Deeper than primes

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doronshadmi said:
And indeed if there is no real number between [0,0] and (0,X] then 0 must be X and "<" relation between [0,0] and (0,X] is nothing but gibberish.
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Well I wouldn't call it 'gibberish' but, yea. Essentially, if there is no difference between two values or intervals then that means they are the same :boggled:
 
AkuManiMani said:
Well I wouldn't call it 'gibberish' but, yea. Essentially, if there is no difference between two values or intervals then that means they are the same :boggled:
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In that case we cannot use "<" relation between [0,0] and (0,X], and the whole notion of predecessor (intermadiate or not) does not hold here.
 
doronshadmi said:
The answer was clearly given also in http://www.internationalskeptics.com/forums/showpost.php?p=4844439&postcount=3950 .

There is no meaning to "<" relation without the numbers, so the question "what number exists between interval A and interval B is meaningless because all we have is only about the relations between numbers, if "<" relation is used.

At the moment that this simple and rigorous notion is understood, we immediately understand that no real number is an immediate predecessor (or successor) of another real number, because -x<-d<0<d<x is a permanent state that is not changed also by infinitely many real numbers.

The illusionary use of intervals as objects that are not related to their contents, is a perfect example of playing with notations without notions.
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[0,0] is < (0,1] if you disagree then show any element of (0,1] that is greater then or equal to 0. If you think there is a number or interval between [0,0] and (0,1] then show it. Otherwise [0,0] meets the definition of predecessor to (0,1] in that it is less then with no other numbers or interval in between. You are claiming it is not the predecessor so it is up to you to prove it. Simply claiming “<“ does not apply just demonstrates you are ignoring both the ordered requirement of intervals as well as simply the elements contained in the given intervals.
 
AkuManiMani said:
That's just the thing. Even assuming that 0 is the immediate predecessor of (0, 1], it means that there is no real difference between them.
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Well you have to be clear about what you are referring to as ‘difference between them’. As 0 is included in the interval [0,0] but not in the interval (0,1] that is that primary ‘difference between them’.
 
doronshadmi said:
Let us play the game of the intervals like this:

X>0

[0,0]<[X,X]

Now, it does not matter what X is, [0,0] is not an immediate predecessor of [X,X] because no real number is an immediate predecessor of another real number.

Things are not changed also in the case of [0,0]<(0,X]. Also in this case [0,0] is not an immediate predecessor of any X of (0,X] interval.

And indeed if there is no real number between [0,0] and (0,X] then 0 must be X and "<" relation between [0,0] and (0,X] is nothing but gibberish.
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Yes ‘things’ are changed “in the case of [0,0]<(0,X]” as [X,X] is not (0,X] when “X>0” as you required. [X,X] has only one element ‘X’, (0,X] has an infinite number of elements down to but not including 0. Your ignorance and gibberish about math does not in any way translate to any ignorance or gibberish in math.
 
The Man said:
Well you have to be clear about what you are referring to as ‘difference between them’. As 0 is included in the interval [0,0] but not in the interval (0,1] that is that primary ‘difference between them’.
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By difference I mean the numerical difference you get via subtraction.
 
doronshadmi said:
I'll ask Moshe to make a registration.
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So, has Moshe signed up already?

I see the regular discussion has gone back to discussing intervals. Which seems quite senseless: y'all are discussing with someone (Doron) who by his own admission is incompetent in the field and only parrots formulae provided by others.
 
AkuManiMani said:
By difference I mean the numerical difference you get via subtraction.
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How exactly would one subtract intervals? If you mean subtracting the largest value in the preceding [0,0] interval from the least value of the succeeding interval (0,1]. It is not possible as (0,1] does not have a least value that is included in that interval (0 is the least boundary but is not included in the interval). Subtracting any value that is included in the interval (0,1] will always result is some difference and thus some other number between the one selected and the largest value of the preceding interval [0,0]. It is simply an aspect of the continuous nature of the reals that any immediate predecessor or successors must involve at least one interval. It can be confusing for some since it involves being very clear and specific about what one is talking about.
 
The Man said:
Then agian show the real number between 0 and the interval (0,1].
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Again, all there is in this case is "<" between real numbers.

What you call interval is nothing but an illusion that is based on manipulations with notations without any notion.

So the answer to your question is d, such that 0<d<x and 0 is not an immediate predecessor of any real number x of the interval (0,1].

You still did not get it, so here it is again:

Let us play the game of the intervals like this:

X>0

[0,0]<[X,X]

Now, it does not matter what X is, [0,0] is not an immediate predecessor of X because no real number is an immediate predecessor of another real number.

Things do not change also in the case of [0,0]<(0,X]. Also in this case [0,0] is not an immediate predecessor of any X.

You may claim that in the case of [0,0]<[X,X] d of the expression 0<d<X is not in [0,0] interval and not in [X,X] interval, and as a result [0,0] is not an immediate predecessor of [X,X].

Then you may claim that in the case of [0,0]<(0,X] d of the expression 0<d<X is an element of the interval (0,X] and therefore [0,0] is an immediate predecessor of (0,X] interval.

But this claim is nothing but a manipulation with notations without notions, because "<" relation has a meaning only between the elements of the intervals, where the intervals have nothing to do with "<" relation.

At the moment that you get the simple notion that "<" has a meaning only between the elements of the intervals, you immediately understand that 0<d<X has exactly the same meaning in [0,0]<[X,X] and in [0,0]<(0,X].
 
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doronshadmi said:
Your English skills do not help you to understand that L is about any civilization, including us.
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Clarity is not your main virtue, isn't it? First you don't mention which civilization - then you say your claim applies only to mankind, now you say L is about any civilization, including ours.

Now, have I got news for you: the time it took terrestrial civilization to produce signals that leaked into outer space has very little bearing on the average value of L, as there are probably many other civilizations out there.

And I have more news for you: the time it took terrestrial civilization to come up with signals that went into outer space is pretty well already researched. We know the age of the earth, we know when life started on earth, we know when the first hominids appeared, when signs of human civilization appeared, etc., all with pretty good accuracy. That we know that is due to geology, paleontology, archeology, history, etc., but has not much to do with mathematics - let alone with your crackpottery.

A bit of simple physics calculation also learns that even in the heyday of aerial broadcasting, it was just a bit of noise when observed from Alpha Centauri, and on Betelgeuze (as we all know, the place where the President of the Universe, Zaphod Beeblebrox comes from) not even discernible from the cosmic background radiation.

doronshadmi said:
This is by the way one of the reasons that you don't get OM.

You, as an observer, exclude yourself from the research, and this is your fundamental mistake all along this thread.
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Mathematics is about universal truths. The researcher has no influence whatsoever on the value of the results. Unless, of course, the "researcher" is a crackpot. When you claim the researcher influences the results, you've disqualified any other statement deriving from it ab initio.

doronshadmi said:
The claim that our current and future technologies are completely silent is simply nonsense.
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That sentence is a complete non-sequitur.
 
The Man said:
How exactly would one subtract intervals? If you mean subtracting the largest value in the preceding [0,0] interval from the least value of the succeeding interval (0,1]. It is not possible as (0,1] does not have a least value that is included in that interval (0 is the least boundary but is not included in the interval).
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That's pretty much what I had in mind by difference. So lets say you have two intervals: [1, 5] and [7, 10]. By difference I mean distance between them which would be: (7) - (5) = 2. So the difference between the two intervals is two. But you have the really odd issue of adjacent intervals, like the one brought up by doron.

So what if you had [1, 5] and (6, 10]? What would be the difference then? Maybe 0.99999...., with an infinite number of nines or something? :confused:

The Man said:
Subtracting any value that is included in the interval (0,1] will always result is some difference and thus some other number between the one selected and the largest value of the preceding interval [0,0]. It is simply an aspect of the continuous nature of the reals that any immediate predecessor or successors must involve at least one interval. It can be confusing for some since it involves being very clear and specific about what one is talking about.
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Seems the more specific I try to get with this the more my eyes cross :boggled:
 
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