Cont: Deeper than primes - Continuation 2

[doronshadmi]

it appears that you don't know how to do long division,

Long division has nothing to do with X sum such that |X - L| = 0.

And why do we care about why you think that 0 is the smallest sum?

Because only if |X - L| = 0, L is the limit of X.

You still believe that 0.00...1 is still a number.

Belief is not in involved here, and 0.000...1₁₀ is very simply explained in http://www.internationalskeptics.com/forums/showpost.php?p=10622312&postcount=358.

 

[jsfisher]

Because only if |X - L| = 0, L is the limit of X.

That has nothing to do with 'limit'. Perhaps for doron-limit it would apply, but you have yet to define 'doron-limit'.

 

[doronshadmi]

That has nothing to do with 'limit'.

http://www.internationalskeptics.com/forums/showpost.php?p=10625610&postcount=379 provides exactly the definition of limit, unlike your fallacy (as seen at the beginning of this post) that indeed has nothing to do with limit.

 

[jsfisher]

http://www.internationalskeptics.com/forums/showpost.php?p=10625610&postcount=379 provides exactly the definition of limit, unlike your fallacy (as seen at the beginning of this post) that indeed has nothing to do with limit.

'Limit' has a very precise definition in Mathematics, you don't get to change it, and this isn't it:

It is not 'doron-limit' but simply 'limit'.

Let X be a placeholder for that is summed.

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

In fact, it is not much of a definition of anything since it starts with an undefined referent with "for that is summed". Then there is the ridiculous attempt to lend legitimacy by adopting notation vaguely similar to what is used for 'limit', while really just trying to conceal the rather self-serving result that X is the doron-limit of X.

 

[zooterkin]

Long division has nothing to do with X sum such that |X - L| = 0.

Long division has everything to do with your incorrect statement.

What do you get when you divide 1 by 3?

If you divide something by 3, then multiply the result by 3, why do you not have the number you started with?

 

[Little 10 Toes]

deleted

 

[doronshadmi]

What do you get when you divide 1 by 3?

If you divide something by 3, then multiply the result by 3, why do you not have the number you started with?

Again, the sum of (0.3₁₀, 0.03₁₀, 0.003₁₀, ...) < 1/3 by 0.000...1/3₁₀, where (0.9₁₀, 0.09₁₀, 0.009₁₀, ...) < 1 by by 0.000...1₁₀, and no long division is involved with any of the sums.

 

[doronshadmi]

'Limit' has a very precise definition in Mathematics,

The fallacy of 0 < |a_n - L| AND 0.999...₁₀ = 1 is far from being precise.

On the contrary only if |X - L| = 0, L is the limit of X, where 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) as used by your false definition.

 

[Little 10 Toes]

Again, the sum of (0.3₁₀, 0.03₁₀, 0.003₁₀, ...) < 1/3 by 0.000...1/3₁₀, where (0.9₁₀, 0.09₁₀, 0.009₁₀, ...) < 1 by by 0.000...1₁₀, and no long division is involved with any of the sums.

And how did you determine the series of 0.3, 0.03, 0.003, ..., and 0.9, 0.09, 0.009, ... ?

 

[Little 10 Toes]

The fallacy of 0 < |a_n - L| AND 0.999...₁₀ = 1 is far from being precise.

On the contrary only if |X - L| = 0, L is the limit of X, where by my definition X is a placeholder that is not limited only to countable collections with |N| elements, as used by your false definition.

You mean that a set can have 2.5 elements?

And what happens when |X - L| does not equal zero?

Edit: Please define doron-limit.

 

[doronshadmi]

And how did you determine the series of 0.3, 0.03, 0.003, ..., and 0.9, 0.09, 0.009, ... ?

By add |N| elements in one step.

 

[Little 10 Toes]

By add |N| elements in one step.

And where did you get the values from?

 

[doronshadmi]

You mean that a set can have 2.5 elements?

No, no fraction is involved with the amount of elements in some given collection.

And what happens when |X - L| does not equal zero?

Then the sum of the elements of X is not identical to L.

Edit: Please define doron-limit.

There is no doron-limit, but just simply limit.

 

[doronshadmi]

And where did you get the values from?

From the elements of the summed sequence.

 

[Little 10 Toes]

From the elements of the summed sequence.

But the result of writing the decimal representation of 1/3 does not have a summed sequence.

 

[doronshadmi]

But the result of writing the decimal representation of 1/3 does not have a summed sequence.

0.333...₁₀ is not a decimal representation of 1/3, but it is a number of its own that is distinguished from 1/3 by number 0.000...1/3₁₀, where number 0.000...1/3₁₀ is the result of |N| AND |R| cardinality (where |R| elements (notated as ...1/3₁₀) are relativity taken as one object from the point of view of |N| objects (notated as 0.000...)).

 

[Little 10 Toes]

The fallacy of 0 < |a_n - L| AND 0.999...₁₀ = 1 is far from being precise.

On the contrary only if |X - L| = 0, L is the limit of X, where 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) as used by your false definition.

Wow, let's look at your original post:

The fallacy of 0 < |a_n - L| AND 0.999...10 = 1 is far from being precise.

On the contrary only if |X - L| = 0, L is the limit of X, where by my definition X is a placeholder that is not limited only to countable collections with |N| elements, as used by your false definition.

And you still have not defined "doron-level".

 

[Little 10 Toes]

0.333...₁₀ is not a decimal representation of 1/3, bu it is a number of its own that is distinguished from 1/3 by number 0.000...1/3₁₀, where number 0.000...1/3₁₀ is the result of |N| AND |R| cardinality.

Sheeze, I see that you need to go back to math class. There is no decimal number that has a fraction in it.

I see that you cannot do long division. Is it too hard for you? And 0.00...1 does not exist.

Edit: your edited post

0.333...₁₀ is not a decimal representation of 1/3, bu it is a number of its own that is distinguished from 1/3 by number 0.000...1/3₁₀, where number 0.000...1/3₁₀ is the result of |N| AND |R| cardinality (where |R| elements (notated as ...1/3₁₀) are relativity taken as one object from the point of view of |N| objects (notated as 0.000...)).

 

[Little 10 Toes]

Let me know when you are done editing your messages. And any particular reason why you feel the need to tell people you are using base 10 numbers?

Edit: Man up, and get some integrity. Stop editing your posts after people have responded.

Edit 2: what number do you get when you divide 1 into 3 equal parts?

 

[doronshadmi]

And any particular reason why you feel the need to tell people you are using base 10 numbers?

No, it is just an example without loss of generality, other base can be used as well, for example: 0.111...₂ < 1 by 0.000...1₂, where 0.000...1₂ > 0.000...1₁₀