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Topic: Chapt8 well defined "open set" and well-defined Reals in light of
10^603 #523 Correcting Math 3rd ed

Replies: 10   Last Post: Aug 8, 2011 8:14 PM

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 Earle Jones Posts: 235 Registered: 12/6/04
Re: Chapt10: well-defined Reals in light of 10^603 #648 Correcting Math 3rd ed
Posted: Aug 8, 2011 6:52 PM

In article
Archimedes Plutonium <plutonium.archimedes@gmail.com> wrote:

> On Jul 11, 1:05Â am, "Androcles" <Headmas...@Hogwarts.physics.June.
> 2011> wrote:
>

> > Oh dear... now you've left yourself open to accepting the burden of proof
> > instead of leaving it to Archie.

>
> Let me take on that burden for it needs to be clear with alot of
> clarity, since
> all of us in math, have used irrationals as if they were our right
> hand or left hand
> when in reality they never existed.
>

> > Â  Â  Â  a = 54608393
> > Â  Â  Â  b = 38613965
> >
> > Of course if you'll accept four figure accuracy then
> > Â  Â  Â  a = 8119
> > Â  Â  Â  b = 5741
> >
> > is good enough, and for two figure accuracy
> > a = 99, b = 70

>
>
> It was a good thing that I did the B matrices, and even though that
> exercise and toll and struggle
> never produced the infinity number 6.18033x10^603 from squaring the
> circle or cubing the sphere
> or circumferencing the perimeter. That toll and exercise did pay off
> handsomely by elucidating the Algebraic
> Zone of Completeness. So that irrationals reside just beyond Infinity.
>
> So in New Math, every number that is available for mathematics is from
> 0 to 6.18 x 10^603. The smallest nonzero
> number is 1/(6.18*10^603) the next is 2/(6.18*10^603) and we can
> visualize every number in this arena of legitimate
> mathematics.
>

> >
> > There exists two integers a and b such that a/b = sqrt(2) to any desired
> > accuracy.
> > Provide a counter-example (or other disproof).

>
> Now the zone of algebraic completeness starts at 6.18033x10^603 and
> stretches out to 10^1206 for 2Dimensions and
> to 10^1809 in 3Dimensions.
>
> So here is where the Squaring the Circle helps in understanding the
> square root of 2.
>
> Remember, math can only play with the numbers from 0 to Infinity
> 6.18*10^603.
>
> So that there is no number in that field of play that when multiplied
> by itself yields
> exactly that of 2.000..00 where there are 603 digits of zeroes
> rightward of the decimal point.
>
> But, keep in mind that we can utilize the zone of completeness and
> draw out a number that has 1206 digits starting
> with 1.414..
>
> So now, we draw a number that has 603 digits 1.414... and it likely
> will not give us 2.000... with 603 digits of zeroes. However when we
> get to around 1206 digits or perhaps we need 1207 or 1208 digits of
> 1.414.. and multiply,
> we end up with a number that produces 2.000..00 with exactly 603
> digits of zeroes rightward of the decimal point.
>
> So in Old Math we end up by saying square root of 2 is 1.414... In New
> Math we actually produce what the square root of 2 is with its 1206 or
> more digits, because the only assured or precision math is within the
> region where Logic is
> guaranteed, and we can only borrow or utilize numbers in the zone of
> algebraic completeness.
>
> Now physics has several beautiful examples of what can be called real-
> physics and the outer zone of completeness of physics where we borrow.
>
> (a) QED where we renormalize to get rid of infinities and what remains
> after the renormalization is the real physics
> (b) Quantum Mechanics has the collapsed wavefunction and uncollapsed
> wherein the collapsed is the real physics and the uncollapsed is the
> borrowing zone.
> (c) the spectrum of light is a spectrum in which we realize it has a
> zone of where lightwaves exist but wherein we cannot go lower than the
> lowest, nor higher than the highest
>
> These are but three examples drawn out of physics where we have a tier
> of reality and the reality is confined to a region and where we can go
> beyond the region to a zone of completeness to complete the reality
> region.
>
> In New Math, when we are given a function such as F(x) = 1/x^2 we can
> instantly visualize every point of a graph of that function from 0 to
> Infinity (6.18*10^603). In Old Math, handed any function, we can only
> visualize a few points in a patch of numbers of its graph, and we
> further assume or presume, without logical justification, that the
> function is going to fill in as a solid curve, without holes. New Math
> gets rid of that hypocritic presumptions. New Math instantly pictures
> every point of a function, because every point in mathematics is laid
> out from 0 to 6.18*10^603.

*
Where is the point 7*10^603 ?

How about the point 10^604 ?

Are you saying they don't exist?

earle
*