Cont: Deeper than primes - Continuation 2

[doronshadmi]

Continued from part 2, here.

Posted By: zooterkin

False and false. That there is no element in an infinite sequence with infinitely many segments is independent of the sequence's cardinality.

|N| folded line segments does not mean that one of the folded line segments has |N| sub-segments.

For example, in the case of Koch Fractal the formula is (X/4J)*4J, where j=1 to |N|, such that if j = |N|, this is exactly the case that enables to extend (to go beyond) all the cases of finite sub-segments, in order to get X in the case of 2*(a+b+c+d+...) (this is exactly |N| observation).

This is not the case if X is observed from |R|, exactly because |N| extension < lR|, and we need |R| extension in order to get X.

Please look again very carefully at http://www.internationalskeptics.com/forums/showpost.php?p=10316119&postcount=4298.

 

[jsfisher]

|N| folded line segments does not mean that one of the folded line segments has |N| sub-segments.

Then perhaps, just this once, you should consider defining your terms.

 

[doronshadmi]

Then perhaps, just this once, you should consider defining your terms.

If you read all of

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|).

you are easily realize that |N| is not one of numbers of sub-segments in any degree of Koch Fractal (or in other words there are |N| values in sequence <4¹,4²,4³,...> but no one of them is 4^|N|).

jsfisher, mathematical expressions like n = 1 to ∞ are used, isn't it?

I simply refine ∞ by distinguish between |N| and |R|.

 

[jsfisher]

If you read all of

you are easily realize....

You overrate your power of expression with clarity.

Be that as it may...

You have a (countably infinite) sequence of values that has a limit of a value. The cardinality of the set of reals is irrelevant to this.

On the other hand, if you want to take a line segment view of the process, you have a (countably infinite) sequence of line segments that collectively span a line segment. All of the line segments involved have the same "number" of points, but, again, the cardinality of the continuum is not relevant.

Instead, rather than staying consistent, you switch midway to conflate the two and view the resulting confusion as revelation.

 

[doronshadmi]

... the cardinality of the continuum is not relevant.

It is relevant.

You arbitrarily force |N| as the only possible option to obverse the real-line.

you switch midway

I do not switch midway, on the contrary, I show two different cases that depend of two different observations, as follows:

1) By using |N| observation of the real-line 2*(a+b+c+d+...)=X.

2) By using |R| observation of the real-line 2*(a+b+c+d+...)<X.

 

[jsfisher]

It is relevant.

You arbitrarily force |N| as the only possible option to obverse the real-line.

I did? I don't recall that.

Be that as it may, what does that have to do with a (countably) infinite sequence having a limit?

 

[doronshadmi]

I did? I don't recall that.

Be that as it may, what does that have to do with a (countably) infinite sequence having a limit?

Series 2*(a+b+c+d+...) is based on the convergent sequence <a,b,c,d,...> of |N| values.

2*(a+b+c+d+...)=X by define X as the limit of 2*(a+b+c+d+...), as follows:

|N|+1 = |N| (where this +1 is exactly the way that is used to define X as the limit of 2*(a+b+c+d+...)).

By using the fact that |N|+1 = |N| you can conclude that 2*(a+b+c+d+...)=X.

But this little trick does not work from |R| observation of the real-line simply because |N|+1 = |N| < |R|.

 

[jsfisher]

Series 2*(a+b+c+d+...) is based on the convergent sequence <a,b,c,d,...> of |N| values.

Please stop trying to use |N| as an ordinary number. The sequence has the same cardinality as the set of natural numbers.

...continued attempts to introduce the continuum where it doesn't belong snipped...

 

[doronshadmi]

Please stop trying to use |N| as an ordinary number. The sequence has the same cardinality as the set of natural numbers.

The sequence has |N| values, which is the same cardinality as the set of natural numbers that also have |N| values (natural numbers, in this case).

You arbitrarily continue to ignore |R| as the cardinality of the real-line, which is inaccessible to your |N|+1 trick.

 

[doronshadmi]

Ok, now let's go beyond the real-line in order to deal with the tower of power line.

It goes like this:

Between any two natural numbers along the tower of power line, there are |N| rational numbers.

Between any two rational numbers along the tower of power line, there are |R| irrational numbers.

Between any two irrational numbers along the tower of power line, there are |P(R)|_numbers.

Between any two |P(R)|_numbers along the tower of power line, there are |P(P(R))|_numbers.

...

etc. ... ad infinitum, where the inaccessible limit of the tower of power line is simply the non-composed 1-dimesional space.

 

[jsfisher]

You arbitrarily continue to ignore |R| as the cardinality of the real-line

How, exactly, is the cardinality of the real numbers in any way relevant to the valuation of a convergent series? So far, you have not shown any connection whatsoever. Nor have you show in any way that it would in any way impact the valuation of a convergent series.

 

[doronshadmi]

So far, you have not shown any connection whatsoever.

So far you are using at most |N| observation of the real-line.

 

[jsfisher]

So far you are using at most |N| observation of the real-line.

Did I? Where?

Meanwhile, back to where we were not discussing the real line at all, but the valuation of a convergent series, how is the cardinality of the real numbers relevant?

 

[doronshadmi]

Did I? Where?

Right now, here.

 

[jsfisher]

Right now, here.

Nice dodge. Now, back to the substance:

Meanwhile, back to where we were not discussing the real line at all, but the valuation of a convergent series, how is the cardinality of the real numbers relevant?

 

[doronshadmi]

Nice dodge. Now, back to the substance:

You are free to go back, but in that case all you do is not a nice dodge from the real-line.

 

[jsfisher]

You are free to go back, but in that case all you do is not a nice dodge from the real-line.

A double-dodge. now.

Meanwhile, back to where we were not discussing the real line at all, but the valuation of a convergent series, how is the cardinality of the real numbers relevant?

 

[doronshadmi]

A double-dodge. now.

Meanwhile, back to where we were not discussing the real line at all, but the valuation of a convergent series, how is the cardinality of the real numbers relevant?

http://www.internationalskeptics.com/forums/showpost.php?p=10319593&postcount=4318

http://www.internationalskeptics.com/forums/showpost.php?p=10318701&postcount=4312

 

[jsfisher]

http://www.internationalskeptics.com/forums/showpost.php?p=10319593&postcount=4318

http://www.internationalskeptics.com/forums/showpost.php?p=10318701&postcount=4312

If those posts addressed my question, I won't need to repeatedly ask it. The question was:

Meanwhile, back to where we were not discussing the real line at all, but the valuation of a convergent series, how is the cardinality of the real numbers relevant?

And for the sake of context and example, the series represented by 0.999... is the reference.

 

[doronshadmi]

And for the sake of context and example, the series represented by 0.999... is the reference.

http://www.internationalskeptics.com/forums/showpost.php?p=10306748&postcount=4282 and http://www.internationalskeptics.com/forums/showpost.php?p=10316119&postcount=4298 deal with the same reasoning, which is |N| and |R| observations of the real-line.

This time please do not ignore the details of http://www.internationalskeptics.com/forums/showpost.php?p=10318337&postcount=7 and http://www.internationalskeptics.com/forums/showpost.php?p=10318659&postcount=9.

In other words, there is no

back to where we were not discussing the real line at all.

It is up to you to decide if you wish to continue the discussion on |N| and |R| observations of the real-line.

(http://www.internationalskeptics.com/forums/showpost.php?p=10318701&postcount=4312 goes beyond the real-line).