Cont: Deeper than primes - Continuation 2

[doronshadmi]

Edit: And why even bring up base 3 numbers? Why not use base 17?

You are still missing it.

If 1/3 is represented by a finite amount of symbols, then this string of symbols is exactly 1/3, otherwise it is < 1/3.

http://www.internationalskeptics.com/forums/showpost.php?p=10639476&postcount=439 simply demonstrates these two options, without loss of generality.

 

[jsfisher]

Again, no amount of finitely many partial sums like, for example, (0.9₁₀, 0.99₁₀, 0.999₁₀, ...)

And yet, that is precisely what Mathematics does. The definition (of limit) is both useful and consistent.

...can be used in order to conclude anything about the series of (0.9₁₀, 0.09₁₀, 0.009₁₀, ...)

That is not a series.

...and you, jsfisher, use finite sums like (0.9₁₀, 0.99₁₀, 0.999₁₀, ...) terms in order to conclude something about an infinite sum over (0.9₁₀, 0.99₁₀, 0.999₁₀, ...)

Whenever you can actually define your stuff, only then with it it be examined for its utility and consistence.

...so you are the one that actually use an arbitrary and artificial extension from the finite to the infinite.

There was nothing arbitrary about it, and certainly not artificial.

 

[jsfisher]

I use an effective method for this, as clearly seen in:

http://www.internationalskeptics.com/forums/showpost.php?p=10625610&postcount=379

http://www.internationalskeptics.com/forums/showpost.php?p=10633086&postcount=431

http://www.internationalskeptics.com/forums/showpost.php?p=10622312&postcount=358

Repeating the nonsense does not make it any less nonsensical.

The current stumbling block to your "method" applied to infinite series. It's that "add all at once" step that is most in need of definition.

 

[Little 10 Toes]

You are still missing it.

If 1/3 is represented by a finite amount of symbols, then this string of symbols is exactly 1/3, otherwise it is < 1/3.

http://www.internationalskeptics.com/forums/showpost.php?p=10639476&postcount=439 simply demonstrates these two options, without loss of generality.

But 1/3 is not represented by a finite amount of numbers. Is there a reason that you ignored the first question? Can you do long division?

Edit: Before you have the chance to post, I am specifically talking about base 10 numbers. This eliminates you going for the "but it doesn't in base 3 numbers".

 

[doronshadmi]

And yet, that is precisely what Mathematics does.

Mathematics is not the private property of anyone, so this is what the traditional mathematicians do, even if it is logically false, exactly because you can't conclude anything about the sum of infinitely many terms by using infinitely many finite sums (called by you, partial sums).

That is not a series.

I wrote "the series of ..."

Whenever you can actually define your stuff, only then with it it be examined for its utility and consistence.

Already done. You simply reject it because you are not aware of the fallacy of 0 < |a_n - L| AND 0.999...₁₀ = 1.

There was nothing arbitrary about it, and certainly not artificial.

It is illogical, arbitrary and artificial, and you keep holding it like any believer that can't see anything beyond his\her religious dogma.

 

[doronshadmi]

It's that "add all at once" step that is most in need of definition.

Already addressed in http://www.internationalskeptics.com/forums/showpost.php?p=10637196&postcount=437.

 

[doronshadmi]

But 1/3 is not represented by a finite amount of numbers. Is there a reason that you ignored the first question? Can you do long division?

Edit: Before you have the chance to post, I am specifically talking about base 10 numbers. This eliminates you going for the "but it doesn't in base 3 numbers".

http://www.internationalskeptics.com/forums/showpost.php?p=10639476&postcount=439 got over your head, please try very carefully to understand it (for example, I wrote: "finite amount of symbols" and you wrongly wrote in your reply: "finite amount of numbers"), and the meaning of "without loss of generality", as explained in http://www.internationalskeptics.com/forums/showpost.php?p=10641132&postcount=441.

 

[jsfisher]

Mathematics is not the private property of anyone, so this is what the traditional mathematicians do, even if it is logically false, exactly because you can't conclude anything about the sum of infinitely many terms by using infinitely many finite sums (called by you, partial sums).

So you continue to assert. Some definitions might help your case, but none have appeared.

I wrote "the series of ..."

So you did. My apologies.

Already done. You simply reject it because you are not aware of the fallacy of 0 < |a_n - L| AND 0.999...₁₀ = 1.

If it be a fallacy (despite how nonsensical it is to label a definition a fallacy), then surely you can point out the fallacy. It would need to be something concrete, not just more unfounded assertion.

It is illogical, arbitrary and artificial, and you keep hold it like any believer that can't see anything beyond his\her religious dogma.

Illogical, arbitrary, and artificial do no mean what you think they mean. Your dislike for definitions of series and of limits is all you have.

 

[doronshadmi]

Repeating the nonsense does not make it any less nonsensical.

Repeating the nonsense 0 < |a_n - L| AND 0.999...₁₀ = 1 does not make it any less nonsensical.

 

[doronshadmi]

Your dislike for definitions of series and of limits is all you have.

Your logical fallacy of

 

[jsfisher]

Already addressed in http://www.internationalskeptics.com/forums/showpost.php?p=10637196&postcount=437.

Balderdash.

The question still stands: How does one derive the value of an infinite sum in one step?

Let's apply your method to find the series for the sequence {1, -1/2, 1/3, -1/4, 1/5, ...}

 

[doronshadmi]

Your dislike for definitions of series and of limits is all you have.

Your logical fallacy of 0 < |a_n - L| AND 0.999...₁₀ = 1 is all you have.

 

[doronshadmi]

Balderdash.

The question still stands: How does one derive the value of an infinite sum in one step?

Let's apply your method to find the series for the sequence {1, -1/2, 1/3, -1/4, 1/5, ...}

The sum of 1 + (-1/2) + 1/3 + (-1/4) + 1/5 + ... is the result of a one step among infinitely many numbers.

 

[jsfisher]

The sum of 1 + (-1/2) + 1/3 + (-1/4) + 1/5 + ... is the result of a one step among infinitely many numbers.

Still side-stepping I see. The question remains: How?

 

[jsfisher]

Your logical fallacy of 0 < |a_n - L| AND 0.999...₁₀ = 1 is all you have.

Prove it to be a fallacy.

 

[doronshadmi]

Still side-stepping I see. The question remains: How?

Still stuck in your dogma.

Already addressed in http://www.internationalskeptics.com/forums/showpost.php?p=10637196&postcount=437.

 

[doronshadmi]

Prove it to be a fallacy.

Very simple:

Since no term of the infinite sequence (0.9₁₀, 0.99₁₀, 0.999₁₀, ...) can be used in order to conclude anything about the sum of (0.9₁₀, 0.09₁₀, 0.009₁₀, ...) = 0.999...₁₀ (and in this case 0 < |a_n - L| < ε) then a_n can't be used, so the sum over a_|N| = 0.999...₁₀ is used, and L=1, so (0 < |0.999...₁₀ - 1|) AND (0.999...₁₀ = 1) is false.

Let X be a placeholder for that is summed.

If |X - L| = 0 then L is called the limit of X.

By my definition X is a placeholder that is not limited only to countable collections with |N| elements (for example: ...1₁₀ of number 0.000...1₁₀ is at |R| cardinality that is it at higher level than cardinality |N|, which is the cardinality of .000... of the place value keepers).

So 0 < |0.999...₁₀ - 1| = 0.000...1₁₀ + 0.999...₁₀ = 1 from the relative point of view of |N| w.r.t |R|.

More details are given in http://www.internationalskeptics.com/forums/showpost.php?p=10622312&postcount=358.

 

[Little 10 Toes]

http://www.internationalskeptics.com/forums/showpost.php?p=10639476&postcount=439 got over your head, please try very carefully to understand it (for example, I wrote: "finite amount of symbols" and you wrongly wrote in your reply: "finite amount of numbers"), and the meaning of "without loss of generality", as explained in http://www.internationalskeptics.com/forums/showpost.php?p=10641132&postcount=441.

Ok then,

1/3 is written with a finite amount of symbols. One. It just so happens that the one symbol is used an infinite amount of times. So 1/3 = .333...

Your post #441 does not explain "without loss of generality". The post, in fact, only uses the word "of" once.

I still note that you have quoted my whole post but still have not answered my questions:

1) Do you know how to do long division?
2) What is the base 10 decimal representation of the fraction 1/3, or what is 1 divided by 3?

 

[doronshadmi]

Ok then,

1/3 is written with a finite amount of symbols. One.

No, there are 3 symbols in 1/3.

It just so happens that the one symbol is used an infinite amount of times. So 1/3 = .333...

No. 0.333...₁₀ < 1/3 by 0.000...1/3₁₀, where 0.000... is at |N| level and ...1/3₁₀ is at |R| level such that 0.000...1/3₁₀ > 0 where 0 is the lowest level.

Your post #441 does not explain "without loss of generality". The post, in fact, only uses the word "of" once.

Sorry but I do not follow you, please explain the reasoning of this part. What do you actually wish to say?

I still note that you have quoted my whole post but still have not answered my questions:

1) Do you know how to do long division?
2) What is the base 10 decimal representation of the fraction 1/3, or what is 1 divided by 3?

1) If you divide 1 by 3₁₀ and does not ignore |N| and |R|, you are able to understand the relative difference between 0.000... and ...1/3₁₀ in number 0.000...1/3₁₀ and how this number is the relative complement of number 0.333...₁₀ to number 1/3.

2) Again, 0.333...₁₀ is a number of its own < number 1/3 by number 0.000...1/3₁₀, where all these three numbers > 0, which is the lowest level.

In order to understand that please read carefully http://www.internationalskeptics.com/forums/showpost.php?p=10642767&postcount=457, and try to capture the definition of limit that is written there.

 

[jsfisher]

Still stuck in your dogma.

Already addressed in http://www.internationalskeptics.com/forums/showpost.php?p=10637196&postcount=437.

It was a failure when you first posted that. In continues to be the same failure each time you reference it.

For any given infinite sequence, how does one derive the sum of all the sequence elements in one step?

Please demonstrate your method using the sequence {1, -1/2, 1/3, -1/4, 1/5, ...}