of Fagin (where S is a
set of possible states, pi is a proposition-valuation function, and
then the agent-indexed operators, see [2]) and a classic Kripke model
<W,R,V> in the case of [3].

Why do those models not expressly specify the set A of agents, as for
example <W,A,R,V>? Moreover, in FOL there’s typically an assignment
function g to map variables g(x) or an interpretation function I to
map constants I(c) in the language to objects (like agents) in a
domain. Yet in propositional ELs there are also symbols in the
language to serve as names for agents, yet no assignment protocol for
mapping them to agents in the domain. Why? Even more confusing to me,
look at Definition 1 of [3], agents (denoted by ‘a’) clearly seem to
be defined as being *in the language*, as if the name for an agent ‘a’
is the same thing as an agent it names. (That is actually done in some
logics where ‘parameters’ may serve dual roles as both elements in a
language and entities in the domain, which seems like throwing the
concept of ‘semantics’ out the window (except in the case of Herbrand
models where all objects in the language are in its domain, but that’s
different than the mixed cases I’m describing).)

I’d think that one should want to not only specify a set A of agents
in the model of an agent-denoting EL, but also define an assignment
function for mapping names in the language to agents in the domain,
even if the EL is propositional. So long as the language has names
that denote specific agents, it would seem that a rigorous semantics
must as well define a name-assignment function. Yet this isn’t the
case in any EL I can find, and so I’m hoping someone can set me
straight on why these features are apparently not necessary, or if
including them would in some way be an error. ~Wonderer

_________________________________________
[1] http://www.amazon.com/dp/0262562006
[2] http://en.wikipedia.org/wiki/Epistemic_logic
[3] http://www.philos.rug.nl/~barteld/6_kooi.pdf

Modern Godellian and Tarskian endeavours in mathematics may seem to
bring us some unusual consequences in language and computation/engineering:

1)
A Godellian Frenchman can devise a sentence in French that only the
Englishman can understand. So while French may be consistent as a
language, it is also "incomplete".

The Tarskian Frenchman could not know which French sentences can only be
understood by an Englishman, or even which French sentences could be
understood at all. Which begs the question of how the Tarskian Frenchman
knows that it is actually sentences that can be understood or not
understood.

2)
A Godellian machine can be tasked to produce machines that have no
recognisable task (there is no associated outcome with these latter
machines). A Tarskian machine can be tasked to produce machines for
which we do not know in advance whether they have a task or not.

So, our Godellian machine is not a machine at all until we can state its
task. On the other hand, the Tarskian machine is merely broken because
only a broken machine cannot be relied upon to bring us an outcome.

Select the truths from the following 1) – 5)

1) If [ if P, then Q ], then there can be the case in which [ if not-P,
then not-Q ].

2) If [ if P, then Q or R ], then either [ if P, then Q ] or [ if P,
then R ].

3) If and only if [P and not-Q] is a contradiction, [ if P, then Q ]
holds true.

4) If and only if there is a case in which Q does not hold true despite
that P holds true, [ if P, then Q ] does not hold true.

5) If there is a case in which P does not hold true, then P is a
contradiction.

The physical space is evidence of the metaphysical space, because
Equator of self-contradiction (gluon of pair), is the Absolute Logic
of self-creation of Spacetime-Continuum.-Aiya-Oba (Poet/Philosopher).

The material universe is evidence of the immaterial universe.
Hence the Absolute Logic:

  ( 2A + B )  +  ( 2B  + A )…=  3( A + B )

Where A and B, can be any positive integer, but never both zero.

There is a definite software for every hardware!

Dear Mr. Jones:

Why do you insist on wasting everyone’s (and that includes your own)
time by posting to sci.logic, when there are so many other newsgroups
better suited to your interests?

There are 1161 Google Groups related to philosophy. These include such
general groups as alt.philosophy, alt.philosophy.debate,
talk.philosophy.misc, as well as alt.philosophy.kant (which is all
about — you guessed it! — Kant), and newsgroups like Continental
Philosophy and UCSB Continental Philosophy (which — you guessed it!
— are all about continental philosophy).

Wouldn’t it make more sense for you to post to such groups as the
above, where your posts can be read by, and you can respond to and
interact with, like-minded people who share your philosophical
interests? Rather than post to sci.logic — a newsgroup unrelated to
your philosophical interests — only to be greeted by derision and
hostility? What is it that you’re trying to accomplish by posting to
sci.logic, given that you are, in fact, greeted by such derision and
hostility? What do you get out of it? What do you hope to gain?

Sincerely,
Colin Oakes