Deeper than primes

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doronshadmi said:
In other words, I am right.

You simply do not wish to understand things that are not derived from "How to define and\or use"? question.

As a result you do not get that your reasoning is nothing but an arbitrary deremination of some snapshot of an "hand-waving".
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Is that really what you got out of all this? Ok. Have a nice life.

By the way, you are still avoiding the question. What's the difference between 1 and 0.999..., then?
 
doronshadmi said:
Accept the corrections (and thank you very much for them), you did not try at all to read and undertand http://www.internationalskeptics.com/forums/showpost.php?p=4767578&postcount=3316 , beyond your agreed determinations.
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You didn't present any "determinations" that changed the answer. The question was always about an infinite geometric series. The presumed origin of the terms, or the origin of the origin of the terms, doesn't change the series under inspection.
 
I have a request. Please do not reply to any part of this post, before you read all of it, thank you.


Ok, let us see what we got from the last very interesting dialog with jsfisher.

Jsfisher is, without a doubt a perfectly trained and skilful expert of serial thinking (also known as analysis) that was educated for many years to research and understand things by using one and only one question, which is:

"How (by using only serial thinking (also known as analysis)) to define and\or use?"

But like any expert of a one and only one thinking style, this is his strength and this is his weakness.

From one hand he will immediately find any mistake that may exist in the limits of his expertise (you can see his fine corrections of my last posts, along this last dialog), but on the other hand he misses the deeper understanding that can be derived from a more comprehensive view of the researched (which transcendent the limits of his expertise).

Our last discussion was about the relations between the Q sequence (0.9[base 10], 0.99[base 10], 0.999[base 10], …) (that each one of its elements is obviously < 1) and the Q sequence (0.9[base 10], 0.09[base 10], 0.009[base 10], …) (that each one of its elements is obviously < 1).

In both cases we deal with a non-finite sequence of finite Q members that each one of them is obviously < 1.

I asked this question:

Why in the case of (0.9[base 10], 0.99[base 10], 0.999[base 10], …) it is obvious that we always < 1, but in the case of the sum of (0.9[base 10], 0.09[base 10], 0.009[base 10], …) we get the result = 1?

Jsfisher, by using his expertise, used this argument:

jsfisher said:
Every element of your second set {0.9, 0.99, 0.999, ...} is the sum of a finite sequence of elements from your first set {0.9, 0.09, 0.009, ...}.
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(Remark: what jsfisher calls "second set" in his argument, is the first set in this post, and what jsfisher calls "first set" in his argument, is the second set in this post) .

By following his argument I wrote post http://www.internationalskeptics.com/forums/showpost.php?p=4767578&postcount=3316 (this version is the result of several important corrections of jsfisher, that help me to write it according to the required term of jsfisher's expertise).

Jsfisher's reply to this post was:

jsfisher said:
All this hand-waving with sequences derived from other sequences is irrelevant. The original answer stands.
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First let us see jsfisher's original answer:
jsfisher said:
Every element of your second set {0.9, 0.99, 0.999, ...} is the sum of a finite sequence of elements from your first set {0.9, 0.09, 0.009, ...}.

The value 1 is the sum of an infinite sequence of elements. Big difference between sums over finite and infinite sequences.

By the way, you may notice that even though 1 does not appear as an element of the second set (in either 1 or 0.999... form), it is the limit of the sequence represented by the set. This exactly parallels the summations. Even though 1 is not the sum of any finite sequence from the first set, it is the limit of those sums.
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As I said, jsfisher choose (without any given reason) to ignore http://www.internationalskeptics.com/forums/showpost.php?p=4767578&postcount=3316 content.

Instead of dealing with it, he wrote these posts:

Post 1:
doronshadmi said:
The sum is the result of infinitely many addends where each added value is finite.

So why do you think that inifintely many finite values can reach their limit?
jsfisher said:
I think that because I have quite the understanding of Mathematics, including how limits work. By Standard Mathematics (which you have already conceded as the domain of discourse, here), it is a geometric series of the form:

[latex]$$ S = a + ar + ar^2 + ar^3 + ... $$[/latex]

The series converges to a value given by:

[latex]$$ S = \sum_{n \ge 0} ar^n = \frac{a}{1 - r} $$[/latex]

Simple substitution with a=0.9 and r = 0.1 gives S = 0.9/(1-0.1) = 0.9/0.9 = 1.
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This post is again, a string of agreed notations, that is based on one and only one question, which is:

"How (by using only serial thinking (also known as analysis)) to define and\or use?"

where this is the only agreed fundamental question of jsfisher's community of experts.

Post 2:
jsfisher said:
If you can't accept that 0.999... is equal to 1, then please tell us what the difference between the two is. That is, what is 1 - 0.999..., and please restrict you response to standard mathematics constructs.

(When I do the subtraction, I get 0.000..., which for all practical purposes is just 0.)
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My answer to post 2 was:
jsfisher said:
(When I do the subtraction, I get 0.000..., which for all practical purposes is just 0.)
doronshadmi said:
It is possible because you already say that 1=0.999... so your "practical purposes" is based on circular reasoning.
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In post 2 jsfisher asked an important question, which is:
jsfisher said:
If you can't accept that 0.999... is equal to 1, then please tell us what the difference between the two is. That is, what is 1 - 0.999..., and please restrict you response to standard mathematics constructs.
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but he had a condition, which is:
jsfisher said:
… please restrict you response to standard mathematics constructs.
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In other words "I will not accept anything that is not based on standard mathematics constructs".

My answer to this question (I have to admit that I did not immediately answered to this jsfisher's particular post) was:

0.111...[base 2] < 0.222...[base 3] ... < 0.999...[base 10] ... < ... < ... 1

Jsfisher's reply to my answer was:
jsfisher said:
You still are evading the answering the question. It asked for the difference between 1 and 0.999....
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Here is my reply to this jsfisher's post:

1) Jsfisher missed the general conclusion that is derived from the non-finite base\value sequence (where 0.999...[base 10] is nothing but some particular case of it).

2) If we use "a" in base 11 , in the same manner as "9" is used in base 10 then:

0.999…[base 10] < 0.aaa…[base 11] < 1

3) The general case of this is:

For any given base n>1 and any 0.kkk…[base n] (where k=n-1) there is 0.nnn…[base n+1] such that 0.kkk…[base n] < 0.nnn…[base n+1] < 1

The typical response of experts like jsfisher to (3) is:

No, these are different representations (numerals) of the same number (1 in this case).

You do not distinguish between numerals and numbers.

---------------------------------------------------------------------------

At this point we get an unclosed gap between jsfisher's reasoning and OM's reasoning, which can be closed only by a paradigm-shift about the base\value form.

By OM, the base\value form is a kosher number exactly as 1 is a kosher number.

By OM the base\value form is called a non-local number, and for further reading about this number, please read at least page 11 of http://www.geocities.com/complementarytheory/OMPT.pdf .

By OM, the Q sequence (0.9[base 10], 0.99[base 10], 0.999[base 10], …) and the Q sequence (0.9[base 10], 0.09[base 10], 0.009[base 10], …) are actually two aspects of a one thing, called a non-local number.

For technical considerations, let us use a more convenient example (that is based on the non-local number 0.111…[base 2]) in order to demonstrate the following:

base2_3.jpg


This is a rigorous expression of a geometric series in terms of OM, exactly as a geometric series of the form
jsfisher said:
[latex]$$ S = a + ar + ar^2 + ar^3 + ... $$[/latex]

The series converges to a value given by:

[latex]$$ S = \sum_{n \ge 0} ar^n = \frac{a}{1 - r} $$[/latex]
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is a rigorous expression in terms of Standard Math.

But unlike Standard Math, OM explicitly shows that the Q sequence (0.1[base 2], 0.11[base 2], 0.111[base 2], …) and the Q sequence (0.1[base 2], 0.01[base 2], 0.001[base 2], …) are actually two aspects of a one thing, called a non-local number, as follows:

The non-finite case of 0.111…[base 2] is clearly shown by the bolded double line, and it is easily shown that 0.222…[base 3] is a non-local number between 0.111…[base 2] and 1, such that 0.111…[base 2] < 0.222…[base 3] < 0.999…[base 10] < 0.aaa…[base 11] < … < … 1 .

By OM expression of a geometric series, it is also rigorously shown that the Q sequence (0.1[base 2], 0.11[base 2], 0.111[base 2], …) and the Q sequence (0.1[base 2], 0.01[base 2], 0.001[base 2], …) are (respectively) "horizontal" and "vertical" aspects of the same mathematical object, called the non-local number.

EDIT:

OM is based on deeper notions than Standard Math, because its foundations transcendent the single question ("How (by using only serial thinking (also known as analysis)) to define and\or use?") of Standard Math.

In order to realize this fact, one has to read all of http://www.geocities.com/complementarytheory/OMPT.pdf before he airs his view about any part of it.

Furthermore, one cannot understand any part of http://www.geocities.com/complementarytheory/OMPT.pdf if his reasoning is based only on "How (by using only serial thinking (also known as analysis)) to define and\or use?" question.

( About jsfisher's basic attitude about this thread, please see http://www.internationalskeptics.com/forums/showpost.php?p=4753962&postcount=3196 )
 
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Doron,

If you really want a dialog, don't be so condescending and insulting.
 
doronshadmi said:
jsfisher and The Man,

I actually wish to know your real names, in order to add you to http://www.geocities.com/complementarytheory/OMPT.pdf Acknowledgements.

I have no doubt that I had no chance to develop it to its current stage, without you.
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Forget it, if we were actually contributors you would have been listening to what we have been saying. This fantasy of yours that ignoring the ‘standard math’ you claim to be supplanting and what people tell you about it somehow “develops” your notions is certainly not one I will indulge you in. The ignorance is entirely yours Doron, if you want to proclaim that ignorance as some ‘developed theory’ that is your choice and you can place all the ‘credit’ and responsibility exactly where it belongs, on yourself.

ETA:

If you want to be honest in your acknowledgements and give credit to the efforts of all those involved, then I would suggest the following statement.

“At various times and on numerous forums people have tried to explain ‘standard math’ to me and I would like to sincerely acknowledge and thank them all for their efforts. However, my theories are entirely dependent on misinterpreting ‘standard math’ so actually understanding ‘standard math’ would be counterproductive to the development of my theory.”
 
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The Man said:
Forget it, if we were actually contributors you would have been listening to what we have been saying. This fantasy of yours that ignoring the ‘standard math’ you claim to be supplanting and what people tell you about it somehow “develops” your notions is certainly not one I will indulge you in. The ignorance is entirely yours Doron, if you want to proclaim that ignorance as some ‘developed theory’ that is your choice and you can place all the ‘credit’ and responsibility exactly where it belongs, on yourself.

ETA:

If you want to be honest in your acknowledgements and give credit to the efforts of all those involved, then I would suggest the following statement.

“At various times and on numerous forums people have tried to explain ‘standard math’ to me and I would like to sincerely acknowledge and thank them all for their efforts. However, my theories are entirely dependent on misinterpreting ‘standard math’ so actually understanding ‘standard math’ would be counterproductive to the development of my theory.”
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http://www.internationalskeptics.com/forums/showpost.php?p=4767637&postcount=3320
 
doronshadmi said:
http://www.internationalskeptics.com/forums/showpost.php?p=4767637&postcount=3320
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What? So your argument against my assertions that you simply dismiss and ignore the contributions of those you claim you want to acknowledge, is a post where you simply claim you will dismiss and ignore the contributions of others because you feel it is limited by what you call being “derived from "How to define and\or use"? question” and “an arbitrary deremination of some snapshot of an "hand-waving"”? The cup of irony overfloweth, again.
 
The Man said:
What? So your argument against my assertions that you simply dismiss and ignore the contributions of those you claim you want to acknowledge, is a post where you simply claim you will dismiss and ignore the contributions of others because you feel it is limited by what you call being “derived from "How to define and\or use"? question” and “an arbitrary deremination of some snapshot of an "hand-waving"”? The cup of irony overfloweth, again.
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He thinks that the rejections actually help him clarify his views, by using other terms/graphics. His basic view stays the same, and you summed it up quite accurately.
 
sympathic said:
He thinks that the rejections actually help him clarify his views, by using other terms/graphics. His basic view stays the same, and you summed it up quite accurately.
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Category theory also uses "graphics", so what is exactly your point?
 
zooterkin said:
What's the immediate predecessor of 7.3? What's the definition of 'crisp', and an example crisp id?
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Oh come on zooterkin, we all know you’re just looking for an acknowledgement is Doron's PDF. That certainly seems more likely then you getting any kind of substantial response to those questions.
 
sympathic said:
He thinks that the rejections actually help him clarify his views, by using other terms/graphics. His basic view stays the same, and you summed it up quite accurately.
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Thanks, I just whish instead of simply wanting to put some acknowledgement of others into his 'paper', Doron actually acknowledged what those others have been telling him.
 
doronshadmi said:
This is insulting...condescending.
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Yes, but I wasn't trying to engage you in a dialog on a topic of my choosing. If you want a favor from someone, it is best not to punch him first.


doronshadmi said:
jsfisher and The Man,

I actually wish to know your real names, in order to add you to http://www.geocities.com/complementarytheory/OMPT.pdf Acknowledgements.

I have no doubt that I had no chance to develop it to its current stage, without you.
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No, thank you.
 
jsfisher said:
Yes, but I wasn't trying to engage you in a dialog on a topic of my choosing. If you want a favor from someone, it is best not to punch him first.
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Engage?? Favor?? :eye-poppi

Are these the words that guided you along this long dialog? :jaw-dropp

No wonder that :covereyes is what you get.
 
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jsfisher said:
Every element of your second set {0.9, 0.99, 0.999, ...} is the sum of a finite sequence of elements from your first set {0.9, 0.09, 0.009, ...}.

The value 1 is the sum of an infinite sequence of elements. Big difference between sums over finite and infinite sequences.
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jsfisher said:
Given any two real numbers X and Y where X < Y, there is another number Z between them. (That is, X < Z and Z < Y).
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Jsfisher, did you notice that each Z < h < Y expression in your proof by contradiction, and each X < Z < Y expression of "dense" definition, are both equivalent to each finite member of the set {0.9, 0.99, 0.999, ...}?

This is exactly the reason of why Y has no immediate predecessor (which is equivalent to the reason of why 1 > any finite member of the non-finite set {0.9, 0.99, 0.999, ...}).

By using only the Standard Mathematics framework, let us use here the "Big difference between sums over finite and infinite sequences", exactly as you claim jsfisher.

Now jsfisher, by following your own arguments do you understand that you can show that "there is always another real number between any two real numbers" exactly because you are always based on a finite case (each "X < Y < Z" or "Z < h < Y" expression is a finite case exactly as each member of the set {0.9, 0.99, 0.999, ...} is a finite case)?

EDIT:

Again, by using only arguments taken from Standard Math, it is easily shown that "Z < h < Y" or "X < Z < Y" expression is not equivalent to the sum of the non-finite members of the set {0.9, 0.09, 0.009, ...} (because if it is equivalent to the sum of the non-finite members of the set {0.9, 0.09, 0.009, ...}, then, according to Stndard Math, Y must = to this sum, which prevents from us to use "< Y" expression
in both "Z < h < Y" or "X < Z < Y" expressions).

By using only Standard Math reasoning, the proof by contradiction and the "dense" definition do not hold exactly because there is a "big difference between sums over finite and infinite sequences" under Standard Math framework.
 
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doronshadmi said:
Jsfisher, did you notice that each Z < h < Y expression in your proof by contradiction, and each X < Z < Y expression of "dense" definition, are both equivalent to each finite member of the set {0.9, 0.99, 0.999, ...}?
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This is just a baseless assertion on your part. Got any sort of proof to back it up?

This is exactly the reason of why Y has no immediate predecessor (which is equivalent to the reason of why 1 > any finite member of the non-finite set {0.9, 0.99, 0.999, ...}).
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Another assertion without basis.

By using only the Standard Mathematics framework, let us use here the "Big difference between sums over finite and infinite sequences", exactly as you claim jsfisher.

Now jsfisher, by following your own arguments do you understand that you can show that "there is always another real number between any two real numbers" exactly because you are always based on a finite case (each "X < Y < Z" or "Z < h < Y" expression is a finite case exactly as each member of the set {0.9, 0.99, 0.999, ...} is a finite case)?
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No, you cannot show that from the premises you cite.

EDIT:

Again, by using only arguments taken from Standard Math, it is easily shown that "Z < h < Y" or "X < Z < Y" expression is not equivalent to the sum of the non-finite members of the set {0.9, 0.09, 0.009, ...}
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This statement is trivial. Logical propositions of order relationships and sums are orthogonal.

(because if it use equivalent to the sum of the non-finite members of the set {0.9, 0.09, 0.009, ...}, then, according to Stndard Math, Y must = to this sum, which prevents form us to use "< Y" expression).
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This statement is gibberish.

By using only Standard Math reasoning, the proof by contradiction and the "dense" definition do not hold exactly because there is a "big difference between sums over finite and infinite sequences".
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Your conclusion is based on a false premise, and therefore it is irrelevant. Moreover, there is not apparent chain of logic between your false premise and your conclusion.
 
jsfisher said:
This is just a baseless assertion on your part. Got any sort of proof to back it up?



Another assertion without basis.



No, you cannot show that from the premises you cite.



This statement is trivial. Logical propositions of order relationships and sums are orthogonal.



This statement is gibberish.



Your conclusion is based on a false premise, and therefore it is irrelevant. Moreover, there is not apparent chain of logic between your false premise and your conclusion.
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It does not work like this, jsfisher. You answer without first read all of it and think about it, before you reply.

I have a request. Please refreash your screen, read it again and do not reply to any part of http://www.internationalskeptics.com/forums/showpost.php?p=4775838&postcount=3341 before you read all of it and then think about it, thank you.
 
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zooterkin said:
I have request; how about you post what you mean to the first time?
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Each time is the first time, as long as you do not get what you read, and you don't.

EDIT:

I asked jsfisher to refreash his screen, because I fixed some typos, that's all.
 
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doronshadmi said:
Each time is the first time, as long as you do not get what you read, and you don't.

EDIT:

I asked jsfisher to refreash his screen, because I fixed some typos, that's all.
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Nearly two hours after you posted it, and after he replied.

If they were simply typos, then they would not have made much difference. Even if they did, it is extremely rude to just make changes, without indicating what they were, and demand that he read the whole post again.

Of course, that is ignoring the fact that you seem incapable of understanding anything that is explained to you, preferring to believe that it is everyone else in the world who has the problem with comprehension.


ETA: In fact I notice you edited it at least twice, the second time being after I had commented above. If I recall correctly, you edited at 12:43, and then again at 12:49. At least the second time you added an indication of what you were adding.
 
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doronshadmi said:
It does not work like this, jsfisher. You answer without first read all of it and think about it, before you reply.
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You incorrectly assume. Perhaps you might actually consider what I wrote and respond directly to that.

I have a request. Please refreash your screen, read it again and do not reply to any part of http://www.internationalskeptics.com/forums/showpost.php?p=4775838&postcount=3341 before you read all of it and then think about it, thank you.
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It has been explained to you enough times how rude this practice of yours is. I will not indulge you in this.
 
jsfisher said:
See hi-lighted part.
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jsfisher said:
Perhaps you might actually consider what I wrote and respond directly to that.
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No details.

Please provide some detials about this "orthogonal" relation (some paper or web page).

After all you are the one that use Logic in order to conclude somthing abuot some sequence of numbers along the real-line, isn't it?
 
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zooterkin said:
Nearly two hours after you posted it, and after he replied.

If they were simply typos, then they would not have made much difference. Even if they did, it is extremely rude to just make changes, without indicating what they were, and demand that he read the whole post again.

Of course, that is ignoring the fact that you seem incapable of understanding anything that is explained to you, preferring to believe that it is everyone else in the world who has the problem with comprehension.


ETA: In fact I notice you edited it at least twice, the second time being after I had commented above. If I recall correctly, you edited at 12:43, and then again at 12:49. At least the second time you added an indication of what you were adding.
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And I was going to add, but when I hit the Save button it was one minute too late, that comparing what jsfisher quoted with your post, I couldn't spot any significant differences anyway.
 
doronshadmi said:
No details.

Please provide some detials about this "orthogonal" relation (some paper or web page).

After all you are the one that use Logic in order to conclude somthing abuot some sequence of numbers along the real-line, isn't it?
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I apologize. I used the word orthogonal for one of its more obscure meanings. It relates to the mathematical notion of linear independence, but was used with non-mathematical connotations. I could have used another colloquialism involving the comparison of dissimilar fruit.
 
jsfisher said:
I apologize. I used the word orthogonal for one of its more obscure meanings. It relates to the mathematical notion of linear independence, but was used with non-mathematical connotations. I could have used another colloquialism involving the comparison of dissimilar fruit.
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Can you please explain why logical propositions of order relationships and sums do not have a common reasoning?
 
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doronshadmi said:
Can you please explain why logical propositions of order relationships and sums do not have a common reasoning?
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Rather than picking and choosing tidbits from my post - especially ones that aren't all that important in and of themselves - how about you start at the beginning?
 
doronshadmi said:
By the way, it is easy to show the inconsistency of Standard Math, in this case:

1) From one hand it claims that Y of X<Y has no immediate predecessor, and for that d must be > 0.

2) On the other hand it claims that 0.999…[base 10] = 1 , and for that d must be 0.

I know that (2) is a sum of non-finite Q members, but it has no significance in this case, because both R and Q are dense, by Standard Math.
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doronshadmi said:
There is no inconsistency in those two statements. In fact, they are closely related. If 0.999... were not identical to 1, then you'd have an inconsistency between statements (1) and (2).
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Jsfisher by your reply it is clearly understood that there is a common reasoning to both X<Y non-immediate predecessor case and the sum of the members of set {0.9, 0.09, 0.009, …}, exactly because you say that "If 0.999... were not identical to 1, then you'd have an inconsistency between statements (1) and (2)."

We cannot conclude such a thing unless (1) and (2) have a common reasoning.

After it was clearly shown (by your own words) that there is a common reasoning to (1) and (2), I ask you to read again http://www.internationalskeptics.com/forums/showpost.php?p=4775838&postcount=3341 .

Please do not reply to any part of it before you read all of it and then think about it, thank you.
 
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