Deeper than primes

[jsfisher]

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:

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]

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.

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]

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]

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. ?

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.

...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]

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]

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]

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]

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]

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?

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.

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]

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]

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

I wrote:

-------

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]

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. ...

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).

"{{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.

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.

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.

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]

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]

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]

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

Wrong.

 

[The Man]

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]

... 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.

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.

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]

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]

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

I must preserve a few of my new favorites:

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).

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

"{{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.

Notation is king in this fantasical doronetics.

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.

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.

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.

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.

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

 

[doronshadmi]

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.