Deeper than primes

epix · Jul 22, 2011

doronshadmi said:
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 · Jul 22, 2011

doronshadmi said:
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 · Jul 22, 2011

doronshadmi said:
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 · Jul 23, 2011

jsfisher said:
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 · Jul 23, 2011

jsfisher said:
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.

jsfisher said:
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.

jsfisher said:
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 · Jul 23, 2011

epix said:
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 · Jul 23, 2011

epix said:
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 · Jul 23, 2011

epix said:
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 · Jul 23, 2011

doronshadmi said:
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 · Jul 23, 2011

jsfisher said:
0.999... = 1.

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

jsfisher said:
The real numbers are dense.

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

jsfisher said:
2 is a member of {2}.

2 and {2} are different expressions.

jsfisher said:
"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 · Jul 23, 2011

jsfisher said:
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 · Jul 23, 2011

doronshadmi said:
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 · Jul 23, 2011

doronshadmi said:
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 · Jul 23, 2011

jsfisher said:
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.

jsfisher said:
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.

jsfisher said:
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.

jsfisher said:
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.

jsfisher said:
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}.

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

You are still closed under your left hemisphere.

doronshadmi · Jul 23, 2011

epix said:
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 · Jul 23, 2011

doronshadmi said:
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 · Jul 23, 2011

doronshadmi said:
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 · Jul 23, 2011

jsfisher said:
You were still wrong either way.

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

jsfisher said:
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:

jsfisher said:
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).

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

What previous statement?

jsfisher said:
...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"

jsfisher said:
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.

jsfisher said:
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 · Jul 23, 2011

epix said:
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 · Jul 24, 2011

doronshadmi said:
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.

jsfisher · Jul 24, 2011

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

Ah, Doron, when it comes to defending stupid, you seldom disappoint. Let's review, shall we? Here's the statement you are defending:

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

Are you sure you don't want to reconsider? Defending it would be far more entertaining, but you decide.

epix · Jul 24, 2011

Originally Posted by epix

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.

doronshadmi said:
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

Wrong? When was the last time you divided 5 into 3, for example? If you use the long division method and divide 3 into 1, then the result is 0 in the integer part and an endlessly repeating string of 3's in the fractional part, which is expressed as 0.333... If I decide that "1\3" means "do the long division," then

1\3 = 0.333...

If I decide on a numerical system in other base, and if I love staring at a bunch of 3's after the decimal point, then I can chose base 5, for example, and do the long division that way:

3₅ \ 4₅ = 0.333...₅

So once again: If 1/3 > 0.333... [all base 10], then what does "1/3" mean if not the long division? Can't you answer a simple question without converting numbers to another bases -- or yourself to Christianity?

doronshadmi · Jul 24, 2011

jsfisher said:
Here's the statement you are defending:

It is not about defending or rejecting it.

Cardinality, by the traditional meaning is defined as the number of members of a given set, for example:

{} has cardinality 0

{a} has cardinality 1

{a,b} has cardinality 2

{a,b,c,..} has infinite cardinality

If you think it is wrong, then please provide the agreed definition of the traditional meaning of Cardinality.

doronshadmi · Jul 24, 2011

jsfisher said:
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.

Do you pay attention that the membership of some set's object is notated (also by you} as {2}, {{45, {1,3} 2}, ... , etc. , and never as 2, ... , etc. ?

jsfisher said:
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.

D={{{M},{N}}, where what's between the outer "{" "}" are the members of D.

So by following this fact DUD={{M},{N}}}U{{M},{N}}}={{M},{N}}}, or in other words, D is indeed the union of its members.

The members of {M,N}, which is definitely not set D, are the members of the members of set D.

jsfisher said:
...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.

How excellent of you to provide a totally irrelevant example to "support" your claim, for example:

A={A}

AUA={A}U{A}={A}

So also by this example a set is the union of its members.

-------

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

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

So C is the result of the union of set A with set B, which is different than the result of the union of the members of these sets, which is {1,2,3,4} and it is defiantly not set C.

-------

Once again it is shown how your local brain can't get out of its agreed box.

doronshadmi · Jul 24, 2011

epix said:
what does "1/3" mean

Exactly 1/3 size of size 1

0.333...[base 10] is not exactly 1/3 size of size 1

jsfisher · Jul 24, 2011

doronshadmi said:
It is not about defending or rejecting it.

Cardinality, by the traditional meaning is defined as the number of members of a given set

{} has cardinality 0

{a} has cardinality 1

No one except for you has said otherwise.

jsfisher · Jul 24, 2011

doronshadmi said:
D={{{M},{N}}, where what's between the outer "{" "}" are the members of D.

You continue to inflate notation to a level of significance it does not have. The members of D are {M} and {N}. "{{M},{N}}" stripped of its outermost braces is not a member of D.

So by following this fact DUD={{M},{N}}}U{{M},{N}}}={{M},{N}}}

If doesn't follow at all from the "fact" of membership. It follows from the definition of union.

...or in other words, D is indeed the union of its members.

Nope. {{M},{N}} remains not a member of D. D U D is not the union of the members of D.

jsfisher · Jul 24, 2011

doronshadmi said:
How excellent of you to provide a totally irrelevant example to "support" your claim

Seriously, you need to work on your reading comprehension skills. It was your example, not mine, and in your example A was not a member of A, etc.

...for example:

A={A}

Not only is this not the set you started with, so you are making new stuff up on the fly, this is not even a set.

The Man · Jul 24, 2011

doronshadmi said:
The right phrase is this:

"So it would seem my “non-strict” and “indeterminate” AB is different than determined strict A or B"

“The right phrase”? Are you now claiming that your assertion “AB means that "A=bottom and B=top" is indeterminate so we can't determine if it is "bottom", "top" or some intermediate state between them.” Was an improper ‘phrasing’ by you and asserted restrictions and determinations you had not intended?

doronshadmi said:
Contradiction, in this case, is the result of forcing determination on the indeterminate or the strict on the non-strict, and this is exactly what you are doing, The Man.

Doron I didn’t force anything, you stated the above relations yourself, though it seems now you just want to contradict yourself as usual and as expected.

doronshadmi said:
You are still forcing strictness and determination on AB, and as a result you can't get it.

Nope, again I didn’t force anything, you asserted the above relationships not me. However, as you evidently simply can not even agree with just your own assertions how do you expect anyone else to possibly agree with you?

epix · Jul 24, 2011

doronshadmi said:
Exactly 1/3 size of size 1

0.333...[base 10] is not exactly 1/3 size of size 1

Miracle!

So Doronetics distinguishes between complete and incomplete processes where exactness and incompleteness don't go along well at all. That make sense. So if you want to reduce the length of a line segment 1 feet long by cutting it in three sub-segments, you won't be able to use any decimal-based measuring device to make an exact mark where point A = 1/3 or point B = 2/3 are located, coz point A is situated 1/3(long div.) or 0.333... feet (incomplete process) away from point 0. So you need to use some yardstick with numbers showing in base 3, for example. Then you make the "exact" mark, which is 1/3 [base 10] away from point zero. That means incomplete 0.333...[base 10] = complete 0.1 [base 3], right?

So if 1/3 > 0.333... then in the process of the intuitive sequential expansion of the fractional part given by the long division of 1 by 3, 1/3 is the lowest number expressed in the exact format that 0.333... can never reach. Isn't that so? In other words, 1/3 is the limit of 0.333...

Can you convert the limit fraction 1/3 into the approximate format so it can be proven that 1/3(exact) > 0.333...(aproximate). In base 10, of course.

doronshadmi · Jul 25, 2011

I wish to correct the last part of http://www.internationalskeptics.com/forums/showpost.php?p=7401418&postcount=16064 .

I wrote:

doronshadmi said:
-------

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

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

So C is the result of the union of set A with set B, which is different than the result of the union of the members of these sets, which is {1,2,3,4} and it is defiantly not set C.

-------

It has to be:

-------

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

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

So C members are the result of the union of the members of set A with the members of set B, which is different than the result of the union of the members of the members of these sets, which is {1,2,3,4} and it is defiantly not set C members.

-------

doronshadmi · Jul 25, 2011

jsfisher said:
You continue to inflate notation to a level of significance it does not have.

Wrong.

You continue to miss the fact that membership is defined only among a given set, where the least set is {}.

{}U{}={}
{{}}U{{}}={{}}
{{},{{}}}U{{}}={{},{{}}}

etc. ...

jsfisher said:
The members of D are {M} and {N}.

Wrong, they are considered as members of some set only they are defined, for example, as {{M},{N}} (which is D set, in this case).

jsfisher said:
"{{M},{N}}" stripped of its outermost braces is not a member of D.

Exactly, and this is the reason of why {M} form or {N} form is not considered as a member of {{M},{N}} form.

jsfisher said:
If doesn't follow at all from the "fact" of membership. It follows from the definition of union.

In that case the agreed definition of union does not understand what a set is.

In other words, Traditional Math is consistent by its ignorance about fine distinctions, for example:

By this ignorance 2 is a member of set {2} (where there is nothing about membership in 2 expression).

By this ignorance 0.111...[base 2] = 0.999...[base 10] = 1

By this ignorance a 1-dimensional space is completely covered by 0-dimensional spaces.

By this ignorance Cantor set has Lebesgue measure 0.

By this ignorance a convergent infinite series equals to some value (called Limit), which is actually inaccessible to all the added values of this series.

etc. ... etc. ... more and more ignorance of fine distinctions.

jsfisher said:
Nope. {{M},{N}} remains not a member of D.

So what, we are talking about D as the union of its members, and not about D as the member of itself, in {{M},{N}} case.

jsfisher said:
D U D is not the union of the members of D.

D is the union of its members, whether you like it or not.

doronshadmi · Jul 25, 2011

jsfisher said:
Seriously, you need to work on your reading comprehension skills. It was your example, not mine, and in your example A was not a member of A, etc.

Not only is this not the set you started with, so you are making new stuff up on the fly, this is not even a set.

Wrong.

{A} is a non-empty set where A is its name.

{A}U{A}={A}, where the name of {A} is A.

AUA=A does not change the fact that the union of the members of the set named as A, is {A}.

doronshadmi · Jul 25, 2011

The Man said:
Are you now claiming that your assertion “AB means that "A=bottom and B=top" is indeterminate so we can't determine if it is "bottom", "top" or some intermediate state between them.” Was an improper ‘phrasing’ by you and asserted restrictions and determinations you had not intended?

Non-strict strictness is non-strictness.

Strict non-strictness is non-strictness.

doronshadmi · Jul 25, 2011

epix said:
That means incomplete 0.333...[base 10] = complete 0.1 [base 3], right?

Wrong.

The Man · Jul 25, 2011

doronshadmi said:
Non-strict strictness is non-strictness.

Strict non-strictness is non-strictness.

You forgot ‘non-strict strict non-strictness that is strictly non-strictly restrictive.”

Your assertions Doron are still only your assertions, whether you claim "non-strictness" in one post, restrict it another and then try to purport "non-strictness" once again after that, it is all just you (contradicting just you). Again if you can’t even agree with yourself how can you expect others to even possibly agree with you?

So is your assertion “AB means that "A=bottom and B=top" is indeterminate so we can't determine if it is "bottom", "top" or some intermediate state between them.” Correct or not? If it is then you have restricted your “AB” by that asserted relation. If not then your “AB” remains currently unrestricted but then you still don’t know what your “AB means”. You’ve painted yourself into another corner Doron either your “AB” means something and thus that meaning has certain restrictions or your “AB” has no restrictions and is thus meaningless.

doronshadmi · Jul 25, 2011

The Man said:
... that is strictly non-strictly restrictive.”

Strictly non-strictly restrictive
is strict non-strictness,
which is non-strictness.

In other words,
you have no case.

The Man said:
Your assertions Doron are still only your assertions, whether you claim "non-strictness" in one post, restrict it another

Wrong, AB is non-strict, no matter what twisted maneuvers are done by you (for example: "AB is strictly non-strict") The Man.

The Man said:
So is your assertion “AB means that "A=bottom and B=top" is indeterminate so we can't determine if it is "bottom", "top" or some intermediate state between them.” Correct or not? If it is then you have restricted your “AB” by that asserted relation.

Translation:

Strict non-strictness
is non-strictness,

And The Man
has no case.

Poor The Man, no matter ho many twisted maneuvers you are doing, AB is non-strict and it is distinguished from strict A or strict B.

The Man · Jul 25, 2011

doronshadmi said:
Strictly non-strictly restrictive
is strict non-strictness,
which is non-strictness.

In other words,
you have no case.

Wrong, AB is non-strict, no matter what twisted maneuvers are done by you, The Man.

Translation:

Strict non-strictness
is non-strictness,

And The Man
has no case.

Again, not my "maneuvers" Doron just your own assertions about what you claim your “AB means” and if you can't even agree with just yourself on that, how can anyone even possibly agree with you on that.

Unless of course we just disagree with you, which would be agreeing with your disagreement with yourself. Hey,…

looks like we've had this "OM" stuff down pat from the start. The only way to agree with Doron and his “OM” is to disagree with him and his “OM” as that is all he and his "OM" do, just disagree.

jsfisher · Jul 25, 2011

Wow, just wow. No one discredits Doron's posts better than Doron.

I must preserve a few of my new favorites:

doronshadmi said:
jsfisher said:

The members of D are {M} and {N}.

Click to expand...

Wrong, they are considered as members of some set only they are defined, for example, as {{M},{N}} (which is D set, in this case).

Or, put more directly, the members of D are {M} and {N}.

jsfisher said:
jsfisher said:

"{{M},{N}}" stripped of its outermost braces is not a member of D.

Click to expand...

Exactly, and this is the reason of why {M} form or {N} form is not considered as a member of {{M},{N}} form.

Notation is king in this fantasical doronetics.

jsfisher said:
jsfisher said:

If doesn't follow at all from the "fact" of membership. It follows from the definition of union.

Click to expand...

In that case the agreed definition of union does not understand what a set is.

Well, there is a fail to understand what a set is, but it is located in Israel, not in Mathematics.

By this ignorance 2 is a member of set {2} (where there is nothing about membership in 2 expression).
By this ignorance 0.111...[base 2] = 0.999...[base 10] = 1
By this ignorance a convergent infinite series equals to some value (called Limit), which is actually inaccessible to all the added values of this series.

This just in, through the ignorance of Mathematics, check books still balance.

jsfisher said:
jsfisher said:

Nope. {{M},{N}} remains not a member of D.

Click to expand...

So what, we are talking about D as the union of its members, and not about D as the member of itself, in {{M},{N}} case.

jsfisher said:

D U D is not the union of the members of D.

Click to expand...

D is the union of its members, whether you like it or not.

Doron refuses to be swayed by inconveniences like definitions and such.

doronshadmi · Jul 25, 2011

jsfisher, you still do not understand that the members of a given set are its organs, where a set is an organism.

If you take them out of their organism, they are not its organs anymore.

For example, {{N},{M}} is an organism, and this organism is the union of its organs.

By {N}U{M} = {N,M} you get another organism, which its organs are different than the organs of {{N},{M}} organism, exactly because {N} or {M} are not organs of {{N},{M}} organism.

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