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Topic: Reviewing whether the Ancient Greek Proof that sqrt2 is irrational,
whether it is mired in flaws, thus, invalid

Replies: 37   Last Post: Oct 9, 2017 9:09 AM

 Messages: [ Previous | Next ]
 plutonium.archimedes@gmail.com Posts: 18,572 Registered: 3/31/08
my history of Fraction increment goes back to 2015 at least, where
1/3 = .3333...33(+1/3) Re: Reviewing whether...

Posted: Oct 7, 2017 5:10 AM

On Saturday, October 7, 2017 at 12:15:43 AM UTC-5, Archimedes Plutonium wrote:
> Now, it was several years back, that I discovered a Logical error in current mathematics of representation of Reals. Several years ago I insisted that the Reals have a "suffix". So I was saying some years ago that 1/3 had to be .3333...33(+1/3).
>

It was around 2015 that I introduced this concept of Fractional Increment, a advanced form of what I earlier called a "suffix of a number" back in 2011. But my mistake, as seen below, is a neglect of using a addition sign within the parentheses so that instead of (1/3) it should be (+1/3) and instead of (1/7) it should be (+1/7) and instead of (8/9 +1/9) it should have been (+8/9+1/9)

The plus sign sort of interferes with the decimal representation, so you can apply along anywhere in the decimal flow stream for example 1/7 is .142857...14(+1/7) or just as well as .14.....85(+1/7), because if one wants to know a particular place value, can always just use 1/7.

Newsgroups: sci.math
Date: Wed, 3 Jun 2015 00:15:44 -0700 (PDT)

Subject: alright, saved most all the fractions to be Rational with
Decimal-Fraction Representation
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Wed, 03 Jun 2015 07:15:45 +0000

alright, saved most all the fractions to be Rational with Decimal-Fraction Representation

Alright, in my last post I was gloomy and distraught with fears that numbers like 1/7 would be root-irrational rather than rational with a repeating block of 142857.

What I did not factor into the discussion was "Algebraic Completeness" so if the borderline is 1*10^-604 we can go all the way out to 1*10^-1208.

In New Math, we need a Completeness so that any number that is finite, multiplied by itself is a number that is included in the overall system. The smallest number is 1*10^-604 and multiplied by itself allows us to use numbers all the way up to having 1208 digits rightward of the decimal point, even though, after 604 digits the numbers are infinite-numbers.

In New Math, the way we know a set is infinite or finite is that it must have 1*10^604 elements within the domain of 0 to 1*10^1208. So primes are an infinite set and perfect squares are an infinite set, but Fibonacci primes are a finite set and perfect cubes are a finite set since their density from 0 to 1*10^1208 is not large enough of a density.

So, the fraction representation of 1/7 is .142857142... and so we have to go to 606 digits rightward of decimal point and stick or place the (1/7) at the 607 digit place-value as this .14285714..142857(1/7).

In this manner the rationals are all saved except those whose digit repeating block starts repeating after 1208 digits are used up.

So, the Decimal Fraction representation is a new innovation to mathematics, and one thing it dismisses is the fakery proofs that .9999... was equal to 1, for that was a complete and utter nonsense fakery of Old Math that had no infinity borderline. The .9999... was the progression of 9/10, then 99/100 then 999/1000, and the stupid people in Old Math who believed this fakery, believe that magically somehow that 9999.../ 10000...  was equal to 1.

In New Math 8/9 = .888888..88(8/9) plus 1/9 = .1111..11(1/9) does not equal .9999..99 which Old Math would get, but rather it  equals .9999..99(8/9 +1/9), where the increment of the fraction at the tail end makes .9999... become 1.0000....

So, I saved Decimal Fraction Representation and more importantly, saved most every fraction from being a irrational number. Of course, 0 is still a root irrational, and then fractions with repeating blocks of more than 1208 digits are root-irrational.

There, I can go to bed much more happier.

AP
----- end of old 2015 post ---