Deeper than primes - Continuation

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laca said:
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.
Click to expand...

Take, for example:

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

Now, try to show some inconsistency in it, which leads to the conclusion that 0 = 0.000...110
 
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doronshadmi said:
Take, for example:

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

Now, try to show some inconsistency in it, which leads to the conclusion that 0 = 0.000...110
Click to expand...

Doron, did you miss this?

zooterkin said:
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?
Click to expand...
 
doronshadmi said:
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.
Click to expand...

If x is not equal to y, then 4x is not equal to 4y.



Thus, since you think 1/4 is not equal to 0.25, you must claim either that 4/4 is not 1 or that 4*0.25 is not 1. I am interested to hear which is not 1 and why.
 
BenjaminTR said:
If x is not equal to y, then 4x is not equal to 4y.



Thus, since you think 1/4 is not equal to 0.25, you must claim either that 4/4 is not 1 or that 4*0.25 is not 1. I am interested to hear which is not 1 and why.
Click to expand...

The inequality is among the structural properties of these expressions, and not among the quantitative properties of these expressions.

for example:

There is a structural difference among

.__.*4

or

.__________.__________.__________.__________. /4

or

.__________. /1

but not a quantitative difference among them.
 
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doronshadmi said:
Of any form, where structure is important, for example the structures of fractals (even the fractal nature of the numeric system itself).
Click to expand...

I said define precisely and I get inane gibberish. Typical.

doronshadmi said:
http://www.ijpam.eu/contents/2008-49-3/5/5.pdf
Click to expand...

:dl:

Please look up relevance in the dictionary.

doronshadmi said:
Please train your mind, before you deal with the considered subject.
Click to expand...

You have not even established that there is a subject to consider. Until you do, my mind is quite fine, thank you.
 
zooterkin said:
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?
Click to expand...
9 is not a digit of base 9, exactly as 10 is not a digit of base 10

So if you wish to use base 9 in the right way, then do it like this:

1 - 8/8 = 0/8 = 0
1 - 7/8 = 1/8 > 0.1111...9 by 0.000...89
1 - 6/8 = 2/8 > 0.2222...9 by 0.000...79
1 - 5/8 = 3/8 > 0.3333...9 by 0.000...69
1 - 4/8 = 4/8 > 0.4444...9 by 0.000...59
1 - 3/8 = 5/8 > 0.5555...9 by 0.000...49
1 - 2/8 = 6/8 > 0.6666...9 by 0.000...39
1 - 1/8 = 7/8 > 0.7777...9 by 0.000...29
1 - 0/8 = 8/8 > 0.8888...9 by 0.000...19
 
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doronshadmi said:
9 is not a digit of base 9, exactly as 10 is not a digit of base 10

So if you wish to use base 9 the right way to do it is like this:

1 - 8/8 = 0/8 = 0
1 - 7/8 = 1/8 > 0.1111 ... by 0.000...89
1 - 6/8 = 2/8 > 0.2222 ... by 0.000...79
1 - 5/8 = 3/8 > 0.3333 ... by 0.000...69
1 - 4/8 = 4/8 > 0.4444 ... by 0.000...59
1 - 3/8 = 5/8 > 0.5555 ... by 0.000...49
1 - 2/8 = 6/8 > 0.6666 ... by 0.000...39
1 - 1/8 = 7/8 > 0.7777 ... by 0.000...29
1 - 0/8 = 8/8 > 0.8888 ... by 0.000...19
Click to expand...

Come on, it's clear to everyone that unless specified, the base is 10. zooterkin's post stands as is. Your post is nonsense, as always.
 
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doronshadmi said:
No problem, here it is according to your claims:

1 - 0/9 = 9/9 = 1 > 0.999...10 by 0.000...110

So, as you see, 0.000...110 did not disappear.
Click to expand...

What you don't seem to realize is that 0.000...110 is just a weird way to write 0.
 
doronshadmi said:
9 is not a digit of base 9, exactly as 10 is not a digit of base 10

So if you wish to use base 9 in the right way, then do it like this:

1 - 8/8 = 0/8 = 0
1 - 7/8 = 1/8 > 0.1111...9 by 0.000...89
1 - 6/8 = 2/8 > 0.2222...9 by 0.000...79
1 - 5/8 = 3/8 > 0.3333...9 by 0.000...69
1 - 4/8 = 4/8 > 0.4444...9 by 0.000...59
1 - 3/8 = 5/8 > 0.5555...9 by 0.000...49
1 - 2/8 = 6/8 > 0.6666...9 by 0.000...39
1 - 1/8 = 7/8 > 0.7777...9 by 0.000...29
1 - 0/8 = 8/8 > 0.8888...9 by 0.000...19
Click to expand...

As laca pointed out, I did use base 9 in the right way. Numbers are base 10 unless otherwise specified. Please show where I went wrong.


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?
 
doronshadmi said:
What you don't seem to realize is that 0 is not 0.000...110
Click to expand...

That is your claim, but you have yet to substantiate it in any way. If by "..." you mean an infinite number of zeroes, it doesn't even make sense to put anything after it. It's impossible.
 
laca said:
That is your claim, but you have yet to substantiate it in any way. If by "..." you mean an infinite number of zeroes, it doesn't even make sense to put anything after it. It's impossible.
Click to expand...
It is possible if you understand that no amount of points completely covers a line, simply because a line is irreducible into a point.

The "1" after infinitely many zeros in the expression "0.000...1" is exactly the irreducibility of a line into a point.

As long as you get a line in terms of collection of points, what I claim indeed makes no sense.

Please try this time to deal with http://www.internationalskeptics.com/forums/showpost.php?p=9326076&postcount=2523, such that a line is not a collection of points.
 
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doronshadmi said:
It is possible if you understand that no amount of points completely covers a line, simply because a line is irreducible into a point.

The "1" after infinitely many zeros in the expression "0.000...1" is exactly the irreducibility of a line into a point.

As long as you get a line in terms of collection of points, what I claim indeed makes no sense.
Click to expand...

Aaaand we're back to this. Show a place on a line where there's no point, please.
 
laca said:
Aaaand we're back to this. Show a place on a line where there's no point, please.
Click to expand...
A place on a line is a point and this point is simultaneously located in one and only one place along the line, but a line is not a point exactly because it is simultaneously located in more than one place, as clearly seen, for example, in:

__.___

As long as you do not get this essential difference among a point and a line, you can't understand an expression like 0.000...1 (which simply formulates the reasoning that no amount of exact places completely covers an element, which its essential property is to simultaneously be located in more than one place. This is a qualitative difference that has quantitative implications that are addressed as stronger power of infinity with respect to the power of infinity of collections).

Laca, I know that this is not an easy task exactly because not lass than a paradigm shift in your mind is needed, in order to get this.
 
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doronshadmi said:
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
Click to expand...
Why don't you illustrate how 0.11111... (bin.) looks like as a series in a binary format? No pics, please - just the series.

The Spirit of Irreversible Discombobulation croaked that if (1/10) < (1/2) then 1(dec.) < 1(bin.), and if |1-10| > |1-2|, then 1(dec.) > 1(bin.)

The problem is that that you write many inequalities in one particular number base, but some of them are wrong, as shown in my previous post. So there is a little confidence in what you write. A difference in a subtraction involving two numbers in two different number bases could be either your point or just another mistake of yours.
 
epix said:
The problem is that that you write many inequalities in one particular number base, but some of them are wrong, as shown in my previous post.
Click to expand...
I do not see wrong inequalities of mine in your previous post.

Please show again some example of them.

epix said:
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.
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Again epix, a number of the form 0.###... (where ###... is a placeholder for any possible string of digits, periodic or non-periodic) is not a member of R or Q sets.

For example:

11.00100100001111...2 < 10.01021101222201...3 < 3.02100333122220...4 < 3.03232214303343...5 < 3.05033005141512...6 < 3.06636514320361...7 < 3.11037552421026...8 < 3.12418812407442...9 < 3.14159265358979...10 < 3.16150702865A48...11 < 3.184809493B9186...12 < 3.1AC1049052A2C7...13 < 3.1DA75CDA813752...14 < 3.21CD1DC46C2B7A...15 < 3.243F6A8885A300...16 ... < ... Pi, where Pi is a local number and the non-local numbers with infinitely many different bases (starting from base 2) < local number Pi.

Only Pi is an irrational number (and a member of R set), where the other numbers above are not members of R set.

As long as you don't get it, you have nothing to say about my numeric system.

As for 0.111...2 and the long addition 1/2 + 1/4 + 1/8 + ..., you are invited to show that they are not equivalent, by not using pics.
 
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doronshadmi said:
A place on a line is a point and this point is simultaneously located in one and only one place along the line, but a line is not a point exactly because it is simultaneously located in more than one place, as clearly seen, for example, in:

__.___
Click to expand...

Adverb "simultaneusly" strongly implies plural. So if a point is simultaneously located in one and only one place, then it it is the line that is actually moving. :boggled:

p = 0.333... The ellipses indicate that that point p approaches its limit. If it is in one and only one place, then it doesn't approach anything - unless the line is moving instead. But sometimes it isn't:
http://www.blackbaudknowhow.com/wp-content/uploads/2013/01/waiting-in-line.jpg
 
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epix said:
Adverb "simultaneusly" strongly implies plural. So if a point is simultaneously located in one and only one place, then it it is the line that is actually moving. :boggled:

p = 0.333... The ellipses indicate that that point p approaches its limit. If it is in one and only one place, then it doesn't approach anything - unless the line is moving instead. But sometimes it isn't:
http://www.blackbaudknowhow.com/wp-content/uploads/2013/01/waiting-in-line.jpg
Click to expand...
0.333... is not a point, but it is a mixture of lines and points that do not reach to a particular point (known as the limit point) exactly because the power of a mixture of 0-dimesional spaces with non-composed segments of 1-dimesional spaces is less than the power of a non-composed 1-dimensional space.

(The power of the composed 0.333...-dimensional space is > non-composed 0-dimesional space AND < non-composed 1-dimesional space).

More about this subject can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=9321966&postcount=2493.

epix said:
Adverb "simultaneusly" strongly implies plural.
Click to expand...
In the case of a point "simultaneusly" is equivalent to "member" in the case of {}.
 
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doronshadmi said:
I do not see wrong inequalities of mine in your previous post.

Please show again some example of them.


Again epix, a number of the form 0.###... (where ###... is a placeholder for any possible string of digits, periodic or non-periodic) is not a member of R or Q sets.

For example:

11.00100100001111...2 < 10.01021101222201...3 < 3.02100333122220...4 < 3.03232214303343...5 < 3.05033005141512...6 < 3.06636514320361...7 < 3.11037552421026...8 < 3.12418812407442...9 < 3.14159265358979...10 < 3.16150702865A48...11 < 3.184809493B9186...12 < 3.1AC1049052A2C7...13 < 3.1DA75CDA813752...14 < 3.21CD1DC46C2B7A...15 < 3.243F6A8885A300...16 ... < ... Pi, where Pi is a local number and the non-local numbers with infinitely many different bases (starting from base 2) < local number Pi.

Only Pi is an irrational number (and a member of R set), where the other numbers above are not members of R set.

As long as you don't get it, you have nothing to say about my numeric system.

As for 0.111...2 and the long addition 1/2 + 1/4 + 1/8 + ..., you are invited to show that they are not equivalent, by not using pics.
Click to expand...

Displaying a long list of inequalities involving different number bases doesn't constitute any proof. If a number is approaching its limit and it is not in R and/or Q, then a proof by contradiction is a logical choice and that's what is NOT happening in your post.

Now prove your previous statement that says

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

so we can match reality with hypothesis:
epix said:
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.)
Click to expand...
 
your mind is needed, in order to get this.[/QUOTE]

doronshadmi said:
0.333... is not a point, but it is a mixture of lines and points that do not reach to a particular point (known as the limit point) exactly because the power of a mixture of 0-dimesional spaces with non-composed segments of 1-dimesional spaces is less than the power of a non-composed 1-dimensional space.

(The power of the composed 0.333...-dimensional space is > non-composed 0-dimesional space AND < non-composed 1-dimesional space).

More about this subject can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=9321966&postcount=2493.


In the case of a point "simultaneusly" is equivalent to "member" in the case of {}.
Click to expand...
It all depends where you are.

0.333... represents an infinite set of points in metric space where d matters and so the points are linearly organized (but not always). There are obviously no points between a = 0.3333 and b = 0.333, for example, which would represent a line between a and b. And nothing approaches anything.

In calculus, 0.333... is a single point which jumps from one location to another with those locations defined by a function and therefore the point approaches its limit point.
 
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If 1/9 = 0.111... + 0.000...9 then 9*1/9 = 0.999... + 0.000...81

therefore 0.000...1 = 0
 
epix said:
Displaying a long list of inequalities involving different number bases doesn't constitute any proof.
Click to expand...
As long as you ignore levels and the structural differences.

Epix, you are running in circles inside you quantitative-only box.

When you are ready to get out of it, please tell me.
 
jsfisher said:
If 1/9 = 0.111... + 0.000...9 then 9*1/9 = 0.999... + 0.000...81

therefore 0.000...1 = 0
Click to expand...
Let us write it as follows:

9*(1/9) = 9*(0.111..10+0.000...910)

But you see jsfisher, the number of the form 0.000...x is a complement of the number of the form 0.xxx... into some number that has an exact position along the real-line.

So if 0.xxx... is increased then 0.000...x is proportionally reduced and vice versa.

In other words, the standard arithmetic does not work among numbers that each one of them does not have an exact position along the real-line, but together they complement each other into an exact position along the real-line, as can be seen in the following example:

1 - 9/9 = 0/9 = 0
1 - 8/9 = 1/9 > 0.111...10 by 0.000...910 (where 0.111...10 and 0.000...910 complement each other into 1/9 by inverse proportionality).
1 - 7/9 = 2/9 > 0.222...10 by 0.000...810 (where 0.222...10 and 0.000...810 complement each other into 2/9 by inverse proportionality).
1 - 6/9 = 3/9 > 0.333...10 by 0.000...710 (where 0.333...10 and 0.000...710 complement each other into 3/9 by inverse proportionality).
1 - 5/9 = 4/9 > 0.444...10 by 0.000...610 (where 0.444...10 and 0.000...610 complement each other into 4/9 by inverse proportionality).
1 - 4/9 = 5/9 > 0.555...10 by 0.000...510 (where 0.555...10 and 0.000...510 complement each other into 5/9 by inverse proportionality).
1 - 3/9 = 6/9 > 0.666...10 by 0.000...410 (where 0.666...10 and 0.000...410 complement each other into 6/9 by inverse proportionality).
1 - 2/9 = 7/9 > 0.777...10 by 0.000...310 (where 0.777...10 and 0.000...310 complement each other into 7/9 by inverse proportionality).
1 - 1/9 = 8/9 > 0.888...10 by 0.000...210 (where 0.888...10 and 0.000...210 complement each other into 8/9 by inverse proportionality).
1 - 0/9 = 9/9 > 0.999...10 by 0.000...110 (where 0.999...10 and 0.000...110 complement each other into 9/9 by inverse proportionality).

Welcome to the non-standard universe of non-local numbers.

EDIT: By second thought, the basic idea is quit standard exactly as, for example, the relations among two partitions of a given natural number, for example:

5=4+1
5=3+2
5=2+3
5=1+4

But unlike among non-local numbers, it is possible to use standard arithmetic among local numbers like natural numbers, as follows:

5*5=5*(4+1)
5*5=5*(3+2)
5*5=5*(2+3)
5*5=5*(1+4)
 
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doronshadmi said:
As long as you ignore levels and the structural differences.

Epix, you are running in circles inside you quantitative-only box.

When you are ready to get out of it, please tell me.
Click to expand...

You are not even capable of proving your claimed inequality spoken in Organic Mathematic language

"2/3 > 0.666... by 0.000...4"

which translates into

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

Let me at least show you how a proof by contradiction looks like.

Theorem: 1 ≠ 0.999...
Proof by contradiction:
If 1 = 0.999... then 1 - 0.999... = 0
however
1 - 0.999... = 0.000...1

Independent proof verification:

x = 0.000...1
10x = 0.000...1
10x - x = 0.000...1 - 0.000...1
9x = 0
x = 0/9 = 0

Darn.
 
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doronshadmi said:
You are not with me epix.

Please look at http://www.internationalskeptics.com/forums/showpost.php?p=9327103&postcount=2549 in order to understand the inverse proportionality among two non-local numbers that complement each other into a given local number.
Click to expand...
Your link is headed by

9*(1/9) = 9*(0.111..10+0.000...910)

which is identity that includes multiplication, division and addition, but not subtraction, and that's what your claim

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

is all about.

Just convert 2/3 into its decimal equivalent according to the rules of Organic Mathematic. If a space alien made the same request to learn something about the earth standard math, I would oblige in a sec.
http://www.online-calculator.com/

2/3 = 0.6666666666666...
 
doronshadmi said:
Let us write it as follows:

9*(1/9) = 9*(0.111..10+0.000...910)

But you see jsfisher, the number of the form 0.000...x is a complement of the number of the form 0.xxx... into some number that has an exact position along the real-line.
Click to expand...

How convenient. Never let actual Mathematics interfere with your really good assumptions.

Good thing I didn't multiply by 0.
 
doronshadmi said:
Let us write it as follows:

9*(1/9) = 9*(0.111..10+0.000...910)

But you see jsfisher, the number of the form 0.000...x is a complement of the number of the form 0.xxx... into some number that has an exact position along the real-line.

So if 0.xxx... is increased then 0.000...x is proportionally reduced and vice versa.

In other words, the standard arithmetic does not work among numbers that each one of them does not have an exact position along the real-line, but together they complement each other into an exact position along the real-line, as can be seen in the following example:

[...]

Welcome to the non-standard universe of non-local numbers.
[...]
Click to expand...
Do I have this right? If we accept your version of mathematics we have to give up the axiom that multiplication distributes over addition? Denying basic arithmetic is not going to gain you many supporters. I recommend you rethink this part.
 
BenjaminTR said:
Do I have this right? If we accept your version of mathematics we have to give up the axiom that multiplication distributes over addition? Denying basic arithmetic is not going to gain you many supporters. I recommend you rethink this part.
Click to expand...

Oh, do let him continue. Doron often invents things on the fly, this being just the latest example. He has already embedded quite a few inconsistencies in this notational gibberish of his, but there is always room for more. The "inverse proportionality" nonsense is such a curious addition to his battery of the inane. I wonder how long it will take Doron to figure out he has made things far, far worse, not better.

Doron has a shovel and continues to dig. Watching him is good fun. His eventual attempts to back pedal will be good fun, too.
 
doronshadmi said:
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
Click to expand...

0.999...10 ≠ n→∞ (1 - 1/10n)
0.111...2 ≠ n→∞ (1 - 1/2n)10

0.999...10 = lim. n→∞ (1 - 1/10n)
0.111...2 = lim. n→∞ (1 - 1/2n)10

lim. n→∞ (1 - 1/10n) - (1 - 1/2n) = lim. n→∞ (1/2n - 1/10n) = 0

and therefore

0.999...10 = 0.111...2

That's why

x = 0.111...2
102*x = 1.111...2
102*x - x = 1.111...2 - 0.111...2
x = 1

and therefore therefore

0.111...2 = 0.999...10 = 1
 
jsfisher said:
How convenient. Never let actual Mathematics interfere with your really good assumptions.

Good thing I didn't multiply by 0.
Click to expand...
By using a given base > 1, we get fractal structures upon infinitely many levels, where these structures have self similarity upon these levels, with respect to unit 1 (the 1-dimesional space among point named 0 and point named 1) which is the common unit for all fractal structures.

As a result, we get an inverse proportionality among the pair of numbers of the forms 0.000...x and 0.xxx... where this inverse proportionality is changed with respect to unit 1 (the 1-dimesional space among point named 0 and point named 1), which is the common unit for all fractal structures.

By understanding these conditions, 0.000...x and 0.xxx... are not impacted by multiplications, since the result is always translated to inverse proportionality according to a given base > 1 with respect to unit 1 (the 1-dimesional space among point named 0 and point named 1) which is the common unit for all fractal structures.

As long as you don't follow these verbal_symbolic AND visual_spatial rules, you are not in the mathematical universe of structures AND quantities, which is more sensitive to changes than the quantitative-only standard mathematical universe.

Soon I'll provide examples, which demonstrate the extra sensitivity of verbal_symbolic AND visual_spatial rules, after I finish some daily life assignments.
 
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doronshadmi said:
0.333... is not a point, but it is a mixture of lines and points that do not reach to a particular point (known as the limit point) exactly because the power of a mixture of 0-dimesional spaces with non-composed segments of 1-dimesional spaces is less than the power of a non-composed 1-dimensional space.

(The power of the composed 0.333...-dimensional space is > non-composed 0-dimesional space AND < non-composed 1-dimesional space).

More about this subject can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=9321966&postcount=2493.


In the case of a point "simultaneusly" is equivalent to "member" in the case of {}.
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Are you saying it's not possible to divide a line segment into thirds?
 
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Ok it is much more interesting that what I thought.

The particular discussed list of complement non-local numbers, is actually the result of overlaps of two fractals, a base 9 fractal and a base 10 fractal, as follows:

9164891933_532ea8a286_o.jpg


Both fractals share the same 0____1 line segment, so according to this knowledge, the involved numbers are as follows:

1 - 9/9 = 0/9 = 0
1 - 8/9 = 1/9 > 0.111...10 by the complement of 0.111...10 into 1/9, where 1/9 is a number of base 9 fractal
1 - 7/9 = 2/9 > 0.222...10 by the complement of 0.222...10 into 2/9, where 2/9 is a number of base 9 fractal
1 - 6/9 = 3/9 > 0.333...10 by the complement of 0.333...10 into 3/9, where 3/9 is a number of base 9 fractal
1 - 5/9 = 4/9 > 0.444...10 by the complement of 0.444...10 into 4/9, where 4/9 is a number of base 9 fractal
1 - 4/9 = 5/9 > 0.555...10 by the complement of 0.555...10 into 5/9, where 5/9 is a number of base 9 fractal
1 - 3/9 = 6/9 > 0.666...10 by the complement of 0.666...10 into 6/9, where 6/9 is a number of base 9 fractal
1 - 2/9 = 7/9 > 0.777...10 by the complement of 0.777...10 into 7/9, where 7/9 is a number of base 9 fractal
1 - 1/9 = 8/9 > 0.888...10 by the complement of 0.888...10 into 8/9, where 8/9 is a number of base 9 fractal
1 - 0/9 = 9/9 > 0.999...10 0.999...10 by the complement of 0.999...10 into 9/9, where 9/9 is a number of base 9 fractal

The complements of the non-local numbers of base 10 fractals into the local numbers of base 9 fractal, are marked by the cyan areas, and these areas are self similarities upon infinitely many levels among the overlap of base 10 fractal and base 9 fractal.

All these self similarities are invariant values > 0.

Yet, some work has to be done in order to symbolize them.

Also it has to be stressed that the structure of the invariant similarities among base 10 fractal and base 9 fractal remains along a given line segment with length 1, where its endpoints can can any integer numbers (which are some form of local numbers).
 
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doronshadmi said:
...gibberish mercifully snipped...
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Again you show you do not know what a fractal is, what inverse proportionality is, nor did you address that actual point of the post you quoted.

However, you do continue to show that your notational nonsense behaves exactly like, indistinguishably from zero. And you have never, ever shown any different.

Care to try now, just this one?
 
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