Deeper than primes

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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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