
Re: Chapt10: welldefined Reals in light of 10^603 #648 Correcting Math 3rd ed
Posted:
Aug 8, 2011 6:52 PM


In article <3690eab49c7b437bb4c8abee268a87e1@h17g2000yqn.googlegroups.com>, 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 counterexample (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 *

