Cont: Deeper than primes - Continuation 2

[doronshadmi]

The rules of boolean algebra do not support your reasoning.

The way you are using boolean algebra, by ignoring the fact that {y} is not necessarily a successor of y ( {y}$y OR {y}~$y ) simply does not fit to my framework.

Yet you insist to force your particular improper use of boolean algebra again and again on my framework, that has nothing to do with the way you are using boolean algebra.

Why are you doing that?

 

[doronshadmi]

That may sound good in your head when you say it, but it is not math.

This is math whether you agree with it, or not.

Let's use a vary simple example, based on fundamental logic:

(There is light outside (in case that the sun shines)) OR (There is no light outside (in case that the sun does not shine))

(y is complete (in case that {y} is not a successor of y)) OR (y is incomplete (in case that {y} is a successor of y))

 

[jsfisher]

The way you are using boolean algebra, by ignoring the fact that {y} is not necessarily a successor of y ( {y}$y OR {y}~$y ) simply does not fit to my framework.

Perhaps if you would correct the definition you gave before for what M IsSuccessorOf N, then we'd all understand your "framework."

M IsSuccessorOf N <=> M = {N}​

Correct or not? If not, then what?

 

[doronshadmi]

It would save some time and trouble if you'd just confirm it is still

X IsSuccessorOf Y <=> X = {Y}​

It would not save some time and trouble, since your reasoning forces X to be a successor of Y, where X is not necessarily a successor of Y.

 

[doronshadmi]

Perhaps if you would correct the definition you gave before for what M IsSuccessorOf N, then we'd all understand your "framework."

M IsSuccessorOf N <=> M = {N}​

Correct or not? If not, then what?

http://www.internationalskeptics.com/forums/showpost.php?p=11271326&postcount=1384.

http://www.internationalskeptics.com/forums/showpost.php?p=11271298&postcount=1382.

 

[jsfisher]

It would save some time and trouble if you'd just confirm it is still

X IsSuccessorOf Y <=> X = {Y}​

It would not save some time and trouble, since your reasoning forces X to be a successor of Y, where X is not necessarily a successor of Y.

You would be more believable in this if you didn't continue to keep the meaning of your IsSuccessorOf relation a secret.

You told us before that it was this:

X IsSuccessorOf Y <=> X = {Y}​

What is it today?

 

[doronshadmi]

You would be more believable in this if you didn't continue to keep the meaning of your IsSuccessorOf relation a secret.

You told us before that it was this:

X IsSuccessorOf Y <=> X = {Y}​

What is it today?

It is exactly based on the the logic that is used in http://www.internationalskeptics.com/forums/showpost.php?p=11271298&postcount=1382.

There is no secret here, accept in the minds of those who force X to necessarily be the successor of Y.

EDIT:

Also a concrete example is given in http://www.internationalskeptics.com/forums/showpost.php?p=11271084&postcount=1374, but it is probably not in the minds of those who force X to necessarily be the successor of Y.

 

[doronshadmi]

Let's give some analogy:

There is number 1.

There is an operator |+| that is used for infinitely many additions.

If |+| is used between 1 and 1, than the result is some infinitely large number that its exact value is not satisfied (it is incomplete) since it is permanently changed without bounds (such numbers are notate, for example, by 1..., 10... etc., where some examples are given in http://www.internationalskeptics.com/forums/showpost.php?p=11259463&postcount=1185).

So in the case of infinitely large numbers, they are distinguished of each other by the numbers of 1's (also called successors) that are permanently beyond the range of some compared infinitely large number, etc.

If there are no successors beyond the range, than the compared numbers are actually the same infinitely large number.

If |+| is not used between 1 and 1, then we remain with 1 (where the non using is notated by ~|+|).

Any number (in this analogy) that is the result of finitely many additions of 1's, its exact value is satisfied (it is complete).

In this case |+| is not used between 1 and 1.

So there are two options:

(1|+|1, and the result is some incomplete number) OR (1~|+|1, and the result is a complete number).

Some example (based on sets) of this analogy, is found in http://www.internationalskeptics.com/forums/showpost.php?p=11271084&postcount=1374).

-------------------------

If we take the basic notion of OR connective from this analogy, it can help to understand the following:

({y}$y (and in that case y is incomplete)) OR ({y}~$y (and in that case y is complete)).

 

[Nonpareil]

A set of the form {{y}$y} is inherently and permanently under construction.

Is it now? Because you haven't established that. You haven't even attempted to define it (and yes, it does require definition), let alone link it to your proposed successor relationship operation.

Meanwhile, Gödel's incompleteness theorems have nothing to do with your proposed operation or sets being "permanently under construction", and your obsession with my avatar continues to establish precisely nothing relevant.

 

[jsfisher]

It is exactly based on the the logic that is used in....

That would invoke circular reasoning.

You need something of the form J IsSuccessorOf K <=> ... where the right-hand side defines IsSuccessorOf and therefore must not rely on the relation itself in the definition (and since IsComplete is defined in terms of IsSuccessorOf, IsComplete cannot appear on the right-hand side of the equivalence, either).

 

[doronshadmi]

Is it now? Because you haven't established that. You haven't even attempted to define it (and yes, it does require definition), let alone link it to your proposed successor relationship operation.

Meanwhile, Gödel's incompleteness theorems have nothing to do with your proposed operation or sets being "permanently under construction", and your obsession with my avatar continues to establish precisely nothing relevant.

Your reply is not informative, if you wish to say something please do it by reply, in details, according to what is written in my posts.

 

[doronshadmi]

That would invoke circular reasoning.

Nothing is circular in http://www.internationalskeptics.com/forums/showpost.php?p=11271298&postcount=1382.

Keep forcing X to necessarily be the successor of Y, and your reasoning indeed takes your to nowhere.

 

[jsfisher]

Keep forcing X to necessarily be the successor of Y, and your reasoning indeed takes your to nowhere.

The expression, X IsSuccessOf Y, is not forcing anything. It is answering a question: Is set X a successor of the set Y? Yes or no? (Well, true or false, actually, since it is an expression in logic.)

 

[Nonpareil]

Your reply is not informative, if you wish to say something please do it by reply, in details, according to what is written in my posts.

I have.

If you do not consider "even taking your (extremely poor) argument as true, it does not establish what you want it to establish" as being informative, there really is no help for you.

 

[doronshadmi]

Is set X a successor of the set Y? Yes or no? (Well, true or false, actually, since it is an expression in logic.)

EDIT:

Once again, X $ OR ~$ Y, and it is equivalent to the following expression:

X = OR ~= Y (also written as X ≤ Y, X ≥ Y).


In other words, (X$Y) is true OR (X~$Y) is true.


If you still don't grasp it, then let's use the following example:

(There is light outside) OR (there is no light outside)

All what is written above is not contradictory, since the OR condition prevents the simultaneity of being $ AND ~$, = AND ~=, light AND ~light, etc. ... ad infinitum.

 

[doronshadmi]

I have.

You have nothing, so far.

 

[jsfisher]

EDIT:

And still no definition for A IsSuccessorOf B to be found.

 

[Nonpareil]

And still no definition for A IsSuccessorOf B to be found.

Or actual answers to any questions of any kind, it seems.

How does a set being defined by the successor relationship necessitate that it is "permanently under construction", doron? What does "permanently under construction" even mean?

Throwing a tantrum in response to simple questions is not a good way to convince people of your new mathematical system's validity.

 

[jsfisher]

How does a set being defined by the successor relationship necessitate that it is "permanently under construction", doron? What does "permanently under construction" even mean?

We are now getting into the side-shuffle phase. Doron will explain his undefined concepts by substituting in new meaningless terms. "Next" is an example of a term he has recently used as a substitute for successor.

Nothing new here. Doron has told us that

IsComplete X <=> {X} IsSuccessorOf X, and
Y IsSuccessorOf Z <=> Y = {Z}​

Unfortunately, they highlight the contradiction inherent in most of Doronetics, so now Doron must side-shuffle and obfuscate. (There is also the Google Gambit wherein some Internet search stumbles across something he can misinterpret as supporting his gibberish.)

 

[doronshadmi]

Doron has told us that

IsComplete X <=> {X} IsSuccessorOf X, and
Y IsSuccessorOf Z <=> Y = {Z}​

Well, this is what you tell only to yourself, and as a result you are going nowhere.

$ is an operator that if used between set y and its singleton set {y} (this case is notated as {y}$y) the property of y is incompleteness.

If $ is not used between set y and its singleton set {y} (this case is notated as {y}~$y) the property of y is completeness.

Both cases (or options, if you will) are true with an OR logical condition between them, so there is no contradiction exactly as shown in http://www.internationalskeptics.com/forums/showpost.php?p=11272022&postcount=1395.