Deeper than primes

[epix]

epix, you still do not get non-local numbers, which are not rational or irrational numbers.

because Traditional Math does not get Non-locality, it has no choose but to define 0.333...[base 10] as 1/3 or 3/14...[base 10] as Pi , etc. ...

You simply ignore verbal_sequential\visual_spatial reasoning as used in http://www.internationalskeptics.com/forums/showpost.php?p=6465716&postcount=12075 and http://www.internationalskeptics.com/forums/showpost.php?p=6470162&postcount=12091 , and continue to use verbal_sequential-only reasoning, exactly like jsfisher and The Man.

You called non-local any number in the approximate format that has its fractional part made of digits whose number is not bounded and these digits are not endlessly repeating zeroes. So non-local numbers can be irrational as well as rational. That means all rational numbers in the irreducible form

q = 1/2ⁿ and q = 1/5ⁿ where n = 1, 2, 3, ...

are local and the rest is non-local. And so 0.333... is a non-local number. But "1/3" doesn't have a fractional part -- those are two integers linked with a relationship symbolized by the slash. What is the term that doronetics uses for this expression? You need to define it to prove that the magnitude of the non-local number 0.333... is less than the magnitude given by the expression 1/3.

 

[jsfisher]

It shows that if the mind understands that no branch of that tree actually reaches any another branch of that tree, even if there are infinity many laves of that tree (where 1 is some branch of that tree), it immediately understands that this tree is actually some case of an infinite interpolation.

Maybe someday you will understand what 'interpolation' means'. Today is not that day.

Infinite interpolation is a direct result of the fact that there is no homeomorphism between 1-dimensional space and 0-dimensional space or between between 2-dimensional space and 1-dimensional space etc. ad infinitum ...

So, you assume your conclusion as a premise, then the proof follows. How convenient.


This just in, 1 continues to exactly equal 0.999...; Doron remains confused.

 

[epix]

epix, you still do not get non-local numbers, which are not rational or irrational numbers.

because Traditional Math does not get Non-locality, it has no choose but to define 0.333...[base 10] as 1/3 or 3/14...[base 10] as Pi , etc. ...

The reason is that you don't provide any info regarding your special categorical distinction. If I came up with local and non-local numbers, I would start the definition the way that I would first map their incidence in the already defined categories. Are any local and/or non local numbers present in Z, N, Q, R, or C?

If you say that non-local numbers are not rational or irrational, then they are not in R.

You used once a comparison between local and non-local case and the only difference was that the example of the local case involved numbers with a finite fractional part and the non-local case was made of numbers with infinitely repeating digits after the decimal point. I suppose that wasn't a coincidence, was it? There was no other feature that would make the difference between "local" and "non-local." So you can blame only yourself for not being followed or being misunderstood.

 

[epix]

This just in, 1 continues to exactly equal 0.999...; Doron remains confused.

Doron should stick with Doronetics, coz the "traditional math" can be very confusing. Take for example two assertions A and B.

A. 0.999... = 1

B. 0.999... ≠ 1

The consequence of A is 1 - 0.999... = 0 and the consequence of B is 1 - 0.999... = d with 0 < d < 1.

If A is true, then equation

0.999... + 1/x = 1

doesn't have a real solution, coz there is no real solution to

1/x = 0

If B is true, then d exists as d = 1/x. That means x = 1/d and therefore x > 0. So the traditional math wouldn't be able to directly prove that difference d equals zero no matter what, but can show that 0.999... = 1, which is a state of affairs that leaves Doron bewildered and that triggers his allergy, so he sneezes all the time. Lols.

 

[doronshadmi]

Maybe someday you will understand what 'interpolation' means'. Today is not that day.



So, you assume your conclusion as a premise, then the proof follows. How convenient.


This just in, 1 continues to exactly equal 0.999...; Doron remains confused.

As can clearly be seen in http://www.internationalskeptics.com/forums/showpost.php?p=7394481&postcount=16035 (and its correction in http://www.internationalskeptics.com/forums/showpost.php?p=7394710&postcount=16037) , your verbal_sequential-only "Death by entropy" reasoning can't deal with verbal_sequential\visual_spatial reasoning "non-entropic" reasoning, no matter how infinitely many twisted maneuvers are taken by you, jsfisher.

No collection (including your infinitely many twisted maneuvers) has the power of the continuum, where the power of the continuum is a natural property of Non-locality, which, again, is inaccessible to collections.

So, you assume your conclusion as a premise, then the proof follows. How convenient.

Wrong.

The inaccessibility of collections to the power of continuum of Non-locality, is an axiom.

This axiom can't be comprehended by using verbal_sequential-only "Death by entropy" reasoning, which is your reasoning, jsfisher.

Maybe someday you will understand what 'interpolation' means'. Today is not that day.

Today is not the day for verbal_sequential-only "Death by entropy" minds.

Today is the day for verbal_sequential\visual_spatial "non-entropic" minds.

 

[doronshadmi]

You need to define it to prove that the magnitude of the non-local number 0.333... is less than the magnitude given by the expression 1/3.

You have to get out of verbal_sequential-only reasoning box in order to get verbal_sequential\visual_spatial reasoning as used in http://www.internationalskeptics.com/forums/showpost.php?p=6465716&postcount=12075 and http://www.internationalskeptics.com/forums/showpost.php?p=6470162&postcount=12091.

As long as you can't do that, you can't get that 0.333...[base 10] < 1/3 is defined.

 

[doronshadmi]

If you say that non-local numbers are not rational or irrational, then they are not in R.

They are between R members along the real-line.

You are still missing http://www.internationalskeptics.com/forums/showpost.php?p=7397770&postcount=16046 .

 

[doronshadmi]

Doron should stick with Doronetics, coz the "traditional math" can be very confusing. Take for example two assertions A and B.

A. 0.999... = 1

B. 0.999... ≠ 1

The consequence of A is 1 - 0.999... = 0 and the consequence of B is 1 - 0.999... = d with 0 < d < 1.

The right one is B because both brain's hemispheres (verbal_sequential AND visual_spatial) are co-operated into a one comprehensive reasoning.

The wrong one is A because only the left hemisphere (verbal_sequential) is used in order to define formal frameworks, which are context-dependent-only, exactly because there is no co-operation between both brain's hemispheres (where the co-operation is naturally expressed as Cross-contexts (right hemisphere) \Context-dependent (left hemisphere) reasoning, as used in B case).

Dedekind's cut ( http://en.wikipedia.org/wiki/Dedekind_cut ) is an example of a mind that uses only his left hemisphere in order to establish a formal framework.

Furthermore, we clearly see now that Traditional Math is mostly developed by left hemisphere minds, and OM's first goal is to develop Math by using the co-operation of Cross-contexts (right hemisphere) \Context-dependent (left hemisphere) as a one comprehensive reasoning , as shown, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=7241076&postcount=15569 and http://www.internationalskeptics.com/forums/showpost.php?p=7255966&postcount=15594 .

 

[jsfisher]

As can clearly be seen in....

Continually referencing posts where you to assert as true things you simply made up doesn't advance your case.

0.999... = 1.

The real numbers are dense.

2 is a member of {2}.

"If-then" and "if-and-only-if" are not equivalent constructs.

 

[doronshadmi]

0.999... = 1.

The non-local number 0.999...[base 10] < local number 1 by non-local number 0.000...1[base 10]

The real numbers are dense.

All real numbers are local, and between them there are non-local numbers.

2 is a member of {2}.

2 and {2} are different expressions.

"If-then" and "if-and-only-if" are not equivalent constructs.

I did not use "If-then" in the formal way, in the considered case.

 

[doronshadmi]

Continually referencing posts where you to assert as true things you simply made up doesn't advance your case.

Continually referencing posts where you to assert as true things by using only your left hemisphere doesn't advance your case.

 

[epix]

You have to get out of verbal_sequential-only reasoning box in order to get verbal_sequential\visual_spatial reasoning as used in http://www.internationalskeptics.com/forums/showpost.php?p=6465716&postcount=12075 and http://www.internationalskeptics.com/forums/showpost.php?p=6470162&postcount=12091.

As long as you can't do that, you can't get that 0.333...[base 10] < 1/3 is defined.

You reference uses the same inequality where PI is involved, but there is no definition of PI that would prove the inequality. In other words, you need to find a way out of here to get your crusade moving in the right direction.

 

[jsfisher]

The non-local number 0.999...[base 10] < local number 1 by non-local number 0.000...1[base 10]

This is just something you made up.

All real numbers are local, and between them there are non-local numbers.

You have been unable to define what you mean by non-local number, nor can your prove your statement.

Real numbers remain dense.

2 and {2} are different expressions.

No one stated otherwise; however, you have been emphatic that 2 is not an element of {2}.

I did not use "If-then" in the formal way, in the considered case.

You have failed to present anything in a formal way, so your statement is vacuously true. Be that as it may, the constructs are not equivalent in any informal way, either. By the way, you claimed the full set--if-then, only-if, and if-and-only-if--were all equivalent. Not even in Doronetics would that be true.

You have also said that 1/4 and 0.25 represent different numbers.
You have also said that sets, maps, and functions are all the same.
You have also said cardinality cannot exceed 1.
You have also said a set, any set, is the union of its members.

You insist on many things, doron, that are patently false.

 

[doronshadmi]

You have failed to present anything in a formal way, so your statement is vacuously true.

In the particular case of "if-than" I did not use any formal way.

It is vacuously true that what you call formal way is the result of using only the left hemisphere of your brain.

You have also said that 1/4 and 0.25 represent different numbers.

In terms of interpolation 0.25[base 10] has a finite interpolation upon two levels, where 1/4 does not have any interpolation.

You have also said that sets, maps, and functions are all the same.

Wrong. Only Mapping and Function (in terms of Set Theory) are equivalent.

You have also said cardinality cannot exceed 1.

Only if cardinality is defined as the power of existence from 0 to 1.

In terms of the traditional way, Cardinality is the number of members of a given set, which is trivially also > 1

In other way, you are talking nonsense, you simply have no ability to re-search concepts.

You have also said a set, any set, is the union of its members.

You still do not get the difference between x and {x}.

You insist on many things, doron, that are patently false.

You are still closed under your left hemisphere.

 

[doronshadmi]

but there is no definition of PI that would prove the inequality. [/url]

Wrong.

Pi = circumference/diameter

Pi is a local number along the real-line.

3.14...[base 10] is a non-local number along the real-line that is < Pi

Using only your left hemisphere is not enough, in order to get it.

 

[jsfisher]

In the particular case of "if-than" I did not use any formal way.

You were still wrong either way.

In terms of interpolation 0.25[base 10] has a finite interpolation upon two levels, where 1/4 does not have any interpolation.

Your misunderstanding of 'interpolation' and your confused belief numbers are inseparable from their representation are just more of your failings.

0.25 and 1/4 continue to represent the same number. For that matter, 1, 1.0, 1.00, and 1.000... all represent the same number, too.

Wrong. Only Mapping and Function (in terms of Set Theory) are equivalent.

Ok, then. Are you now amending your previous statement to something less wrong?

Only if cardinality is defined as the power of existence from 0 to 1.

...which it isn't, but you did.

In terms of the traditional way, Cardinality is the number of members of a given set, which is trivially also > 1

...except it isn't. Care to amend this statement, or would you like to defend this insanity for a bit?

You still do not get the difference between x and {x}.

Is 2 an element of {2} or not? Simple question. You should not need to evade it as you have done.

And what about sets: Are they the union of their members or not?

 

[epix]

As long as you can't do that, you can't get that 0.333...[base 10] < 1/3 is defined.

You don't define a particular inequality; you prove a particular inequality. But you need to define the terms in question.

There is a close relationship between

a:b = "ratio"

and

a/b = "fraction"

The word "rational" and "ratio" share the same etymology and that affects the meaning of "rational number," which is number c, such as that for a and b in Z

1) a:b = c

or

2) a/b = c ?

The obvious choice is (1) where choice (2) is reserved for "fractional number" c.

Well, it's not really so . . .

If I define p and q as integers and relate them as p:q, which means that p is to be divided by q using process called The Long Division, and if p = 1 and q = 3, then

1:3 = 0.333...

and there is nothing you can do about it. And that goes for someone elses choice

1/3 = 0.333....

to perform The Long Division.

If you say that 1/3 > 0.333... then the expression "1/3" is not an instruction to perform The Long Division. What does "one over three" mean? If you can't provide at least a basic functional description without posting links to some lengthy treaties of yours, then there is a very good chance that you don't have the slightest idea about what 99% of your own inventions actually mean.

 

[doronshadmi]

You were still wrong either way.

You continue to force things that are not there, in this case.

Your misunderstanding of 'interpolation' and your confused belief numbers are inseparable from their representation are just more of your failings.

0.25 and 1/4 continue to represent the same number.

If only the final location along the real line is considered, then, yes, 0.25[base 10] and 1/4 is the same number.

If not only the final location along the real line is considered, then, no, for example: 0.25[base 10], 0.01[base 2] and 1/4 are not the same number, as can be seen by using verbal_sequential AND visual_spatial reasoning:

For that matter, 1, 1.0, 1.00, and 1.000... all represent the same number, too.

In this case all locations are indeed the same number, no matter what base is used (please see above).

Ok, then. Are you now amending your previous statement to something less wrong?

What previous statement?

...except it isn't. Care to amend this statement, or would you like to defend this insanity for a bit?

This insanity is shown in http://en.wikipedia.org/wiki/Cardinality

the cardinality of a set is a measure of the "number of elements of the set"

Is 2 an element of {2} or not? Simple question. You should not need to evade it as you have done.

If {2} is written, then what is written between between "{""}" is defined as a member of some set. If only 2 is written it is not necessarily a member of some set.

Again you do not distinguish between "x" expression and "{x}" expression.

And what about sets: Are they the union of their members or not?

Sets are union of members, for example:

A={1,2,3}
B={1,2,4}

C=AUB={1,2,3,4}

Sets can also be the union of their members ( Idempotent law in http://en.wikipedia.org/wiki/Algebra_of_sets ), for example:

AUA={1,2,3}U{1,2,3}={1,2,3}
BUB={1,2,4}U{1,2,4}={1,2,4}
CUC={1,2,3,4}U{1,2,3,4}={1,2,3,4}

 

[doronshadmi]

If I define p and q as integers and relate them as p:q, which means that p is to be divided by q using process called The Long Division, and if p = 1 and q = 3, then

1:3 = 0.333...

and there is nothing you can do about it.

Wrong.

Please use [base 3] in the case of 1/3 and you do not get non-local number 0.333...[base 10] < local number 1/3

 

[jsfisher]

If {2} is written, then what is written between between "{""}" is defined as a member of some set. If only 2 is written it is not necessarily a member of some set.

Notation does not create Mathematical fact nor does it create existence. You seem convinced otherwise.

2 is a member of {2}, and it doesn't matter if you write it down somewhere first. 2 is also a member of the set {45, {1,3} 2}. 2 is a member of many, many sets, and it always has been, is, and always will be so.

Sets are union of members, for example:

A={1,2,3}
B={1,2,4}

C=AUB={1,2,3,4}

How excellent of you to provide a totally irrelevant example to "support" your claim.

Please note that neither A or B are members of C.

On the other hand, for the set, D = {{M}, {N}}, the members are {M} and {N}. Continuing to the union, {M} U {N} = {M, N}, and that is different from the set D.

D is not the union of its members.

Sets can also be the union of their members ( Idempotent law in http://en.wikipedia.org/wiki/Algebra_of_sets ), for example:

AUA={1,2,3}U{1,2,3}={1,2,3}
BUB={1,2,4}U{1,2,4}={1,2,4}
CUC={1,2,3,4}U{1,2,3,4}={1,2,3,4}

...except A is not a member of A, nor is B a member of B, nor is C a member of C. You continue to introduce irrelevant topics (idempotency in this case), and you continue to be wrong with extraordinary consistency.