Deeper than primes

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zooterkin said:
I can highly recommend Alex's Adventures in Numberland by Alex Bellos. It's a very entertaining and informative book, and it also addresses many of the things you find confusing.
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What do you mean by confusing?

It is not confusing, traditional math is simply wrong about fundamental notions of actual infinity.

You are invited to quote from Alex's Adventures in Numberland about this subject.
 
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doronshadmi said:
Why can't you grasp that without non-locality\locality co-existence there is no multiplicity?
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You continue to evade the basic question.

You have claimed (incorrectly) that 1 and 0.999... represent different numbers. You have adopted (without explanation) 0.000...1 as your notation for this difference. That is, according to you,

1 - 0.999... = 0.000...1 and 0.000...1 > 0

In the normal world, 1 and 0.999... represent exactly the same number, and so their difference is exactly zero. You assert otherwise. You do so without proof and for the most part without even bothering to define your tortured vocabulary.

Since you assert 0.000...1 isn't zero, please describe how in Arithmetic it behaves in a way that zero does not.
 
doronshadmi said:
What do you mean by confusing?
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I mean that you clearly don't understand it.
It is not confusing, traditional math is simply wrong about fundamental notions of actual infinity.
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There you go.
You are invited to quote from Alex's Adventures in Numberland about this subject.
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Taking small parts in isolation will probably not help. I would recommend you read the whole thing, as it tends to build on what has gone before. However, it is a fun read, and not too difficult.
 
zooterkin said:
I mean that you clearly don't understand it.
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zooterkin, please give a concrete example and a clear explanation of how I "clearly don't understand it".

If you can't actually do that, then your "you clearly don't understand it" does not hold water.
 
zooterkin said:
Taking small parts in isolation will probably not help.
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Exactly zooterkin, you start to get it.

Only loclity (what you call small parts in isolation) indeed can't help to get non-locality\locality co-existence.
 
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jsfisher said:
You continue to evade the basic question.

You have claimed (incorrectly) that 1 and 0.999... represent different numbers. You have adopted (without explanation) 0.000...1 as your notation for this difference. That is, according to you,

1 - 0.999... = 0.000...1 and 0.000...1 > 0

In the normal world, 1 and 0.999... represent exactly the same number, and so their difference is exactly zero. You assert otherwise. You do so without proof and for the most part without even bothering to define your tortured vocabulary.

Since you assert 0.000...1 isn't zero, please describe how in Arithmetic it behaves in a way that zero does not.
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The algebraic proof of 0.999... = 1 is based on the acceptance that the expression "1/9" is an instruction to perform the long division. That leads to

1/9 = 0.111...

9 * 1/9 = 9 * 0.111...

and consequently to

1 = 0.999...

I personally do not accept the expression a/b as a substitute for a long division; In particular, I regard 1/9 as a limit to the result of L.D.(1,9) = 0.111...

The long division is an algorithm inside a loop. That means if there is no instruction "if condition, then stop," then in the case of L.D.(1,9) the output continues to churn out a string of 1's after the decimal point that is not bound. Since 1=1, there is no discriminating factor necessary to end the loop and it's termination only depends on the amount of time capable of killing the anticipation of some change.

There is no difference between 0.99999... and 3.14159... with limits 1 and Pi respectively, except that Pi as a limit lacks numerical equivalent being an irrational number. There is no way though to prove that "a/b" is the logical choice to represent the long division that supplies numbers in their approximate form.

Doron is using his "0.000...1" expression to support his "discovery" that 1-dim objects are irreducible to the 0-dim object. At least that's what I think he does. 0.999... is divisible by some x in R except zero and so is (1 - 0.999...) and that means 0.000...1 is not the smallest 1-dim object that proceeds infinitely toward zero, as Doron hopes it is. But he will weasel out of the problem by invoking that "local/not local co-existences closed under something" escape hatch anyway. LOL.
 
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doronshadmi said:
You continue to evade the basic answer.
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You have had plenty of opportunity to show how your 0.000...1 is distinguishable from 0 in basic Arithmetic. We can all now rightfully conclude that you cannot distinguish it from 0.

If it walks like a duck....
 
doronshadmi said:
You simply unable to get the irreducibility of 1-dimensional element to 0-dimensional element, exactly because the power of the continuum is at least 1-dimensional element, and no amount of 0-dimensional elements along it has this power.
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The power of the continuum loses its meaning in the case of two parallel lines intersecting real 3-D space where spontaneous discontinuity can manifest itself any time.

powercontinuum.jpg
 
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epix said:
Are you saying that the or in Dorons, "Since input AB is non-strict , then AB AND A or AB AND A output is non-strict, where the commutativity of AND connective has no influence on the non-strict property of the output, was actually meant to be upper-case OR, the logical connective; and not lower-case or, the coordinating conjunction? I don't think there are too many people who would separate a single option by saying, Let's go to the movies or to the movies.
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Well you’ve found at least one of them as that is exactly what he is saying.

epix said:
If the lower-case "or" is functional, then "AB AND A or AB AND A" results in two different inputs which are related by AND, like "movies or theater," for example. But what kind of clue is there to separate the case when the ANDed inputs are identical to each other?

AB AND A = movie
AB AND A = theater

I didn't go that far though and just tried to figure the output for AB AND A when A=True and B=False.
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Again it does not mater as ‘TRUE AND AB’ is just AB as is ‘AB AND TRUE’. While ‘AB AND FALSE’ is just FALSE like ‘FALSE AND AB’
 
doronshadmi said:
Wrong The Man.
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Oh so now you do accept it?

doronshadmi said:
You simply refuse to deal with the fact that the commutativity of AND connective has no influence on the output, which is determined by the property of the input.
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Again Doron it is the commutative property of “AND” that means “AB AND A” is the same as “AB AND A” and again, as you assert “A = TRUE”, the “output” is simply and strictly your “AB” “input”.


doronshadmi said:
Since the input in the case of AB AND A or A AND AB is non-strict, so is the output.
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Once again the output is specifically and strictly just your “AB”


doronshadmi said:
Your limited reasoning can't comprehend, for example, http://www.internationalskeptics.com/forums/showpost.php?p=7318785&postcount=15807.
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Your “direct perception” fails you yet again.


doronshadmi said:
Your weak and limited reasoning is clearly seen by this kind of poor and limited reply:
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The limits are yours Doron as specifically stated by you, that you still just don’t like even just your own asserted limits is just your problem.
 
Complexity said:
I am curious as to why people have encouraged doronshadmi by continuing to participate in this thread.

There is no longer any possibility of reaching him, or responding to any questions in a useful way. There is no chance that anyone will be led into error by his writings and need to be shown the way out. I don't think anything more can be learned from this. It hasn't been amusing for a very long time.

If people wish to continue, by all means do so, but I truly don't understand. Think of the time that you have invested in responding to his posts, and imagine how that time could have been spent otherwise.

Have a great day.
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Well as I have said before the main reason I continue to participate in this thread is because I said I would. In addition to that I spend my time quite productively in replying to his posts by reviewing the mathematical, linguistic or other principles I’ll be employing in that response. Finally anything that helps keep Doron off the streets is probably a worthwhile endeavor. Just imagine him being non-locally strung out on his local street corner seeking his next math fix by threatening passersby with a Dedekind cut or "death by entropy" should they not capitulate.
 
I'm having trouble believing that this thread is still going on.

First off, it was over after PixyMisa's post #2:

PixyMisa said:
No.
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And post #4 should've tipped you off:

Alkatran said:
I'm going to advise people not to respond to this thread. doronshadmi has a history of being totally incomprehensible and his threads always go for dozens of pages without any progress being made.

Doron, you are misusing common terms.
http://en.wikipedia.org/wiki/Information_entropy
http://en.wikipedia.org/wiki/Multiset

I will not be replying to this thread any more.
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Yet we're at 15895... :p
 
The Man said:
Well as I have said before the main reason I continue to participate in this thread is because I said I would. In addition to that I spend my time quite productively in replying to his posts by reviewing the mathematical, linguistic or other principles I’ll be employing in that response. Finally anything that helps keep Doron off the streets is probably a worthwhile endeavor. Just imagine him being non-locally strung out on his local street corner seeking his next math fix by threatening passersby with a Dedekind cut or "death by entropy" should they not capitulate.
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The Man, your replies have no value what so ever about OM, as long as you are stuck in your local dead end street.

For example http://www.internationalskeptics.com/forums/showpost.php?p=7318785&postcount=15807 is beyond your local dead end street.
 
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epix said:
The power of the continuum loses its meaning in the case of two parallel lines intersecting real 3-D space where spontaneous discontinuity can manifest itself any time.
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Wrong, in this case 3-D space is non-local (has the power of the continuum) w.r.t the two given lines.
 
Belz... said:
I'm having trouble believing that this thread is still going on.
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The difficulty of believing is usually ascribed to the turbulent effects of multidimensional atheism. Mathematics eats what is served and that includes irrational numbers. Since irrational numbers are a subset of real numbers, real irrationality exists as a separate field of mathematics and its aspects are heavily discussed here. This particular field heavily influences the very concept of infinity and Cantor's Hypothesis of The Continuum, and so it follows that this thread must continue without bound toward infinity.
 
doronshadmi said:
AB is non-strict, so your "specifically and strictly" does not hold water.
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So are you now claiming your "AB" is something other than just being strictly your "AB"? That would be typically self contradictory of you. The simple fact remains Doron that you simply do not like limitation least of all your own.


doronshadmi said:
The Man, your replies have no value what so ever about OM, as long as you are stuck in your local dead end street.
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As your “OM” has no value that you have demonstrated the lacking and “dead end street” remains simply and strictly still just yours.

doronshadmi said:
For example http://www.internationalskeptics.com/forums/showpost.php?p=7318785&postcount=15807 is beyond your local dead end street.
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Your “direct perception” continues to fail you.
 
jsfisher said:
Referring back to irrelevant posts doesn't make them relevant. You have done nothing to distinguish arithmetically your fantastical 0.000...1 from zero.

...if it talks like a duck....
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All you have to do is to notice the difference in the shape. '0' is not identical symbol to '1'. The arithmetic difference is naturally forthcoming. The difference is negligible, but Doron is a precisionist who doesn't accept the dismissal of the delta increment, or usually h, during the process in which the derivative of a function is determined -- he doesn't accept the concept of limits, which is also solely responsible for "1 - 0.999... = 0" asserted across the board.


eq1.gif


Gee, where did that h go?
 
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The Man said:
So are you now claiming your "AB" is something other than just being strictly your "AB"?
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A is a strict False value.

B is a strict True value.

AB is a non-strict False\True superposition value.

AND connective is a binary operation, which has strict output only if both input values are strict.

The output is non-strict if one of the inputs is non-strict, and the commutativity of AND connective has no influence on the non-strict output.

Since you get AB as strict value, you are unable to get AB as a non-strict False\True superposition value.
 
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jsfisher said:
as is your habit, the fault you claim of others is all yours.

But enough of your repeated efforts to dig up irrelevant posts. Arithmetically, how do 0.000...1 and 0 differ?

Perhaps some examples would help. What's 10 - 9.999...? What's 10*0.000...1?
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10 - 9.999... = (10 - 9) - 0.999... = 0.000...1

10*0.000...1 = 0.000...10
 
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doronshadmi said:
Only by your local-only reasoning.

(...it's a closed box reasoning that can't deal with http://www.internationalskeptics.com/forums/showpost.php?p=7351173&postcount=15887)


0.999...

0.000...1/10 = 0.000...0.1
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That would make "some authors" climb multidimensional walls...
Some authors forbid decimal representations with an infinite sequence of digits 9.
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http://en.wikipedia.org/wiki/Decimal_representation

You are using symbolism left and right in similar way someone ignores the dead end sign and proceeds. What is really 0.999... ?

This number rendition features decimal expansion of period one. That means it is a rational number. But the other definition -- the quotient definition -- says that a rational number exists as a result of q being divided into p during a process called the long division that takes care of the decimal expansion. The problem is that there is no p and q, such as

p:q = 0.999...

and therefore by one definition, 0.999... is a rational number and by the other it is not. Since Q is a subset of R, you need to visit the axiomatic framework that governs over R to resolve the issue. Better yet, you ask the top mathematicians about it to enjoy the different views of "traditional mathematics." But there is a consensus that I join: arithmetic operations involving numbers ended with ellipses is a big no-no. Only Rampepurdian Scholars who balance their checkbooks according to OM use it to the joy of the God of Perpetual Discombobulation.
 
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doronshadmi said:
For local-only minds this is the case.
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The "non-local mind" can deliver a classic example of the ultimate decomposition of reason.

Exhibit 1.
10*0.000...1 = 0.000...10
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Following the syntax, we get

100*0.000...1 = 0.000...100
1000*0.000...1 = 0.000...1000
10000*0.000...1 = 0.000...10000

It's easy to see that OM axioms hold 0.1 and 0.10000 as two different values.

Exhibit 2.
0.000...1/10 = 0.000...0.1
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Here, OM makes a revolutionary step toward the unification of all fields of known and uknown mathematics by introducing two decimal points in one number.

The Great Re-paganisation of mathemacs by OM will prove that the monotheistic system of only One Decimal Point is a one way ticket toward the global confusion in all numerical and analytic procedures to come. Our Savior has landed. Welcome. Any baggage?

8.88...54.3...45.56.

:confused:
 
epix said:
Here, OM makes a revolutionary step toward the unification of all fields of known and uknown mathematics by introducing two decimal points in one number.
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1/10 = 0.1

0.000...0.1 is 10 times smaller than 0.000...1 , where both are non-local numbers.

0.000...0.000...1 is infinitesimally smaller than 0.000...1 , where both are non-local numbers.

0.000...0.000...0.1 is 10 times smaller than 0.000...0.000...1 , where both are non-local numbers.

These non-local numbers are infinitesimally smaller than some local number like 1, etc.
 
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doronshadmi said:
Wrong.

0.1 = 0.1000... < 0.1000...1
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But that's not what is being said here and what I referred to.
10*0.000...1 = 0.000...10
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Let me show you the proper usage of the elipses (...):

1. DesperaDo... (ron)

2. Desperado, why don't you come to your senses?
You been out ridin' fences for so long now...

 
epix said:
But that's not what is being said here and what I referred to.
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You wrote 0.1 and 0.1000 (which is the same value) but we are talking about 0.000...1 and (for example) 0.000...1000, where 0.000...1 is 1000 times smaller than 0.000...1, which are indeed two different values.

B.T.W (for example) 0.000...0.1[base 10] = 0.000...1[base 100], etc.

epix, why can't you get out of your "no-no" box?
 
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