Deeper than primes - Continuation

Status
Not open for further replies.
jsfisher said:
All this time and effort, and you still have no positive result, just a history of denial. Many people would be embarrassed by such a colossal failure.
Click to expand...
So now you are in the mood of personal attack.

Yet |R| size observation of the real-line enables finer resolution of the numbers along it and new arithmetic (which is not possible from |N| size observation of the real-line) is available for further development.

You have tried but did not show, yet, any problem with my new approach of the number system along the real-line, that is based on the actual mathematical fact that |N|<|R|.

Here is the latest version:

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

The definition of size:

The number of values, which is used in a given parallel-summation, in order to be, to get, to reach, etc. a given value along the real-line.

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

This size can be finite (at least |2|), |N| or |R|, such that finite size < |N| size < |R| size.

This size is identical to what is known as cardinality (except the fact that it is at least |2|).


Here is an example of infinite size |N| (the |N| observation of the real-line):

The series (the parallel-summation of |N| values) value 0.9 + value 0.09 + value 0.009 +... = value 0.999... = value 1


Here is an example of infinite size |R| (the |R| observation of the real-line):

The series (the parallel-summation of |N| values) 0.9 + value 0.09 + value 0.009 +... = value 0.999... < value 1 by value 0.000...1


By using my definition of size and by using |R| size as an observation's view of the real-line (where this view is done beyond any one of the values along the real-line), the value 0.000...1 is the complement of value 0.999... to value 1 (where 0.000...1, 0.999... and 1 are values along the real-line).

The value 0.000...1 acts differently than value 0, as follows:

The ".000..." is used as a |N| size place value keeper that is inaccessible to "...1" that is at |R| size.

--------

|N| or |R| are not values along the real-line.

Moreover, since |R| size is uncountable, it can't be expressed by a string of notations, as used, for example, by the place value method (the best that can be done is, for example, of the form "...1").

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

Some examples are seen in http://www.internationalskeptics.com/forums/showpost.php?p=10305716&postcount=4275.
 
Last edited:
doronshadmi said:
So now you are in the mood of personal attack.
Click to expand...

If you think it was that, you should report it for violating the Membership Agreement. Be aware, though, that the truth is usually an adequate defense:
  • You have spent many years on this.
  • You have not produced a single positive result.
  • You have harped continually on how mathematicians were wrong (this being your history of denial), but never are quite able to show mathematicians to be wrong.
 
Doron, what makes you think that there is no good reason to separate N and R ?

Because there is a mathematical good reason and you just want to ignore it.

What you are doing is simply claiming that water behaves like sand and then blame us for pointing out to you that they are different entities.
 
doronshadmi said:
The value 0.000...1 acts differently than value 0, as follows:

The ".000..." is used as a |N| size place value keeper that is inaccessible to "...1" that is at |R| size.
Click to expand...

*WRONG*

By no definition whatsoever can you designate a final member on an infinite series.

Infinite, from the stem 'fin' meaning 'end', means literally 'no end'.

So by putting an end to it, you have something, but not something infinite.

Period. End of story. End of Doron Shadmi's nonsense.
 
jsfisher said:
If you think it was that, you should report it for violating the Membership Agreement. Be aware, though, that the truth is usually an adequate defense:
  • You have spent many years on this.
  • You have not produced a single positive result.
  • You have harped continually on how mathematicians were wrong (this being your history of denial), but never are quite able to show mathematicians to be wrong.
Click to expand...
The fact is that you have failed to show what is wrong with http://www.internationalskeptics.com/forums/showpost.php?p=10306748&postcount=4282, and your last reply (as quoted in http://www.internationalskeptics.com/forums/showpost.php?p=10305555&postcount=4270 , exposed your misunderstanding of the difference between size (as defined by me) and parallel-summation.

Any way, I wish to sat thank you for your help to develop my framework in terms that are based on the established mathematical fact |N|<|R|.

I chose to use this established mathematical fact after many years of dis-communication because of the inability of traditional mathematics to deal with Unity and its agent known as multiplicity (where |N| and |R| are an example of multiplicity).

Unfortunately it is realized that even if the established mathematical fact |N|<|R| is used, you still choose not to deal with it.

jsfisher, if you have something useful to say about |R| observation of the real-line, then please share it, talking about history will not take you there.
 
Last edited:
doronshadmi said:
jsfisher, if you have something useful to say about |R| observation of the real-line, then please share it.

The fact is that you have failed to show what is wrong with http://www.internationalskeptics.com/forums/showpost.php?p=10306748&postcount=4282 , so you are invited to do so instead of speaking about history.

I am waiting.
Click to expand...

You are doing it all ass-backwards... it is not up to jsfisher to show you are wrong, which you are, but up to you to show you are right.

Reductio ad absurdum is a game only dilettantes play.

But then again, even if we were to concede and say 'Ok, suppose you are right, then what?' you would stutter and fall still. There is no then what, because there is no practical use for this 'observation'.
 
Please look at Ford Circle of rational numbers along the real line, where the vertical red line is some irrational number, that obviously dose not cross the center of any ford circle, or in other words, it is inaccessible to |N| rational numbers that are located at its left or right side.

15540109000_a445e2c424_z.jpg


In other words, Dedekind cut is an insufficient reasoning, if the real-line is observed from |R| size.

On the other hand Dedekind cut is a insufficient reasoning, if the real-line is observed from, at most, |N| size.
 
Last edited:
doronshadmi said:
Please look at Ford Circle of rational numbers along the real line, where the vertical red line is some irrational number, that obviously dose not cross the center of any ford circle, or in other words, it is inaccessible to |N| rational numbers that are located at its left or right side.

[qimg]http://farm4.staticflickr.com/3953/15540109000_a445e2c424_z.jpg[/qimg]

In other words, Dedekind cut is an insufficient reasoning, if real-line is observed from |R| size.
Click to expand...

You seem to be saying that irrational numbers are not rational. Is this a surprise?
 
zooterkin said:
You seem to be saying that irrational numbers are not rational. Is this a surprise?
Click to expand...
Please read http://www.internationalskeptics.com/forums/showpost.php?p=10306748&postcount=4282.

Also please be aware of the fact that this irrational number does not have immediate predecessor or successor if observed from |R| size, so Dedekind cut works only by using |N| observation of the real-line, and by using dis-continuity from Q members into some irrational member between them.

This dis-continuity misses values of the form 0.000...1 on the real-line.

The main idea here is that mathematical results are actually inseparable of the mathematician's observation ability, or in other words, formal mechanic approach that completely excludes the mathematician as a factor of mathematical development, is, in my opinion, a dead end street.
 
Last edited:
doronshadmi said:
This dis-continuity misses values of the form 0.000...1 on the real-line.
Click to expand...

As to the value of the form 0.000...1 on the real-line; sure, such a number can exist if the ellipsis means "an arbitrary finite sequence of numbers".

However there never *can* exist a complimentary number on the real-line for 1 - 0.999... where the ellipsis denotes an infinite repetition.

Were you to claim otherwise, you would be *WRONG* simply because there is no final digit.

But do not let that deter you from proving otherwise. Mind you, proving, not claiming, or using reductio ad absurdum.

Trying to prove this visually will not be possible as you can never show infinity, only a location along the line into infinity.
 
Doron, why not try the following:

1 - Pick a large amount of R numbers.
2 - Try to pick a larger amount of N numbers. If you can not go to 6
3 - Try to pick a larger amount of R numbers. If you can not go to 5
4 - Go to 2.
5 - N is larger. End.
6 - R is larger. End.

There you go.
 
Last edited:
According to Real-Analysis a given line segment (some finite length > 0) has |R| points (where each point has exactly 0 length) along it.

Let's analyze the following diagram:

4430320710_686e9e991b.jpg


According to this diagram the series 2*(a+b+c+d+...) is the result of the projections of the endpoints of |N| folded line segments with invariant finite length X>0 upon itself, where each folded line segment is some degree of Koch Fractal.

There are |N| folded line segments because the cardinality of the sequence <41,42,43,...> (which is the number of sub-segments at each degree of Koch Fractal) is |N|.

As mentioned above, each one of the projected |N| degrees of Koch Fractal has an invariant finite length X>0 according to the general formula (X/K)*K (where K is the number of sub-segments along X for each degree, (in the case of Koch Fractal the formula is (X/4J)*4J, where j=1 to |N|)).

In other words, 2*(a+b+c+d+...) (where the convergent sequence <a,b,c,d,...> has only |N| values) is < X if the invariant length X is observed from |R| points along it, because |N|<|R|.

So, the concept of limit holds (2*(a+b+c+d+...)=X) only if X is observed from |N| points along it.
 
Last edited:
doronshadmi said:
So, the concept of limit holds (2*(a+b+c+d+...)=X) only if X is observed from |N| points along it.
Click to expand...

You are not supposed to be able to read my posts; you claim you are ignoring me.

There is a nice body of evidence building up that you are a less than truthful person.

But that aside...

You are *WRONG*, the concept of limit holds in any collection and any realm as it is defined as: "The limit L means all values are nearing, but not reaching the L".

If graphed out on an X and Y axis, let's say Y = lim LX, in R this produces a curve that goes on infinitely along the value L but never reaches L.

If you were to do a limit in N, let's say Y = lim LX, the curve would end at L-1 or L+1, because that is the limit.

How hard is this?
 
jsfisher said:
Never.
Click to expand...
In that case the cardinality of the sequence <41,42,43,...> is < |N|, which is not true.

Actually your Never is equivalent to the claim that the cardinality of the sequence <1,2,3,...> is not |N|.
 
Last edited:
doronshadmi said:
In that case the cardinality of the sequence <41,42,43,...> is < |N|, which is not true.

Actually your Never is equivalent to the claim that the cardinality of the sequence <1,2,3,...> is not |N|.
Click to expand...

False and false. That there is no element in an infinite sequence with infinitely many segments is independent of the sequence's cardinality.
 
Status
Not open for further replies.

Back
Top Bottom