Re: can BD organize a MIT seminar?? ; #112; 2nd ed; Euclid

Iain Davidson wrote:

On 15 Sep, 07:13, "plutonium.archime...@xxxxxxxxx"
<plutonium.archime...@xxxxxxxxx> wrote:
Iain Davidson wrote:
On 13 Sep, 17:00, BD <B...@xxxxxxxxxxxxxxxxxx>
wrote:
juandiego <sttscitr...@xxxxxxxxx> wrote:

I see you still unable to answer
the question I asked you previously.


You know, I answered you three times on that same subject, and
all you seem to do is come back saying "you never answered me"

That is probably why Bill Dubuque calls you "disingenuous" and
politely tells you to go away.

How many times have I asked you to write out your full rendition
of Euclid's Indirect method plus Direct Method proofs, perhaps 3 or 4 times, including this post. And you never comply. You keep wanting
me to answer your questions over something you gave in midstream
and never fully gave a Euclid's proof.

I constantly improve my Euclid IP attempt, but you seem to only want
to post one attempt, an attempt that starts in midstream. An attempt
that a outsider could not even recognize is a Euclid Infinitude of Primes
proof unless someone told them it was such.
Why is that? And probably another reason Bill Dubuque wants you to
go away. In fact, I remember a post of yours that you were critiquing
me, which you had not the decency of quoting what it was you were
critiquing of me. And where Bill stepped into the fray and said to you
words to the effect -- have the decency to quote what it is you find
fault with me.

So your behaviour in this thread has become this: you constantly
say I never answered your question when in fact I did so three or four
times. So I am about to tell you as Bill told you-- go away.

--- quoting my proofs of Euclid Infinitude of Primes---
Euclid IP Proofs, both Direct and Indirect methods

DIRECT Method, long-form; Infinitude of Primes Proof

(1) Definition of prime as a positive integer divisible
only by itself and 1.

(2) Statement: Given any finite collection of primes
2,3,5,7,11, ..,p_n possessing a cardinality n Reason: given

(3) Statement: we find another prime by considering W+1 =(2x3x...xpn)
+1 Reason: can always operate on given numbers

(4) Statement: Either W+1 itself is a prime Reason: numbers are either
unit, composite or prime

(5) Statement: Or else it has a prime factor not equal to any of the
2,3,...,pn
Reason: numbers are either unit, composite or prime

(6) Statement: If W+1 is not prime, we find that prime factor Reason:
We take the square root of W+1 and
we do a prime search through all the primes from 2 to
square-root of W+1 until we find that prime factor which
evenly divides W+1

(7) Statement: Thus the cardinality of every finite set can be
increased. Reason: from steps (3) through (6)

(8) Statement: Since all/any finite cardinality set can be increased
by one more prime, therefore the set of primes is an infinite set.
Reason:
going from the existential logical quantifier to the universal
quantification

INDIRECT Method, Long-form; Infinitude of Primes Proof

(1) Definition of prime as a positive integer divisible
only by itself and 1.

(2) The prime numbers are the numbers 2,3,5,7,11, ..,pn,... of set S
Reason: definition of primes

(3.0) Suppose finite, then 2,3,5, ..,p_n is the complete series set
with p_n the largest prime Reason: this is the supposition step

(3.1) Set S are the only primes that exist Reason: from step (3.0)

(3.2) Form W+1 = (2x3x5x, ..,xpn) + 1. Reason: can always operate and
form a new number

(3.3) Divide W+1 successively by each prime of
2,3,5,7,11,..pn and they all leave a remainder of 1.
Reason: can always operate

(3.4) W+1 is necessarily prime. Reason: definition of prime, step (1).

(3.5) Contradiction Reason: pn was supposed the largest prime yet we
constructed a new prime, W+1, larger than pn

(3.6) Reverse supposition step. Reason (3.4) coupled with (3.0)

(4) Set of primes are infinite Reason: steps (1) through (3.6)

--- the above are the Direct and Indirect, longforms of
Euclid Infinitude of Primes proof ---

Iain Davidson further writes:

If p> 1 is the last prime, is p+1 composite ?


For the umpteenth time, since you do not show a full argument,
I can only assume p+1 you are talking about is W+1, the Euclid
Number.

a) subargument: assume W+1 is composite
b) subargument: apply Davidson Lemma that W+1 has no prime divisor
c) subargument: contradition that W+1 is composite
d) subargument: hence W+1 is prime
BACK to the full-argument instead of the subargument

Typically, now Iain goes rambling on into some irrelevancy

Presumably, you agree that 99 is the last integer
that can be represented using two and only two
decimal
digits.

Do you think that 100 has two digits or three
digits ?

Do you think any number greater than 99 can be
represented using two digits ?

Perhaps because 1000 can be coprified in the AP
loadobollocks space, there is some subtle reason why
1000 has a pseudo-AP-crapistic representation as a
two digit number. Thus showing that mathematicians
througout the ages have incorrectly believed that
1000
is a four digit number when any fool can see that
it really has two digits.


Iain, did you ever stop to think why Bill Dubuque said this:

Bill Dubuque wrote:
Smaill wrote:
Something tells me I will regret pointing this out;
but of course it aint necessarily so.

Actually it is correct. In the hypothetical structure
consisting
of the integers with only finitely many primes, one
can organize

It is because Bill Dubuque finally recognized that IP Indirect
forces W+1 as necessarily prime.

Iain, did you ever stop to think why Karl Heuer gave this
analysis:


Sun, 20FEB1994, 21:05:13 GMT sci.math
INCONSISTENT PEANO AXIOMS AND MATH PROFESSORS
Lines: 36
Sender: k...@xxxxxxxxx (Karl Heuer)

k...@xxxxxxxxxxxxxxxxxxxx (Karl Heuer) writes:

In article (5JChA8g2...@xxxxxxxxxxxxxx>

det...@xxxxxxxxxxxxxx (Detlef Bosau) writes:
Ludwig.Pluton...@xxxxxxxxxxxxx meinte am 18.02.94
det...@xxxxxxxxxxxxxx (Detlef Bosau) writes:
Wrong. Your two numbers are not necessarily prime
NO, YOU ARE WRONG. Those numbers are necessarily prime, due to
UPFAT, all the primes that exist in the finite set leave a remainder
of 1.
I'll give you a lesson of elementary arithmetics. . .

I really shouldn't bother to get involved in this discussion again,
but
Ludwig is right. In logical terms, his key statement is "if P is a
finite set containing all the primes, then prod(P)+1 is prime." This
is
a true statement.

Let's step through your alleged counterexample:

consider your set of primes to be: {2,3,5,7,11,13}, as I assert 13 to be
the largest prime. [. . .] Now, you made the assertion, that
(2x3x5x11x13) + 1 [=30031] must be prime.

Yes, it's true that if 13 is the largest prime, then 30031 is prime.
Do
you disagree with that assertion?

As you stated before, there exists an unique prime decomposition of
30031. This is 59x509. It could be easily shown, that 59 and 509
both are prime.

If 13 is the largest prime, then 59x509 is not a factorization of
30031.

--- end quoting Karl Heuer's post of 1994 ---

It is because Karl recognized that in the IP Indirect that W+1 is
necessarily prime.

So if Bill Dubuque can recognize it, surely, given some time
Iain Davidson should be able to recognize it, provided, of course
Iain has an ounze of logic.

Iain, unless you post a full Direct and Indirect, full proofs, step by
step, let this post be the last I ever discuss the subject with you
because as Bill said, you are disingenuous in your questioning.

AP
.

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