Deeper than primes

[doronshadmi]

Well, at least you seem willing now to admit your original strip-the-parenthesis plan was nonsense.

Yes, your nonsense.

Not necessarily gibberish. Not necessarily. Your reading comprehension skills fail you get again.

It is necessarily gibberish, unless {...} form is used (you simply can't avoid this form if you really wish to avoid nonsense).

Yes, that would be appropriate.

Only if your "reasoning" is transformed into reasoning.

Can you do this transformation?

 

[jsfisher]

Yes, your nonsense.

More projection. It was your nonsensical view, not mine. It is still good, though, that you've come around to accept it as nonsense.

It is necessarily gibberish, unless {...} form is used (you simply can't avoid this form if you really wish to avoid nonsense).

In addition to a profound ability to ignore meaning, you have an equally profound reliance on symbolic notation to invent meaning.

No, there is no requirement for explicit brackets somewhere on printed page before a set is allowed to come into existence. If 2 is understood to mean {0, 1} by virtue of some background convention, then, yes, 2 U {{1}, 2} is perfectly valid.

 

[doronshadmi]

You never meant a definition you couldn't ignore, have you, doron?

Your left_hemisphere-only reasoning can't get definitions of left_hemisphere\right_hemisphere reasoning, isn't it, jsfisher?

The members of {1, 2} are 1 and 2.

The members of {1, 2} are exactly what is between { and }.

...unless, of course we adopt a special convention...

Your special convention is simply translating objects into sets (whether they are empty, or not) in order to avoid nonsense, so?

 

[epix]

Originally Posted by doronshadmi
. __

__ . . .

Who wants to go next?

Me go. The word is "Continuum," coz after . __ [base Morse] comes __ . . . [base Morse] and so the next is __ . __ . [base Morse] = C [base Alphabet]

Since __ ... also implies "line followed by ellipses," which is like 1, 2, 3, ... , it calls for unbound continuation of the line. So it means that the word that starts with C [base non-Morse] is "Continuum" or "Chimney." It can go both ways.

End of proof.

... and up is the roof
where once was a chimney.

 

[doronshadmi]

More projection. It was your nonsensical view, not mine. It is still good, though, that you've come around to accept it as nonsense.

This is the projection of yourself on yourself.

In addition to a profound ability to ignore meaning, you have an equally profound reliance on symbolic notation to invent meaning.

jsfisher, profound ignorance is your original invention all along this thread.

No, there is no requirement for explicit brackets somewhere on printed page before a set is allowed to come into existence. If 2 is understood to mean {0, 1} by virtue of some background convention, then, yes, 2 U {{1}, 2} is perfectly valid.

If 2 is understood to mean {0, 1}, then it is {0,1} with members and {0,1,{1},2} is the result of the union between the members of set {0,1} and the members of set {{1},2}, which is notated as {0,1}U{{1},2}={0,1,{1},2}.

 

[jsfisher]

The members of {1, 2} are exactly what is between { and }.

I see you have now gone full circle on this whole strip-the-brackets concept.

Be that as it may, "1, 2" (with the quotation marks elided) is not a member of the set, {1, 2}. So, no, the members of {1, 2} are not exactly what is between { and }.

The set {1, 2} has two members. One is 2, and the other is 1. The members of {1, 2} are 2 and 1. The union of the members of {1, 2} would be 1 U 2, and that may or may not be defined depending on possible background assumptions.

Similarly, the the sum of the members of {1, 2} is 1 + 2 and that equals 3. It is not {1,2} + {1,2} as the obvious analogy to Doron's mathematical torture would insist.

 

[epix]

If 2 is understood to mean {0, 1}, then it is {0,1} with members and {0,1,{1},2} is the result of the union between the members of set {0,1} and the members of set {{1},2}, which is notated as {0,1}U{{1},2}={0,1,{1},2}.

You have the talent to make a simple notion an undecidable proposition.

A set is a collection of distinct objects, considered as an object in its own right.

If the members of a set are expressions, then A is a set.

A = {1+5, 24/4, 2*3}

If the members of set A are redefined as not expressions, then set A is no longer a set, coz the arithmetic returns members that are not distinct.

The set R whose members are real numbers is a set of characters called numbers, each of them representing a different magnitude, which assures the requirement of distinction for the collection to be called a "set," until it is proven that 0.999... = 1.000...

Sets are one of the most fundamental concepts in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived.

The "mathematics" of 0.999... and 1.000... doesn't seem to be backed by the set theory, even though Cantor used the approximate format a.b₁b₂b₃ ... of real numbers to show that set R is uncountable.

Of course, you prefer to argue issues which are well beyond anything remotely instrumental to the theory of the sets -- unless you try to demonstrate the doronized version of the theory.

 

[The Man]

When you finally open your mind in order to get the difference between AB and A,B , let me know.

Did that already, but you still just couldn't agree with yourself. So are the restriction you asserted for your “AB” by claiming “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.” valid or not? Again until you can at least agree with just yourself no one else can even possibly agree with you.

 

[epix]

Did that already, but you still just couldn't agree with yourself. So are the restriction you asserted for your “AB” by claiming “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.” valid or not? Again until you can at least agree with just yourself no one else can even possibly agree with you.

Let's compromise, otherwise temper may flare up with unforeseen consequences. Just let AB be some initials A.B. instead of bottom and top.

Btw, does listening to violin promote violence?

No-way!
http://www.nme.com/news/pop-will-eat-itself/58256

A.B. couldn't solve the riddle
so he aimed and shot a fiddle
then came C. and D. with E.
to start another shooting spree.

We must buy a mosquito repellent to defend the purity of organized thought in order to prevent the violent dismemberment of craftily shaped wood. We must buy crazy glue too.

 

[doronshadmi]

I see you have now gone full circle on this whole strip-the-brackets concept.

Wrong, you don't see.

Be that as it may, "1, 2" (with the quotation marks elided) is not a member of the set, {1, 2}.

Exactly.

So, no, the members of {1, 2} are not exactly what is between { and }.

Worng. The quotation marks are explicitly not elided in order to define objects as members of some set, in the first place.

The set {1, 2} has two members. One is 2, and the other is 1.

Wrong, 2 or 1 are considered as members of some set only according to {1,2} form and not less than that.

 

[doronshadmi]

Did that already,

Not even in your dreams.

All you are doing is wasting energy by running in loops in your closed box.

 

[doronshadmi]

You have the talent to make a simple notion an undecidable proposition.

You don't have the talent to not distinguish between {x} and x.

 

[doronshadmi]

Please look at the following symbols (from left to right, in this case):

2 { 2 , { 2 } }

The first symbol is not a member of a set.

The second symbol is a member of a set.

The third symbol is a member of a member of a set.

 

[zooterkin]

Please look at the following symbols (from left to right, in this case):

2 { 2 , { 2 } }

The first symbol is not a member of a set.

The second symbol is a member of a set.

The third symbol is a member of a member of a set.

What about the other 5 symbols?

 

[doronshadmi]

What about the other 5 symbols?

"{" and "}" are used to denote a set and "," is used as distinction between set's members that exist at the same level of a given set.

 

[zooterkin]

"{" and "}" are used to denote a set and "," is used as distinction between set's members that exist at the same level of a given set.

Whoosh!

 

[jsfisher]

I see you have now gone full circle on this whole strip-the-brackets concept.

Wrong, you don't see.

Be that as it may, "1, 2" (with the quotation marks elided) is not a member of the set, {1, 2}.

Exactly.

So, no, the members of {1, 2} are not exactly what is between { and }.

Worng. The quotation marks are explicitly not elided in order to define objects as members of some set, in the first place.

The set {1, 2} has two members. One is 2, and the other is 1.

Wrong, 2 or 1 are considered as members of some set only according to {1,2} form and not less than that.

This post of Doron's is so brilliant in its self-contradiction, I had to preserve it.

 

[epix]

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.

Wrong.

If you have 4 elements and 2 set unions, then the result is 1 element. Since 4² = 16, the result defines the element.

16 = {S}U{L} {F}U{R}

Since 16 = 38 - 22, then by Ezekiel Theorem,

I will execute judgment on him with plague and bloodshed; I will pour down torrents of rain, hailstones and burning sulfur on him...
Ezekiel 38:12

your insight into the set theory doesn't meet the moral standards necessary to stay within the safe distance from the The Wok of Masterfully Prepared Formulae. In other words, your ill-conceived voyage into the Set Theory can't lift the Anchor of Mutual Agreement between The Captain and The Deck Hand. In yet other words, the cruise has been postponed awaiting your decision to adjust the syntax of your sequential thoughts.

 

[doronshadmi]

This post of Doron's is so brilliant in its self-contradiction, I had to preserve it.

Your ignorance is preserved, no doubt about.

 

[doronshadmi]

your insight into the set theory doesn't meet the moral standards ...

Wrong.

The mechanical reductionist set theory that claims that, for example, {} is a member of many sets, does not understand the organic difference between {} , {{}}, {{},a}, {{},{{}}}, {{},{{a}}}, ... etc., which stands at the fundamental understanding of complexity's development.

From the mechanical reductionist set theory point of view the bold form {} , {{}}, {{},a}, {{},{{}}}, {{},{{a}}}, ... etc., is actually the same form, no matter how it is related to some organism's complexity.

The understanding of organisms' complexity is a must have notion for moral standards, which, at least, avoids the destruction of their depth and diversity.

The mechanical reductionist set theory can't have this fundamental understanding exactly because organism's complexity is beyond its framework.