Deeper than primes

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By the way - you will get a degree if you demonstrate that you understand the material, and this is true for any academic domain.
 
sympathic said:
A perfect example - you ignored the second part of the question...
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On the contrary, I invited you use your knowledge and explicitly show that I am wrong, exactly as I do in the case of Standard Math.

If you refuse to do that, then we can conclude that your notions are nothing but beliefs that are not supported by any reasoning.
 
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You did not answer to: "Is this the only case where you refused to accept something you thought was wrong and afterwards after gaining more knowledge actually realized that it was right?". I have no wish to address your posts as long as you refuse to get proper education.
 
doronshadmi said:
jsfisher, you say:

The use of the word all doesn't guarantee they exist. As for the "no gaps" characteristic, that's what guarantees they don't exist.

I say:

The use of all + the fact that distinct R members have "no gaps" (and both of them are used by Standard Math) guarantees (in the framework of Standard Math) that Y has an immediate predecessor
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Nope, that provides no guarantee. You need to provide proof of your allegation.

...that cannot be found by using any particuler and finite case of pair of R members, as used in your "proof".
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Now, this part is just illogical and silly. If it exists, then we can give it a name and explore its properties. If not, well, then this is just another Doron fantasy.
 
doronshadmi said:
Jsfisher, if Z is the largest element of [X,Z]...
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Z is in fact the largest element of the interval [X,Z]. You are so busy trying to reinterpret what others write to cover your lack of understanding, you can't follow even simple sentences, can you?


And then there is this little gem:

...there is no room for h between Z and Y, exactly because [X,Y) is an interval of all R members, and all R members have no room ("gap") for your h.
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You just guessed what no gaps means, didn't you? The reason I say this is because you got it completely backwards. Try again.
 
jsfisher said:
You just guessed what no gaps means, didn't you? The reason I say this is because you got it completely backwards. Try again.
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Please provide the formal definition of "not gaps" (what is known as c)

Here is what we find at wikipadia:
http://en.wikipedia.org/wiki/Continuum_(mathematics)

The term the continuum sometimes denotes the real line. Somewhat more generally a continuum is a linearly ordered set of more than one element that is "densely ordered", i.e., between any two members there is another, and it lacks gaps in the sense that every non-empty subset with an upper bound has a least upper bound.
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So, by using an example (based on a finite case) that between a finite amount of two distinct members, there is another member, Standard Math concludes (and I would say guesses) that this is also the case about an interval of the all non-finite elements.
 
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wiki said:
… it lacks gaps in the sense that every non-empty subset with an upper bound has a least upper bound.
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Every finite example of a non-empty subset with an upper bound has an arbitrary element that is greater than the smallest element of the finite subset, and smaller than Y, so?

Let us add "no gaps" to the hijacked words.


I continue to claim that you force the finite on the non-finite.


This time please reply in details to http://www.internationalskeptics.com/forums/showpost.php?p=4748547&postcount=3128 .
 
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Another example:

http://en.wikipedia.org/wiki/Dense_order

In mathematics, a partial order ≤ on a set X is said to be dense (or dense-in-itself) if, for all x and y in X for which x < y, there is a z in X such that x < z < y.

The rational numbers with the ordinary ordering are a densely ordered set in this sense, as are the real numbers. On the other hand, the ordinary ordering on the integers is not dense.
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Again, any given example of this claim, must be based on a finite case (x and y must be two (where two is a finite cardinal) distinct elements).

We can add "Dense" to the list of hijacked words.

Some claims that x z or y of the expression x < z < y have no particular values.

EDIT:

This claim does not change the fact that Standard Math uses a finite construction of different elements of X (x,z and y must be different of each other) in order to determine something about the non-finite case of X (where the term ALL is used on a non-finite collection of distinct elements).

So, again we find that Standard Math forces the finite on the non-finite (the non-finite+ALL term).
 
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doronshadmi said:
Another example:


Again, any given example of this claim, must be based on a finite case (x and y must be two (where two is a finite cardinal) distinct elements).
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What else could they be? It wouldn't make a lot of sense if they had the same value.
We can add "Dense" to the list of hijacked words.
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I can think of another application of the word 'Dense'...
Some claims that x z or y of the expression x < z < y have no particular values.
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Would you like to complete that thought so that it actually says something?

This claim does not change the fact that we deal with a finite amount of different elements of X (x,z and y must be different of each other) in order to determine something about the non-finite case of X.
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What?
 
zooterkin said:
What?
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Standard Math forces the finite on the non-finite (uses notions based on the finite, in order to determine things about the non-finite).

EDIT:

Again:

This claim does not change the fact that Standard Math uses a finite construction of different elements of X (x,z and y must be different of each other) in order to determine something about the non-finite case of X (where the term ALL is used on a non-finite collection of distinct elements).
 
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doronshadmi said:
Let us add "no gaps" to the hijacked words.
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So, in addition to the phrase no gaps, we can add the word hijacked to the list of things you don't comprehend.

I continue to claim that you force the finite on the non-finite.

This time please reply in details to http://www.internationalskeptics.com/forums/showpost.php?p=4748547&postcount=3128 .
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You claim has already been addressed in detail. You started with a faulty premise (regarding the meaning of no gaps), so the premise and everything following it gets rejected.

While you may continue to claim anything you like, your claim continues to be without a base.


ETA:
So, upon what do you base your claim that every real number has an immediate predecessor and an immediate successor?
 
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jsfisher said:
So, in addition to the phrase no gaps, we can add the word hijacked to the list of things you don't comprehend.



You claim has already been addressed in detail. You started with a faulty premise (regarding the meaning of no gaps), so the premise and everything following it gets rejected.

While you may continue to claim anything you like, your claim continues to be without a base.


ETA:
So, upon what do you base your claim that every real number has an immediate predecessor and an immediate successor?
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The straightforward meaning of the word "no gaps" is "no interval".

In that case there is no room for z between x and y, if we deal with the non-finite collection of all members of set X.

Standard Math hijacked the words "all" and "no gaps", reversed their straightforward meaning, and used a finite case in order to determine things about the non-finite case.

Again, one can say that under Standard Math, The words "all", "no gap", "finite", "non-finite" etc. have different meaning than the original meaning, where these meanings, are derived from the axioms, definitions, terms, etc. of a formal language.

This claim does not hold in the cases I gave, because I clearly show in

http://www.internationalskeptics.com/forums/showpost.php?p=4748547&postcount=3128

http://www.internationalskeptics.com/forums/showpost.php?p=4748974&postcount=3150

http://www.internationalskeptics.com/forums/showpost.php?p=4749296&postcount=3154

excactly how the formal language forces notions taken form the finite and forces them on the non-finite.

Jsfisher, you have nothing but illusion about anything the is related to the non-finite.

You know it, and this is exactly the reason of why you do not reply in details to any one of the attached links.
 
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zooterkin said:
I think I see your problem. 'gap' and 'interval' are not synonyms, at least not in this context.
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They are synonyms as long as they are related to the same mathematical case, which deals with what exists (or not) between a collection of all non-finite ordered elements.


EDIT:

As for "no gap" in the case of x < z < y.

If there is really no gap, then x = z = y.

Since we deal with x < z < y, then "no gap" is meaningless in the real sense.
 
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