Deeper than primes - Continuation

[realpaladin]

<snip>
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

--------

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

Again, this uses sleight of hand to add a convenient 'final digit' on an *in*finite series.

Since that, by definition is *WRONG*, Doron Shadmi is *WRONG*

There is no need to heed any further information divulged by him as he demonstrably has got the basics *WRONG*

As long as Doron needs linguistical mangling for his "work", no grade school mathematician need fear him...

 

[doronshadmi]

The most straightforward approach might involve showing how |1 - 0.999...| acts differently than 0.

By understanding the concept of "size" as used in http://www.internationalskeptics.com/forums/showpost.php?p=10302577&postcount=4240 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.

Again, 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, where 0.000...1, 0.999... and 1 are values along the real-line.

 

[jsfisher]

0.000...1 acts differently than 0...

Assertions don't make something true.

 

[realpaladin]

By understanding the concept of "size" as used in http://www.internationalskeptics.com/forums/showpost.php?p=10302577&postcount=4240 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, which 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 kipper that is inaccessible to "...1" that is at |R| size.

Again

Place value 'keeper'... that is algorithmic talk.

Show me an algorithm that ever arrives at the ...1 and I´ll smoke you a kipper for breakfast.

If you can not show an algorithm (let alone a mathematical proof) then this is just another wind egg.

 

[doronshadmi]

Assertions don't make something true.

Using the fact that |N|<|R| and by using |R| size as an observation's view of the real-line (where |N| or |R| are not values along the real-line), is not an assertion, but it is a rigorous observation of the real-line as taken from |R| size, where size (as used here) is:

The number of values that are used in a given parallel sum, in order to be, to get, to reach, etc. a given value along the real-line.

(This definition is a correction of the one that was given in http://www.internationalskeptics.com/forums/showpost.php?p=10302577&postcount=4240).

So size here has nothing to do with length, as you used it in the quote in http://www.internationalskeptics.com/forums/showpost.php?p=10302577&postcount=4240.

 

[doronshadmi]

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|.

Let's use what you have wrote here, not in terms of length, but in terms of values along the real-line.

The definition of size, as used by me here is:

The number of values that are used in a given parallel sum, in order to be, to get, to reach, etc. a given value along the real-line.

So, by using a finite number of values that are used in a given parallel sum, in order to be, to get, to reach, etc. a given value along the real-line, you "get" value b.

Here are examples of infinite sizes:


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

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| observation of the real-line):

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

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").

 

[realpaladin]

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

You are not supposed to be reading my posts Doron...

This means you avoid confronting anything that you can not kibitz about.

Admitting defeat can also be done by ignoring someone

 

[realpaladin]

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.

Let me spell it out:

Which. Steps. Lead. To. The. End. Of. Infinity. So. It. Finally. Reaches. ...1 ?

If you do not have steps, be they formulaic or be they algorithmic, you only have assertions.

Assertions which are *WRONG* because, as I explained to you years ago, infinity is 'without end' or 'not finite' or 'for each position you have, I can tack another one to it' or 'there is no final digit'.

 

[jsfisher]

Let's use what you have wrote here, not in terms of length, but in terms of values along the real-line.

Then you won't be using what I wrote. You will be using something completely different. Something you, as you are wont to do, made up, fabricated, pulled out of the air.

 

[doronshadmi]

Then you won't be using what I wrote.

Are you claiming that a, b or |a - b| are not values along the real-line?

If not, then please define what are a, b or |a - b|?

Thank you.

 

[jsfisher]

Are you claiming that a, b or |a - b| are not values along the real-line?

If not, then please define what are a, b or |a - b|?

Thank you.

Just as I wrote, a and b were distinct points along the real number line, and |a - b| was the distance between them.

 

[doronshadmi]

Just as I wrote, a and b were distinct points along the real number line, and |a - b| was the distance between them.

EDIT:

Please pay attention that |a - b| can't be defined as a given point along the real-line, but it can be defined as a value along the real-line, and my purpose was the define a, b, or |a - b| by using the same concept (value, in this case).

After all you are the one that (for purpose of generalization) used the term value, in order to define objects along the real-line, for example:

1/2 does not have length. It is a value.

(http://www.internationalskeptics.com/forums/showpost.php?p=10297296&postcount=4196)

 

[jsfisher]

EDIT:

Please pay attention that |a - b| can't be defined as a given point along the real-line, but it can be defined as a value along the real-line

Defined? That would be twisted.

...and my purpose was the define a, b, or |a - b| by using the same concept (value, in this case).

Then, just as I said before, you are not talking about anything I posted, but instead about stuff you just made up, fabricated, pulled out of thin air.

After all you are the one that (for purpose of generalization) used the term value, in order to define objects along the real-line

I did not.

...for example:

(http://www.internationalskeptics.com/forums/showpost.php?p=10297296&postcount=4196)

Precisely!

 

[doronshadmi]

Precisely!

Precisely? ,let's see:

As you put it, a or b are distinct points along the real line, where the length of a point is defined by value 0 (which is some value along the real-line).

It is clear that the length of |a - b| is defined by some value > 0 (which is some value along the real-line), in case that a is not identical to b.

a+|a - b| is the finite parallel-summation, in case that a<b.

a+(-|a - b|) is the finite parallel-summation, in case that b<a.

Both finite parallel-summations = b

So, your argument is some case of finite parallel-summation that does not address my argument, which is at least |R| parallel-summation.

The definition of size, in this case is:

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

Finite size < |N| size < |R| size is defiantly defined by actual mathematics.

 

[jsfisher]

Precisely? ,let's see:

As you put it, a or b are distinct points along the real line, where the length of a point is defined by value 0 (which is some value along the real-line).

It is clear that the length of |a - b| is defined by some value > 0 (which is some value along the real-line), in case that a is not identical to b.

Defined? No.

a+|a - b| is the finite parallel-summation, in case that a<b.

a+(-|a - b|) is the finite parallel-summation, in case that b<a.

Both finite parallel-summations = b

"Parallel-summation" is a term of your invention.

So, your argument is some case of finite parallel-summation, which does not address my argument, which is at least |R| parallel-summation.

Meaningless.

The definition of size, in this case is:

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

No, it's not. That's just nonsense.

Finite size < |N| size < |R| size is defiantly defined by actual mathematics.

Defined? Definitely not, and your use of language continues to be extremely awkward.

 

[doronshadmi]

"Parallel-summation" is a term of your invention.

jsfisher, it is not so hard to understand that, for example, 1+1+1+1+1+1+1+1 = 8, where the sum of 1+1+1+1+1+1+1+1 is done in parallel (no step-by-step is involved here) without any kind of, so called, process.

Parallel-summation holds also in case of |N| values, and since |N|<|R|, the parallel-summation of the |N| values of, for example, sequence <0.9, 0.09, 0.009, ...> (if observed from |R|) is value 0.999... < value 1 by value 0.000...1, as very simply explained and demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=10303144&postcount=4246.

No, it's not. That's just nonsense.

Why?

 

[jsfisher]

Why?

I have no idea why you posted nonsense.

Perhaps it has something to do with your insistence on replacing established meanings with your own private vocabulary and your refusal to define what your invented terms mean. Your awkward use of language plays into it, too.

 

[jsfisher]

jsfisher, it is not so hard to understand that, for example, 1+1+1+1+1+1+1+1 = 8, where the sum of 1+1+1+1+1+1+1+1 is done in parallel

How would you propose to do this parallel addition? You invented the term; you need to define it. Be careful, too, in your definition, since the order of operations can be important for series.

...(no step-by-step is involved here) without any kind of, so called, process.

You have hand-waved your way to one step, not zero.

And be all that as it may, what has this to do with infinite series, since their evaluation is completely determined by limits?

 

[doronshadmi]

How would you propose to do this parallel addition?

In parallel, not so hard, isn't it?

You have hand-waved your way to one step, not zero.

jsfisher, talking about particular values along the real line, is done by at least one step known as distinction, which is a step from the all possible values to the particular values.

Without this step, no particular values are available for discussion.

In this case (without loss of generality) the particular values are the |N| values of sequence <0.9, 0.09, 0.009, ...> where 0.9+0.09+0.009+... = 0.999... is the parallel-summation based on this one step of distinction.

And be all that as it may, what has this to do with infinite series, since their evaluation is completely determined by limits?

The definition of size, in this case is:

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

The |N| size series 0.9+0.09+0.009+..., if observed from |N| size, it is = 1.

The |N| size series 0.9+0.09+0.009+..., if observed from |R| size , it is < 1 by 0.000...1, as very simply addressed in http://www.internationalskeptics.com/forums/showthread.php?p=10305282#post10305282.

 

[jsfisher]

In parallel, not so hard, isn't it?

You can't provide a definition, can you? It remains meaningless.

jsfisher, talking about particular values along the real line, is done by at least one step known as distinction, which is a step from the all possible values to the particular values.

Without this step, no particular values are available for discussion.

More hand-waving. More insertion of your private, undefined vocabulary.

...non sequitur regarding "size"...

And be all that as it may, what has this to do with infinite series, since their evaluation is completely determined by limits?