Deeper than primes

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doronshadmi said:
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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You still do not ‘get it’ simply because of your ignorance or simply lying to yourself

You have already stated..

doronshadmi said:
The Man said:
[0,0] is < (0,1] if you disagree …
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I agree. <snip>
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So [0,0] is < (0,1], the only other requirement for an immediate predecessor is that no other real numbers or intervals are between [0,0] and (0,1]. So again please show a real number or interval between [0,0] and (0,1].
 
The Man said:
So [0,0] is < (0,1], the only other requirement for an immediate predecessor is that no other real numbers or intervals are between [0,0] and (0,1]. So again please show a real number or interval between [0,0] and (0,1].
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Hmmm... There's definitely no rational number between them.

Maybe the answer is ((1) - (0.999...)) = ?
 
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AkuManiMani said:
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.
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It is not that odd or different from what you have just said in discrete math (like with integers). However, in a continuous frame work it can get confusing unless you are very specific and consistent in the definitions and relationships.

AkuManiMani said:
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:
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.99999.. Is still just 1 unless one wants to claim that 3 times 1/3 does not equal 1. In this last example we can assert the interval (5,6] as between the two you referenced succeeding one and proceeding the other. This is the primary reason immediate successors or predecessors are not defined using differences even in discrete math.

AkuManiMani said:
Seems the more specific I try to get with this the more my eyes cross :boggled:
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That is completely understandable, but at least you note your eyes crossing. While Doron ascribes his poor vision as an aspect of the math itself.
 
The Man said:
It is not that odd or different from what you have just said in discrete math (like with integers). However, in a continuous frame work it can get confusing unless you are very specific and consistent in the definitions and relationships.
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Yea, I've heard that there have been mathematicians who literally went nuts over stuff like this. Some people take their numbers too seriously :D



The Man said:
.99999.. Is still just 1 unless one wants to claim that 3 times 1/3 does not equal 1. In this last example we can assert the interval (5,6] as between the two you referenced succeeding one and proceeding the other. This is the primary reason immediate successors or predecessors are not defined using differences even in discrete math.
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Uhm...ionno.

Wouldn't (0.999...) only be considered the same as (1) if you rounded it? I mean, sure, they are virtually allllllmost the same but I think its just that our notation system doesn't have a means of writing out the answer to stuff like ((1) - (0.999...)). This continuum stuff is really freaky *_*
 
AkuManiMani said:
Yea, I've heard that there have been mathematicians who literally went nuts over stuff like this. Some people take their numbers too seriously :D





Uhm...ionno.

Wouldn't (0.999...) only be considered the same as (1) if you rounded it? I mean, sure, they are virtually allllllmost the same but I think its just that our notation system doesn't have a means of writing out the answer to stuff like ((1) - (0.999...)). This continuum stuff is really freaky *_*
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1/3 is 0.33333..., three times 1/3 is 0.9999..., it is in fact exactly 1 without rounding unless you have to round 3/3 to get to 1. The only difference is that 0.9999... is an infinite decimal notation of one, while 1.00 is a finite decimal notation.
 
The Man said:
1/3 is 0.33333..., three times 1/3 is 0.9999..., it is in fact exactly 1 without rounding unless you have to round 3/3 to get to 1. The only difference is that 0.9999... is an infinite decimal notation of one, while 1.00 is a finite decimal notation.
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Okey, good. I got some other questions :)

Once, I asked my HS geometry teacher "If there are two rods that are infinitely long but one is 2 ft wide and the other only 1ft wide, is one bigger than the other?" He just kinda shook his head and said that was a question for philosophers >_<

Got a more satisfactory answer for me?

And my other questions are: How many points are there in a line segment 3 units long? And does a line segment with more than 3 units have more points?
 
The Man said:
the only other requirement for an immediate predecessor is that no other real numbers
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No, "<" has a meaning only between real numbers, in this case.

Since this is the simple fact in this case, and since "[0,0]" and "0" are two notations of the same element, which is a real number, then 0 is not an immediate predecessor of any other real number, and it does not matter if this real number is gathered by a name called "interval", because "<" relation has a meaning only if it used between real numbers, in this case.

Any other thing that is not this simple straightforward fact, is simply an illusionary game with notations and extra names like "intervals", which leads to complicated and trivial game with names and notations, without any notion at the basis of it.

Too many minds were twisted down along the past 300 years by this complicated and trivial game with names and notations that are nothing but sterile and mechanical manipulations with symbols.
 
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doronshadmi said:
No, "<" has a meaning only between real numbers, in this case.
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Such linear thinking. Doron, why do you restrict things so arbitarily? Can't the symbol "<" be used as an ordering relation? Can't we adopt -- with full disclosure, of course -- a concise definition for that ordering relation different from the simple less-than relation? Doron, we are aghast that you, of all people, would be so stuck in you in-the-box thinking.

We are disappointed.
 
jsfisher said:
Such linear thinking. Doron, why do you restrict things so arbitarily? Can't the symbol "<" be used as an ordering relation? Can't we adopt -- with full disclosure, of course -- a concise definition for that ordering relation different from the simple less-than relation? Doron, we are aghast that you, of all people, would be so stuck in you in-the-box thinking.

We are disappointed.
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You can do it in this case only if you ignore the numbers that are included in or exist between the intervals, but then you have exactly nothing to order.

So you can't adopt -- even with full disclosure -- a concise definition for that ordering relation different from the simple less-than relation, in this case.

Your inability to get this fact is closely related to your inability to get the ford-circle part of http://www.internationalskeptics.com/forums/showpost.php?p=4840972&postcount=3923 post.

Who is exactly this We, are you more than a one person?

In general jsfisher, your school of thought adopts notions instead of first understand them.
 
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doronshadmi said:
Who is exactly this We, are you more than a one person?
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If you're upset about jsfisher's use of the plural: I agree wholeheartedly with his post. That makes it plural. I guess there are a lot more posters in this thread who agree with it.
 
ddt said:
If you're upset about jsfisher's use of the plural: I agree wholeheartedly with his post. That makes it plural. I guess there are a lot more posters in this thread who agree with it.
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Yes, I know you are many machines that make the same sound, and you are very proud of it.
 
doronshadmi said:
Yes he signed up, and he waits for account verification (it takes 24 to 48 hours).
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That would mean he's using one of the following user names: garybooker, Maklu G, McL, Richard S, or tuoni. Come on, Doron. You can tell us. Which did he use?
 
doronshadmi said:
Yes he signed up, and he waits for account verification (it takes 24 to 48 hours).
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Good. I'll save my question so that I can get his response as well.

Also I'd like to see how he would present Organic Numbers to Anthony Fremont or any other grade schooler.
 
One of the newest members of the Forums is MosheKlein. Welcome, MosheKlein.
 
Now I am in ..

Thank you jsfisher !

I think that the main new idea for us here is to begin with is to observe a number n as a superposition of its partitions Pr(n). Recently I have develop an algorithm to calculate the number of distinctions of a number Or(n) . The sequences started with 1,2,3,9,24,76,236,785, …( we calculate it until or(12))

I made some correction following your remarks – thank you !

Do you have some more remarks?

Moshe Klein

Sorry for my English..:(
 
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Don't you mean the results of your function are 1,2,3,9,24,76,236,785?

Most of the mathematical function equations are above me, but why doesn't the number 5 produce six results? According to doronshamdi, I can "write" the number five like so:
1+1+1+1+1 or 2+1+1+1 or 2+2+1 or 3+1+1 or 3+2 or 4+1

This is based on the "way" he provides the permiutations of 4: 1+1+1+1, 2+2, 1+3, 2+1+1.
 
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