On Dec 31, 4:35 pm, Archimedes Plutonium
<plutonium.archime
...@gmail.com> wrote:
> On Dec 31, 3:56 am, David Bernier <david
...@videotron.ca> wrote:
> > Archimedes Plutonium wrote:
> (snipped)
> > I'll reply according to standard math., which is the kind I
> > understand. Euler discovered the Euler product identity,
> > which holds for zeta(s) when s is real and > 1.
> > zeta(s) can be extended to complex s with Re(s) > 1
> > without convergence problems. Re(s) > 1 means that
> > s = x + i*y, x, y real, and x>1.
> > zeta(1) is divergent. It's possible to extend zeta
> > complex-differentiably to all the complex numbers except 1,
> > or C \ {1}. So there's just one zeta function that extends
> > Euler's zeta while maintaining analyticity, i.e.
> > continuous complex-differentiability. Riemann showed the
> > way in how zeta zeros in the critical strip
> > 0 <= Re(s) <= 1 relate to the distribution of primes,
> > the prime counting function pi(x). This is
> > advanced material, but known for 100 years or more.
> > For example, I think there's an explicit formula for
> > pi(x), but I don't know when it was proved.
> > According to you, there is a border...
> > But then what do you mean by Infinity ?
> > David Bernier
I should address David's question in detail rather than to glide over
it.
And it is not that David thinks he is doing the correct math, but a
failure
to see that David's math is imprecision math, hence no math.
In the Riemann Zeta function we have Z(1) = 1 + 1/2 + 1/3 + . .
And most in Old Math recognize that as the harmonic series, but their
next thought is a travesty of
math. Their next thought is that using an imprecise definition of
finite versus infinity, they come
to a mistaken conclusion that the series diverges to infinity, yet
they never defined infinity with any
sort of precision and that is the boat that David is stuck in also.
So now, what if the Old Math community and David decided to define
infinity with precision.
They would then see that finite transitions into infinity meaning
there must be a border
between them. David and the Old Math community would then look at
where in mathematics a
natural intrinsic border exists and the answer is that in
Circumferencing the Perimeter the
Algebra of mathematics ends at producing a match of a finite square
perimeter with a finite
circle circumference at 10^603. So that David and his Old Math
companions then have a
borderline between finite and infinity and thus defined infinity with
precision.
Now David and Old Math community comes back to the question of the
Riemann Zeta Function
and harmonic series of 1 + 1/2 + 1/3 + . .
When you never have a precision definition of infinite, you are easily
fooled into thinking that
this series diverges but when you recognize that the last term in the
sequence is 1/10^603 then
you instantly recognize it converges to a finite number. What is the
convergence anyway, David?
Looks like it is going to be somewhere around what? 1 + .5 + .33 + .25
+ .20 + .16 + .14 + ..
What is that convergence when Infinity is 10^603, David? Is it a
convergence of about 4. or 5. something?
So now let us look at the Euler multiplication zeta with its primes.
Looking at it term by term we realize
that the last prime to plug into Euler is the prime before 10^603 and
as we plug all those primes from 2,3,5
to the last prime, do we ever have a situation where the addition Zeta
ever equals the multiplication Zeta?
The answer is no.
So the difference between the Old Math and its staleness is that the
Old Math hobbles along without ever
defining Finite versus Infinity and thus has bogus claims of Series
and bogus conjectures such as the
Riemann Hypothesis.
Another area of mathematics, for those handicapped with algebra is the
geometry area where this series nonsense
crops up due to imprecise finite versus infinity. In Geometry with the
surface area and volume of the pseudosphere
where the ill-defined-infinity is claimed, then the pseudosphere
although it extends its arms to infinity has
this finite volume and finite surface area. But now apply precision
definition of infinity as 10^603 and we instantly
recognize that the pseudosphere volume and surface area must be finite
and that the formulas for volume and area of
pseudosphere must incorporate 10^603.
Now the Old Math community thinks the Euler Zeta is equal to the
Riemann Zeta, but the Old Math never defined
infinity and so they were never asked to show where the terms of the
Euler Zeta ever equaled the terms in the
Riemann Zeta. In fact, when going along term by term in the two zetas,
they are never equal. So here we have a famous conjecture that was
built from notions-of-infinity and not well defined infinity, and no
wonder never a proof,
because the conjecture is utterly false at the starting block.
Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
