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Deeper than primes - Continuation

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doronshadmi said:
Did you try to do this thought experiment?
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Doron, your thought experiment is a silly, poorly expressed farce. I can "get" from any point, a, on the real number line to any other point, b, on the real number line in one "step". The size of that step is |a - b|.
 
jsfisher said:
Doron, your thought experiment is a silly, poorly expressed farce. I can "get" from any point, a, on the real number line to any other point, b, on the real number line in one "step". The size of that step is |a - b|.
Click to expand...

This is only the first step of my suggested thought experiment, please take all of its steps.
 
doronshadmi said:
In this case finite or |N| steps can't reach you, and form this point of view 0.999... (which is an |N| size value) can't reach you (and this is the meaning of ...1 in the value 0.000...1, where 0.000...1 is the result of looking at |N| size by using |R| glasses).

If you are looking at the real line by using |R| glasses, then some stronger method then the place value is need in order to reach you by |R| steps, but it does not mean that the place value is not a legitimate value of its own, on the real line (exactly as you are still looking at finite values as legitimate values of their own, on the real line).
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Again, you are ignoring what limit means in Mathematics.

There is no ...1 because there is no final member. The thought experiment is invalid because it is based on a *WRONG* premisse.
 
doronshadmi said:
This is only the first step of my suggested thought experiment, please take all of its steps.
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Which part of "silly, poorly expressed farce" was unclear?

I can always get from one point to another in one step. Your bare assertion that something you call "|N| glasses" or "|R| glasses", whatever those are supposed to be--you failed to define your terms, does not change that fundamental, only one step necessary, fact.
 
jsfisher said:
What has the cardinality of the rational numbers to do with a single point along the real number line?
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jsfisher said:
... applies to single points along the real number line ...
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What you wrote is not about a single point, and so is the case of my experiment.

It is not about a single point, but about the number of steps that are needed in order to reach to a given point.

You are using only the finite glasses of my experiment, so please try the other glasses.
 
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doronshadmi said:
What you wrote is not about a single point, and so is the case of my experiment.
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No, what I wrote was very much about single points. Any single point at all.

It is not about a single point, but about the number of steps that are needed in order to reach to a given point.
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Any point can be "reached" in one step. If you have some non-standard meaning for "step", then you need to make that clear.

You are using only the finite glasses of my experiment, so please try the other glasses.
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...and you need to make clear what you mean by "glasses".
 
jsfisher said:
If you have some non-standard meaning for "step", then you need to make that clear.
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The sum 0.9+0.09+0.009+0.0009+… of the sequence of values <0.9, 0.09, 0.009, 0.0009 …> is the result of at most |N| values.

To each value I call step, and there are finite, |N| or |R| steps that are calculated in parallel.

jsfisher said:
...and you need to make clear what you mean by "glasses".
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This is the tool that enables you to know the number of the needed parallel steps in a given series.

Since the steps are done in parallel, they define a single result for a given series.

I am defiantly not talking about step-by-step.
 
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doronshadmi said:
The sum 0.9+0.09+0.009+0.0009+… of the sequence of values <0.9, 0.09, 0.009, 0.0009 …> is the result of at most |N| values.

To each value I call step, and there are finite, |N| or |R| steps that are calculated in parallel.
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No, 0.999... has no steps. It is a value, not the end of an infinite sequence of partial sums (which doesn't have an end).
 
jsfisher said:
No, 0.999... has no steps. It is a value, not the end of an infinite sequence of partial sums (which doesn't have an end).
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You are still think in terms of step-by-step.

Exactly as {1,2,3,4,5,...} is not taken step-by-step, so is the case about 0.999...
 
jsfisher said:
Let me know when you stop contradicting yourself.
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Let me know when you are able to think in terms of a single parallel steps, which identical to a single value along the real line.

0.999... is a single value along the real line in terms of |N| parallel steps if |R| glasses are used, and 0.000...1 is a single value along the real line in terms of |R| parallel steps if |R| if glasses are used.
 
jsfisher said:
No, 0.999... has no steps. It is a value, not the end of an infinite sequence of partial sums (which doesn't have an end).
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0.999... is the parallel sum (also called series) of the convergent |N| values <0.9, 0.09, 0.009, ...>. I define step as identical to a given value of that parallel sum. Since the sum is done in parallel, no process of any kind is involved here (the illusion of "process" is the result of a step-by-step observation, which is avoided by using parallel observation).

In order to actually do my suggested thought experiment, concepts like step, series or sequence must be taken by parallel observation, otherwise, one misses the thought experiment as given in http://www.internationalskeptics.com/forums/showpost.php?p=10301106&postcount=4215.
 
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jsfisher said:
Doron, your thought experiment is a silly, poorly expressed farce. I can "get" from any point, a, on the real number line to any other point, b, on the real number line in one "step". The size of that step is |a - b|.
Click to expand...
You are using here the term "size" in order to define a given length, but we are not talking here about length, but about a given value along the real-line.

After all, you are the one who wrote in http://www.internationalskeptics.com/forums/showpost.php?p=10297296&postcount=4196:
jsfisher said:
[0, 1/2] and 1/2 are completely different things.
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A given value can be the parallel sum of finitely or infinitely many values, where the term size, as I use it here, is the number of values (by omitting value 0) that are used in a given parallel sum, in order to be, to get, to reach, etc. a given value along the real-line.

Here is an example of a finite size:

value 1 = finite number of parallel sum (called by me the finite glasses) of value 1 + value 0 = value (-1) + value 1.9 + value 0.1 = ... etc. ...


Here is an example of infinite size |N| (the |N| glasses):

The series (the |N| parallel sum) value 0.9 + value 0.09 + value 0.009 +... = value 0.999... = value 1


Here is an example of infinite size |R| (the |R| glasses):

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

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