Deeper than primes - Continuation

jsfisher · Jun 25, 2013

BenjaminTR said:
Yes, this is what I meant.

That is good, since that is what you wrote.

epix · Jun 25, 2013

jsfisher said:
Given two relations stipulated as fact, a third may be concluded without resorting to a common notation.

Benjamin offered a transitivity case whose arguments consisted of rational and irrational terms. How can you expect your math software to keep a library of all "mathematical facts?" such as that some log

is larger than m? If an expression includes an irrational number, all other terms in the expression are converted into the approximate format so the numerical comparison could be effectively made. I can't see how the transitivity would help the principle cause.

Doron says that 2/3 - 0.666... = 0.000...4 That means there is a conflict of facts: your "mathematical fact" - if you don't agree with the result - against his "mathematical fact." How do I decide? The way any math software does. By the conversion of 2/3 into approximate format. That can be done by division, as the slash between 2 and 3 implies.

2/3 => LD(2, 3) = 0.666...

Then I naturally ask the question regarding the conversion number formats native to Organic Mathematics.

But if Doron claims 1 ≠ 0.999...

and I use the same type of conversion

1/1 => LD(1, 1) = 1.000...

then I naturally double ask the question regarding the way Organic Mathematics convert number formats.

laca · Jun 25, 2013

laca said:
Please define your R set, as it's clearly not the set of reals. And by "define" I don't mean "it's the set of locals".

doronshadmi said:
R is the standard set of real numbers, and no one of these numbers is a non-local number.

Nice try doron. Got anything else?

Stamuel · Jun 25, 2013

epix said:
Benjamin offered a transitivity case whose arguments consisted of rational and irrational terms. How can you expect your math software to keep a library of all "mathematical facts?" such as that some log is larger than m? If an expression includes an irrational number, all other terms in the expression are converted into the approximate format so the numerical comparison could be effectively made. I can't see how the transitivity would help the principle cause.

Doron says that 2/3 - 0.666... = 0.000...4 That means there is a conflict of facts: your "mathematical fact" - if you don't agree with the result - against his "mathematical fact." How do I decide? The way any math software does. By the conversion of 2/3 into approximate format. That can be done by division, as the slash between 2 and 3 implies.

2/3 => LD(2, 3) = 0.666...

Then I naturally ask the question regarding the conversion number formats native to Organic Mathematics.

But if Doron claims 1 ≠ 0.999...

and I use the same type of conversion

1/1 => LD(1, 1) = 1.000...

then I naturally double ask the question regarding the way Organic Mathematics convert number formats.

Right, converting everything to decimal notation is a good way to approach this case. I was only making the nitpicky point that converting to a single numbering system is not the only way to make comparisons. You seemed to be claiming it was.

Otherwise, I agree with your arguments against doron's 0.999...<1 arguments.

epix · Jun 25, 2013

doronshadmi said:
By forcing Standard Analysis, the potential infinity upon infinitely many levels (with the invariant length d*(Pi/2) of the semi-circles, and the convergent areas of infinitely many levels of semi-circles (as observed in the quote)) is collapsed into a single-level of 1-dimesional space with length d by quantum leap, and we are left with a finite collection of levels of semi-circles with length d*(Pi/2), a finite collection of levels of semi-circles' areas, and a single limit line with length d.

You keep demonstrating that Organic Mathematics is way too tedious to implement, and so I decided to stick with the standard math instead where things are decided far more effectively with an accent on simplicity. Just look how standard math deals with a certain inconsistency:

In arithmetic, repeating decimal is a way of representing a rational number. Thus, a decimal representation of a number is called a repeating decimal (or recurring decimal) if at some point it becomes periodic, that is, if there is some finite sequence of digits that is repeated indefinitely. For example, the decimal representation of 1/3 = 0.3333333… or 0.3 (spoken as "0.3 repeating", or "0.3 recurring") becomes periodic just after the decimal point, repeating the single-digit sequence "3" infinitely. A somewhat more complicated example is 3227/555 = 5.8144144144…, where the decimal representation becomes periodic at the second digit after the decimal point, repeating the sequence of digits "144" indefinitely.

Rational numbers are numbers that can be expressed in the form a/b where a and b are integers and b is non-zero. This form is known as a common fraction. On the one hand, the decimal representation of a rational number is ultimately periodic, as explained below. On the other hand every real number which has an eventually periodic decimal expansion is a rational number. In other words the numbers with eventually repeating decimal expansions are exactly the rational numbers (i.e.: those that can be expressed as ratios).

As you guessed it, the "certain inconsistency" relates to number 0.9999..., which is a rational number, but it cannot be expressed as p/q. Unlike Organic Mathematics, standard math deals with it this way:

However, a terminating decimal also has a second representation as a repeating decimal, obtained by decreasing the final (nonzero) digit by one and appending an infinitely repeating sequence of nines, a phenomenon students typically find puzzling (see List of common misconceptions#Mathematics). 1 = 0.999999… and 1.585 = 1.584999999… are two examples of this. This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm.

See? Standard math just "unmodifies" things around and that's it.

(I know that you don't accept anything short of formal language, so in order to satisfy your needs...)
https://en.wikipedia.org/wiki/Division_algorithm

jsfisher · Jun 25, 2013

epix said:
Benjamin offered a transitivity case whose arguments consisted of rational and irrational terms....

Yes, he did, and that was a counter to a flat, incorrect statement you'd made. You may have meant a more nuanced set of conditions, but you didn't express them back when BenjaminTR challenged them. Re-qualifying your statement, now, with an "Oh, yeah, you are right, but this is what I meant...." would be fine. Back pedaling to move the goal posts, however, is not.

ETA: Ninja'ed by BenjaminTR, and he said it nicer than I did. Looks like there is no issue to discuss.

epix · Jun 26, 2013

jsfisher said:
Yes, he did, and that was a counter to a flat, incorrect statement you'd made. You may have meant a more nuanced set of conditions, but you didn't express them back when BenjaminTR challenged them. Re-qualifying your statement, now, with an "Oh, yeah, you are right, but this is what I meant...." would be fine. Back pedaling to move the goal posts, however, is not.

ETA: Ninja'ed by BenjaminTR, and he said it nicer than I did. Looks like there is no issue to discuss.

I can't requalify my statement the way you suggested, because I still think that Benjamin was wrong by suggesting that there are cases where number conversion is not needed. Is log₅(√2) larger than 1/5? How do I answer the question when I don't have a list of all mathematical truths where this particular relation is listed?

epix · Jun 26, 2013

BenjaminTR said:
Right, converting everything to decimal notation is a good way to approach this case. I was only making the nitpicky point that converting to a single numbering system is not the only way to make comparisons. You seemed to be claiming it was.

You surely pick an example that completely went by me. Maybe you can elaborate in some detail when Doron is asleep.

epix · Jun 26, 2013

doronshadmi said:
Given {...{{{}}}}...} expression, no amount of members' levels ...{{{}}}... is is accessible to the set's level (where the set's level is notated by the outer "{" and "}" of the expression {...{{{}}}}...}.

Listen, Doron, I wonder if Organic Mathematics has to its disposal something similar to the transitive axiom of algebra. You know, if a = b and b = c, then a = c. It comes handy in all variations, like

if x = 0.999... and x = a, then a = 0.999...

Let me show you the power of that axiom:

x = a
10x = 10a
10x - x = 10a - a
9x = 9a
x = 9a/9 = a = 0.999...

You know what? Forget it. I show you something else with a = 9, b = 0.999... and x = b

x = b
10x = a + b
10x - x = a + b - b
9x = a
x = a/9 = 9/9 = 1

See? You thought that if b = 0.999... and b = x, then x = 0.999... But you thought wrong, pal. Unlike the Organic Mathematicians, we, the Standardized Mathematicians, have many ways to arrive at what we want to see. So don't argue with me that 1 > 0.999...

jsfisher · Jun 26, 2013

epix said:
i can't requalify my statement the way you suggested, because i still think that benjamin was wrong by suggesting that there are cases where number conversion is not needed. Is log₅(√2) larger than 1/5? How do i answer the question when i don't have a list of all mathematical truths where this particular relation is listed?

-1/7 < |√2|

doronshadmi · Jun 26, 2013

zooterkin said:
I think you've just proved that your "non-local number" 0.000...1₁₀ is equal to zero.

I am sure that you have missed that 9/9 > 0.999...₁₀ by 0.000...1₁₀

jsfisher · Jun 26, 2013

doronshadmi said:
I am sure that you have missed that 9/9 > 0.999...₁₀ by 0.000...1₁₀

Zooterkin didn't miss anything. He was merely pointing out that you have again managed to back yourself into proving the thing you tout as 0.000...1 is indistinguishable from zero.

That makes the meaning of "9/9 exceeds 0.999... by 0.000...1" completely true, just not in the way you may have thought.

doronshadmi · Jun 26, 2013

BenjaminTR said:
The arguments about 0.999... are arguments about numbers and numbering systems, not about spaces. Conclusions about spaces cannot settle this. You need a proof that numbers themselves must have some property or relation, and that they can only have that if 0.999... < 1. This is exactly what has been lacking.

0.999...₁₀ is a measurement along a single path of a base 10 fractal, which its dimensional space is > 0-dimensional space AND < 1-dimensional space.

Here are examples of measurements along different fractals' paths with base 2 or base 3, which their dimensional spaces are > 0-dimensional space AND < 1-dimensional space:

so we get 0 < 0.111...₂ < 0.222...₃ < ... < 0.999...₁₀ < 1, where all these numbers are measurements of spaces, whether these spaces are composed (in the case of 0.111...₂, 0.222...₃ or 0.999...₁₀) or non-composed ( in the case of 0 or 1).

doronshadmi · Jun 26, 2013

jsfisher said:
Zooterkin didn't miss anything. He was merely pointing out that you have again managed to back yourself into proving the thing you tout as 0.000...1 is indistinguishable from zero.

That makes the meaning of "9/9 exceeds 0.999... by 0.000...1" completely true, just not in the way you may have thought.

This is very nice but you have missed that 0.000...1₁₀ > 0 because 1-dimesional space is irreducible into 0-dimensional space and 0.000...1 is a composition of 0-dimesional space and 1-dimesional space, that does not have an exact position along 1-dimesional space.

doronshadmi · Jun 26, 2013

epix said:
2/3 => LD(2, 3) = 0.666...

No epix.

2/3 has an exact position along 1-dimensional space, where 0.666...₁₀ does not have an exact position along 1-dimesional space.

Therefore 2/3 is a local number (it has the property of a position of a single point along 1-dimesional space) and 0.666...₁₀ is a non-local number (it has a property of non-exact position of a mixed form of points AND line segments along 1-dimesional space).

doronshadmi · Jun 26, 2013

epix said:
You know what? Forget it. I show you something else with a = 9, b = 0.999... and x = b

x = b
10x = a + b
10x - x = a + b - b

Very nice epix, you have omitted the trouble maker 0.999... from 9.999... in order to get 9x = 9, but then x = 1 and not 0.999...

epix said:
9x = a
x = a/9 = 9/9 = 1

See? You thought that if b = 0.999... and b = x, then x = 0.999... But you thought wrong, pal. Unlike the Organic Mathematicians, we, the Standardized Mathematicians, have many ways to arrive at what we want to see. So don't argue with me that 1 > 0.999...

Yes they arrive at what they want by changing x = 0.999... to x = 1 in order to get their requested result, vary vary nice indeed.

zooterkin · Jun 26, 2013

doronshadmi said:
This is very nice but you have missed that 0.000...1₁₀ > 0 because 1-dimesional space is irreducible into 0-dimensional space and 0.000...1 is a composition of 0-dimesional space and 1-dimesional space, that does not have an exact position along 1-dimesional space.

Then why did you say it was equal to zero at the beginning of the same post?

doronshadmi said:
Let us write it more clearly:

local number 1 - local number 9/9 = local number 0/9 = 0...

local number 1 - local number 0/9 = local number 9/9 = 1 > non-local number 0.9999 ... by non-local number 0.000...1₁₀

Make up your mind; does 0/9 equal zero or your mythical non-local number?

If you can't even be consistent with the basics, how do you expect to do anything with it?

jsfisher · Jun 26, 2013

doronshadmi said:
0.999...₁₀ is a measurement along a single path of a base 10 fractal, which its dimensional space is > 0-dimensional space AND < 1-dimensional space.

No, that is just something you made up. 0.999... is the representation of a particular number using a base-10 positional notation. The particular number being represented happens to be one in this case.

(By the way, we'll add 'fractal' to the list of things you don't understand.)

doronshadmi said:
This is very nice but you have missed that 0.000...1₁₀ > 0 because 1-dimesional space is irreducible into 0-dimensional space and 0.000...1 is a composition of 0-dimesional space and 1-dimesional space, that does not have an exact position along 1-dimesional space.

I missed nothing. Your notational gibberish, 0.000...1, is indistinguishable from zero. That is a fact you have not, cannot refute. Your claims of irreducible, exact position, etc., woven into their own special gibberish, are entirely irrelevant to the issue.

Your bare assertions from personal incredulity are no substitute for actual mathematical arguments. Put some effort into the latter, and you might finally learn how baseless the former is.

epix · Jun 26, 2013

jsfisher said:
-1/7 < |√2|

Benjamin's argument didn't involve any absolute value in his transitive case argument. And that's what I replied to.

BenjaminTR said:
This is not quite true. For example, given that 1/4 < 0.3 and 0.3 < log₁₀2, we can conclude that 1/4 < log₁₀2 without using the same format. These are just names for numbers, after all; they are not parts of the numbers themselves. Doron's methods are suspect, but for other reasons.

You wrote that I might have misread what Benjamin wrote, probably implying that I missed the inclusion of some absolute values in his example. Sorry, maybe I'm blind, but I still don't see them. I wonder why he didn't give an example of such a trivial case. Perhaps he realized that it would be miles away from the issues raised by Doron.

jsfisher · Jun 26, 2013

epix said:
Benjamin's argument didn't involve any absolute value in his transitive case argument. And that's what I replied to.

You need to go back one more step...to the statement BenjaminTR was actually responding to. It was this:

epix said:
I already told you that numbers can be compared only when they appear in the same numerical format.

...and that statement was incorrect. My example is sufficient to show it to be incorrect. BenjaminTR's example is also sufficient to show it to be incorrect.

(BenjaminTR's example was essentially A < B, B < C, and then A < C. If the first two need to be established, then they can be done independently. Establishing A< B and B < C does not require a common numerical format for A and C. The final comparison can be made without A and C ever being in the same numerical format.)

epix · Jun 26, 2013

doronshadmi said:
Very nice epix, you have omitted the trouble maker 0.999... from 9.999... in order to get 9x = 9, but then x = 1 and not 0.999...

Yes they arrive at what they want by changing x = 0.999... to x = 1 in order to get their requested result, vary vary nice indeed.

Doron, there are two separate issues: 1 = 0.999... and a convergence of a series that involves 0.999... When a series, such as S = 1/2¹ + 1/2² + 1/2³ + ... cannot provably reach its limit 1, it doesn't automatically prove that 1 > 0.999... even though it seems to be intuitively so. In other words, 0.999... = 1 doesn't accelerate the series in question to reach its limit 1. Unlike finity, infinity is not a good place for taking the pen out and start comparing. It cannot get more down to earth than here:
http://www.mathsisfun.com/calculus/limits-infinity.html

epix · Jun 27, 2013

BenjaminTR said:
Right, converting everything to decimal notation is a good way to approach this case. I was only making the nitpicky point that converting to a single numbering system is not the only way to make comparisons. You seemed to be claiming it was.

No, I were not. I limited my statement in face of Doron's single inequality, which was 2/3 > 0.666...

If he had claimed 2/3 > -0.666..., I wouldn't have asked him to convert anything - even himself to some fancy religion.

BenjaminTR said:
This is not quite true. For example, given that 1/4 < 0.3 and 0.3 < log₁₀2, we can conclude that 1/4 < log₁₀2 without using the same format. These are just names for numbers, after all; they are not parts of the numbers themselves. Doron's methods are suspect, but for other reasons.

My point still is that before comparison based on your example of transitivity can be used, the terms in both inequalities need to be converted to a common numeric format to show that the inequalities are true. There are surely cases where a familiarity with a function helps to figure an inequality without any number conversion.

doronshadmi · Jun 27, 2013

zooterkin said:
Then why did you say it was equal to zero at the beginning of the same post?

Make up your mind; does 0/9 equal zero or your mythical non-local number?

If you can't even be consistent with the basics, how do you expect to do anything with it?

Here it is again:

local number 1 - local number 9/9 = local number 0/9 = 0
...

local number 1 - local number 0/9 = local number 9/9 = 1

local number 1 - non-local 0.000...1₁₀ = 0.999...₁₀ < local number 1 by non-local 0.000...1₁₀

So what is exactly your problem to get it?

doronshadmi · Jun 27, 2013

epix said:
Doron, there are two separate issues: 1 = 0.999... and a convergence of a series that involves 0.999... When a series, such as S = 1/2¹ + 1/2² + 1/2³ + ... cannot provably reach its limit 1, it doesn't automatically prove that 1 > 0.999... even though it seems to be intuitively so. In other words, 0.999... = 1 doesn't accelerate the series in question to reach its limit 1. Unlike finity, infinity is not a good place for taking the pen out and start comparing. It cannot get more down to earth than here:
http://www.mathsisfun.com/calculus/limits-infinity.html

Epix, S = 1/2¹ + 1/2² + 1/2³ + ... is equivalent to 0.111...₂, where 0.111...₂ < 0.999...₁₀ < 1,
where 0.111...₂ < 1 by 0.000...1₂ and 0.999...₁₀ < 1 by 0.000...1₁₀, and 5*(0.000...1₁₀) = 0.000...1₂

zooterkin · Jun 27, 2013

doronshadmi said:
Here it is again:

local number 1 - local number 9/9 = local number 0/9 = 0
...

local number 1 - local number 0/9 = local number 9/9 = 1

local number 1 - non-local 0.000...1₁₀ = 0.999...₁₀ < local number 1 by non-local 0.000...1₁₀

So what is exactly your problem to get it?

I don't have a problem. You, however, have written something different this time from what I quoted.
Let's compare those last lines again:

doronshadmi said:
local number 1 - local number 0/9 = local number 9/9 = 1 > non-local number 0.9999 ... by non-local number 0.000...1₁₀

doronshadmi said:
local number 1 - local number 0/9 = local number 9/9 = 1

local number 1 - non-local 0.000...1₁₀ = 0.999...₁₀ < local number 1 by non-local 0.000...1₁₀

One of these things is not like the other.

jsfisher · Jun 27, 2013

doronshadmi said:
jsfisher said:

I missed nothing. Your notational gibberish, 0.000...1, is indistinguishable from zero.

Click to expand...

Only in your local-only dry dreams.

Dry dreams? Seriously?

That aside, if your gibberish notation represents something different from zero, then you should be able to demonstrate it in some meaningful way. After years and years of recycling the same nonsense, you haven't managed to do that. Instead, all you have is years and years of recycled nonsense with nothing but your own incredulity to back it.

Don't forget, too: My stuff works; yours, well, maybe someday, but this isn't that day.

doronshadmi · Jun 27, 2013

zooterkin said:
One of these things is not like the other.

Let's write the original stuff:

doronshadmi said:
Let us write it more clearly:

local number 1 - local number 9/9 = local number 0/9 = 0
local number 1 - local number 8/9 = local number 1/9 > non-local number 0.1111 ... by non-local number 0.000...9₁₀
local number 1 - local number 7/9 = local number 2/9 > non-local number 0.2222 ... by non-local number 0.000...8₁₀
local number 1 - local number 6/9 = local number 3/9 > non-local number 0.3333 ... by non-local number 0.000...7₁₀
local number 1 - local number 5/9 = local number 4/9 > non-local number 0.4444 ... by non-local number 0.000...6₁₀
local number 1 - local number 4/9 = local number 5/9 > non-local number 0.5555 ... by non-local number 0.000...5₁₀
local number 1 - local number 3/9 = local number 6/9 > non-local number 0.6666 ... by non-local number 0.000...4₁₀
local number 1 - local number 2/9 = local number 7/9 > non-local number 0.7777 ... by non-local number 0.000...3₁₀
local number 1 - local number 1/9 = local number 8/9 > non-local number 0.8888 ... by non-local number 0.000...2₁₀
local number 1 - local number 0/9 = local number 9/9 = 1 > non-local number 0.9999 ... by non-local number 0.000...1₁₀

So as you see, you have no case.

You have a problem with these expressions:

local number 1 - local number 9/9 = local number 0/9 = 0
...
local number 1 - local number 0/9 = local number 9/9 = 1 > non-local number 0.9999 ... by non-local number 0.000...1₁₀

So let us write it in this way:

1 - 9/9 = 0/9 = 0
...
1 - 0/9 = 9/9 = 1 > 0.9999 ... by 0.000...1₁₀

Now, how can you conclude that the result of 1 - 9/9 is the same as the result of 1 - 0.999 ... according to what is written in

1 - 9/9 = 0/9 = 0
1 - 8/9 = 1/9 > 0.1111 ... by 0.000...9₁₀
1 - 7/9 = 2/9 > 0.2222 ... by 0.000...8₁₀
1 - 6/9 = 3/9 > 0.3333 ... by 0.000...7₁₀
1 - 5/9 = 4/9 > 0.4444 ... by 0.000...6₁₀
1 - 4/9 = 5/9 > 0.5555 ... by 0.000...5₁₀
1 - 3/9 = 6/9 > 0.6666 ... by 0.000...4₁₀
1 - 2/9 = 7/9 > 0.7777 ... by 0.000...3₁₀
1 - 1/9 = 8/9 > 0.8888 ... by 0.000...2₁₀
1 - 0/9 = 9/9 > 0.9999 ... by 0.000...1₁₀

?

You are invited to demonstrate your argument that 0 = 0.000...1₁₀ by using:

1 - 9/9 = 0/9 = 0
1 - 8/9 = 1/9 > 0.1111 ... by 0.000...9₁₀
1 - 7/9 = 2/9 > 0.2222 ... by 0.000...8₁₀
1 - 6/9 = 3/9 > 0.3333 ... by 0.000...7₁₀
1 - 5/9 = 4/9 > 0.4444 ... by 0.000...6₁₀
1 - 4/9 = 5/9 > 0.5555 ... by 0.000...5₁₀
1 - 3/9 = 6/9 > 0.6666 ... by 0.000...4₁₀
1 - 2/9 = 7/9 > 0.7777 ... by 0.000...3₁₀
1 - 1/9 = 8/9 > 0.8888 ... by 0.000...2₁₀
1 - 0/9 = 9/9 > 0.9999 ... by 0.000...1₁₀

zooterkin · Jun 27, 2013

doronshadmi said:
So let us write it in this way:

1 - 9/9 = 0/9 = 0
...
1 - 0/9 = 9/9 = 1 > 0.9999 ... by 0.000...1₁₀

Can you make up your mind whether 9/9 equals 1 or not, please?

jsfisher · Jun 27, 2013

zooterkin said:
doronshadmi said:

So let us write it in this way:

1 - 9/9 = 0/9 = 0
...
1 - 0/9 = 9/9 = 1 > 0.9999 ... by 0.000...1₁₀

Click to expand...

Can you make up your mind whether 9/9 equals 1 or not, please?

It saddens me to say this, but I'm with Doron on this one. He's been consistent of late that 9/9 = 1 and 0.999.... doesn't.

His reiterated nonsense which has risen beyond the level of spamming this thread is riddled with contradiction and other inconsistencies, but not recently on the value of 9/9.

(I say "not recently" because Doron has stated in the past that, for example, 1/4 and 0.25 are not the same number. Go figure. It is probably just the case the Doron is flexible on when and whether things are equivalent.)

zooterkin · Jun 27, 2013

jsfisher said:
It saddens me to say this, but I'm with Doron on this one. He's been consistent of late that 9/9 = 1 and 0.999.... doesn't.

His reiterated nonsense which has risen beyond the level of spamming this thread is riddled with contradiction and other inconsistencies, but not recently on the value of 9/9.

(I say "not recently" because Doron has stated in the past that, for example, 1/4 and 0.25 are not the same number. Go figure. It is probably just the case the Doron is flexible on when and whether things are equivalent.)

Ok, I see what the problem is. I was misreading the statement:

1 - 0/9 = 9/9 = 1 > 0.9999 ... by 0.000...1

I was mis-parsing from the '>' onwards.

Of course, none of this changes the fact that .999... is the same as 1, and that 0.0000...1 is nonsense.

Doron, how about this:

1 - 0/9 = 9/9 = 1
1 - 1/9 = 0.8₉
1 - 2/9 = 0.7₉
1 - 3/9 = 0.6₉
1 - 4/9 = 0.5₉
1 - 5/9 = 0.4₉
1 - 6/9 = 0.3₉
1 - 7/9 = 0.2₉
1 - 8/9 = 0.1₉
1 - 9/9 = 0₉

Where did your 0.000...1₁₀ disappear to?

epix · Jun 27, 2013

doronshadmi said:
Epix, S = 1/2¹ + 1/2² + 1/2³ + ... is equivalent to 0.111...₂, where 0.111...₂ < 0.999...₁₀ < 1,
where 0.111...₂ < 1 by 0.000...1₂ and 0.999...₁₀ < 1 by 0.000...1₁₀, and 5*(0.000...1₁₀) = 0.000...1₂

I don't think there is an inequality as a result of that comparison. Look at it again. If 0.111(b) = 0.875(d) and 0.1111(b) = 0.93759(d), then 0.111...(b) = ?(d)

I also think that it doesn't make sense to say this is incorrect and switch to this is not true if the former meets resistence. This is exactly what you are doing by switching between mumber bases.

When the identity 0.999... = 1 is plugged into different functions, it supports the result or it doesn't. I show you some examples. The identity is useless on its own, it's just displays two equivalent numbers in different number formats - approximate/decimal and exact/fractional.

If you did some research on math symbolism, you would find out that, the way you write it, &.###... is a way of expressing a limit of a sequence or a series (& is the integer part). It means if 0.999... is limit L in approximate/decimal format, then 1/1 is the limit L in exact/fractional format.

epix · Jun 27, 2013

doronshadmi said:
As for multiplication of non-local numbers, for example 0.333...₁₀*2 = 0.666...₁₀, where 0.666...₁₀ < 2/3 by 0.000...4₁₀, as clearly given in http://www.internationalskeptics.com/forums/showpost.php?p=9313916&postcount=2454.

Doron, do you care for a detour into the field of forensic mathematics? If so, have your scalpel ready...

Before anything, unless there is a switch to some other bases, the math texts use base 10 as its default base. You have a statement all in base 10, but for some reason, you needed to stress the fact by attaching quite redundant base subscript into the works. But "2/3" is not subscripted. One of the goals of forensic mathematics is to figure out what was the cause of Mr. Statement's expiration. Did he suffer from 2/3(hexadecimal), or 2/3(octal) or some other base option?

The other internal organs are in decimal base, but 2/3 is not subscripted. Obviously a mathematician/pathologist would concentrate on that issue. But that wasn't the reason why Mr. Statement became a member of the set of the deceased. See, the conclusion

0.666...₁₀ < 2/3 by 0.000...4₁₀

leads to a very strong suspicion that the fraction 2/3 is also in base 10 - there is no pathogen.

The above inequality, which I already asked you about, says in other words that

2/3 - 0.666... = 0.000...4

How did you figure that out?

Here is the report from the coroner. It may not be correct, but given the advanced state of mathematical decay... youknowwhatimean.

Normally, seeing the result in approximate format, a person would attempt to convert 2/3 into its decimal equivalent via the long division, because that's how the results are displayed in calculators. So here is the calculator
http://www.online-calculator.com/
and here is the result adjusted for infinite case:

2/3 = 0.6666666666666...

I guess that after seeing the result which proves your inequality incorrect, you decided to convert 0.666... into the fractional format p/q.

0.666... is a periodic number and so it is a rational number expressible as p/q, where p and q are integers (q is different from zero.) So you converted 0.666... into a fraction.

0.666... => 0.666... / 1

It's all good except that p = 0.666... is not an integer. So you decided to multiply the fraction the way p would become an integer. It looks to me, that you used number 6 to accomplish the task

(0.666... / 1) * 6 = (3.999...6 / 6)

because you found out that the numerator is by 0.000...4 shy of becoming integer 4, thus satisfying the requirement on p. (Use the online calculator to verify the result of the "long multiplication.) And that's what you actually wanted to see, because the result supports the inequality.

So here is the gastrointestinal conflict:

If 0.666... cannot be expressed as p/q, then 0.666... is an irrational number. But the result of 2/3 supports the idea that 0.666... is a rational number. Use the calculator again.

2/3 => LD(2, 3) = 0.6666666666666...

The other issue concerns the way you attempted to finalize the conversion. Isn't it true that

(0.666... / 1) * 3 = (1.999...8 / 3)

with 2.000... - 1.999...8 = 0.000...2?

So the difference is not "by 0.000...4," but "by 0.000...2." (We go by irreducible fractions.)

But that's a minor deficiency in the spectacle grande. The clash of the titans: Long Division versus Long Multiplication.

doronshadmi · Jun 28, 2013

jsfisher said:
It saddens me to say this, but I'm with Doron on this one. He's been consistent of late that 9/9 = 1 and 0.999.... doesn't.

His reiterated nonsense which has risen beyond the level of spamming this thread is riddled with contradiction and other inconsistencies, but not recently on the value of 9/9.

(I say "not recently" because Doron has stated in the past that, for example, 1/4 and 0.25 are not the same number. Go figure. It is probably just the case the Doron is flexible on when and whether things are equivalent.)

Let's look at this diagram:

Organic Mathematics is sensitive also to the structural differences among mathematical objects.

In this case 1/4, 0.01₂ and 0.25₁₀, are measurements of different mixtures among several non-composed dimensional spaces (0-dimesioanl space AND 1-dimesional space).

In other words, Organic Mathematics finds these differences as important in terms of Information.

This is not the case with Standard Mathematics, which reduces Information into quantitative expressions, by ignoring the structural differences among them.

laca · Jun 28, 2013

doron, just because you say something is important does not make it so. You have to show why it's important. One way of doing that is showing some non-trivial result stemming from those "structural differences". Got any?

doronshadmi · Jun 28, 2013

laca said:
doron, just because you say something is important does not make it so. You have to show why it's important. One way of doing that is showing some non-trivial result stemming from those "structural differences". Got any?

Measurements of complexity, which are not based only on quantitative differences.

Moreover, even if I did have any non-trivial examples currently, still refinement of Information of mathematical objects can be vary useful in the near or far future, so it is not a good idea to ignore it as long as the suggested framework is consistent.

If you have something to say about the consistency of this Information's refinement, then please clearly express it in details.

doronshadmi · Jun 28, 2013

epix said:
If you did some research on math symbolism, you would find out that, the way you write it, &.###... is a way of expressing a limit of a sequence or a series (& is the integer part). It means if 0.999... is limit L in approximate/decimal format, then 1/1 is the limit L in exact/fractional format.

Epix, according to Standard Mathematics 0.999...₁₀ or 0.111...₂ are different representations (numerals, out of infinitely many possible representations) of one and only one mathematical objects, which is number 1.

According to Organic Mathematics (which does not ignore the structural AND quantitative differences among numbers (which are derived from associations among different levels of non-composed spaces)) 0.999...₁₀ or 0.111...₂ are numbers, and by ordering these numbers w.r.t number 1 we get:

0.111...₂ < 0.999...₁₀ < 1

doronshadmi · Jun 28, 2013

epix said:
0.666...₁₀ < 2/3 by 0.000...4₁₀

leads to a very strong suspicion that the fraction 2/3 is also in base 10

You are invited to show that the exact position of 2₄/3₄ is different than the exact position of 2₁₀/3₁₀ along a 1-dimensional space.

Any way, number 1 is a common unit for all bases > 1, which are based on natural numbers.

laca · Jun 28, 2013

doronshadmi said:
Measurements of complexity, which are not based only on quantitative differences.

What does that mean? Complexity of what? Please define your terms or put them in proper context.

doronshadmi said:
Moreover, even if I did have any non-trivial examples currently, still refinement of Information of mathematical objects can be vary useful in the near or far future, so it is not a good idea to ignore it as long as the suggested framework is consistent.

Look, even if it were so, this is an internet forum, not a mathematical publication where it's perfectly fine to construct frameworks with no apparent practical application. We already know that you have no publication in any mathematical journal of any relevance. This tells us you could not sell your idea. All we're left with is asking for results. And you have absolutely none.

doronshadmi said:
If you have something to say about the consistency of this Information's refinement, then please clearly express it in details.

I don't even understand what you're babbling about, please define your terms precisely before we can formulate proper questions or comment on them.

laca · Jun 28, 2013

doronshadmi said:
According to Organic Mathematics (which does not ignore the structural AND quantitative differences among numbers (which are derived from associations among different levels of non-composed spaces)) 0.999...₁₀ or 0.111...₂ are numbers, and by ordering these numbers w.r.t number 1 we get:

0.111...₂ < 0.999...₁₀ < 1

We all know what 0.999...₁₀ means in mathematics that actually works. What does it mean in doronetics? Please show your construction or whatever, so we can see a difference between the two. Otherwise you're just asserting that there's a difference when there's none whatsoever.

doronshadmi · Jun 28, 2013

laca said:
What does that mean? Complexity of what? Please define your terms or put them in proper context.

Of any form, where structure is important, for example the structures of fractals (even the fractal nature of the numeric system itself).

laca said:
We already know that you have no publication in any mathematical journal of any relevance.

http://www.ijpam.eu/contents/2008-49-3/5/5.pdf

laca said:
I don't even understand what you're babbling about, please define your terms precisely before we can formulate proper questions or comment on them.

Please train your mind, before you deal with the considered subject.

Deeper than primes - Continuation

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