Deeper than primes

[doronshadmi]

OK, so as locations, points still meet your requirement for being your ‘sides’.

Here it is again: A single element that there is more than a one location on it, each one of those locations is called a side w.r.t this single element.


A point is a single element, but is does not have more than a one location on it, therefore it cannot be considered as a single element that there are sides w.r.t it.

The details about the differece between a point and a side can be seen at http://www.internationalskeptics.com/forums/showpost.php?p=4731113&postcount=2940 .

 

[doronshadmi]

http://www.internationalskeptics.com/forums/showpost.php?p=4733964&postcount=2957

You do not get that in Pure Math, a concept like "process" is meaningless.

 

[The Man]

Here it is again: A single element that there is more than a one location on it, each one of those locations is called a side w.r.t this single element.


A point is a single element, but is does not have more than a one location on it, therefore it cannot be considered as a single element that there are sides w.r.t it.

Here it is again.

OK, so as locations, points still meet your requirement for being your ‘sides’.

I did not say points have your ‘sides’, I said they still meet your given requirements for being your ‘sides’. Furthermore what is your requirement for distinguishing one of your ‘sides’ from any other of your ‘sides’?

 

[The Man]

You do not get that in Pure Math, a concept like "process" is meaningless.

So addition is not a "process" of summation?

http://www.answers.com/topic/mathematical-process-mathematical-operation-operation

Kinds of ...: mathematical process, mathematical operation, operation

Top
kinds of:

permutation — the act of changing the arrangement of a given number of elements

combination — the act of arranging elements into specified groups without regard to order

differentiation — the mathematical process of obtaining the derivative of a function

maximization — the mathematical process of finding the maximum value of a function

integration — an operation used in the calculus whereby the integral of a function is determined

exponentiation, involution — the process of raising a quantity to some assigned power

arithmetic operation — a mathematical operation involving numbers

matrix operation — a mathematical operation involving matrices

construction — drawing a figure satisfying certain conditions as part of solving a problem or proving a theorem

relaxation, relaxation method — a method of solving simultaneous equations by guessing a solution and then reducing the errors that result by successive approximations until all the errors are less than some specified amount

ETA: The fact that “process” is meaningless and nonexistent in your notions, particularly in determining your ’magnitude of existence’, does not make it meaningless or nonexistent in math.

 

[doronshadmi]

I did not say points have your ‘sides’, I said they still meet your given requirements for being your ‘sides’.

There are sides if they are on the single element that has more than a one location on it. No point has a side but a single location can be used as a side. A side has different relations than a point, with the single element that it is on it, as can be seen at http://www.internationalskeptics.com/forums/showpost.php?p=4731113&postcount=2940 .

In the case of ________ :

If the location in the middle is a point, then the requirement is to be not blue AND not red.

If the location in the middle is a side, then the requirement is to be blue OR red.



A single element that has sides on it (it is not made of these sides) is called a non-local element.

Any single element that has no sides is a local element.

A point is the minimal example of a local element.

A line segment is the minimal example of a non-local element.

A line segment is non-local w.r.t the sides along it, but it can be considered as a local element, if it is completely included or excluded w.r.t some given domain.

A local element is completely included xor excluded w.r.t some given domain xor not included AND not excluded w.r.t to some given domain.

Furthermore what is your requirement for distinguishing one of your ‘sides’ from any other of your ‘sides’?

Its location w.r.t the non-local element that it is on it (no side is a building-block of the single element that it is no it).

But there are also the cases where locations are non distinguished (in the case of superposition of identities, as shown by Organic Numbers).

 

[doronshadmi]

So addition is not a "process" of summation?

http://www.answers.com/topic/mathematical-process-mathematical-operation-operation



ETA: The fact that “process” is meaningless and nonexistent in your notions, particularly in determining your ’magnitude of existence’, does not make it meaningless or nonexistent in math.

This is nonsense. Before that we drag a point, and now we are talking about process, but is has no meaning in Pure Math, because Time is not involved in Pure Math.

Here is the original question and answer about this case: http://www.internationalskeptics.com/forums/showpost.php?p=4731116&postcount=2941 .

 

[The Man]

This is nonsense. Before that we drag a point, and now we are talking about process, but is has no meaning in Pure Math, because Time is not involved in Pure Math.

Here is the original question and answer about this case: http://www.internationalskeptics.com/forums/showpost.php?p=4731116&postcount=2941 .

A process does not involve so much time as it does sequence or more specifically ordering. Sequence is important to math since variations is sequence can give different results. Again, the fact that “process” is meaningless and nonexistent in your notions, particularly in determining your ’magnitude of existence’, does not make it meaningless or nonexistent in math and just goes to show how little you understand about math or the word ‘process’.

 

[doronshadmi]

A process does not involve so much time as it does sequence or more specifically ordering.

Then call it ordering or what ever you like, except process, because time is involved in any process.

You the mathematicians hijack words and by force change their straightforward original meaning. This is one of the reasons that your framework is mechanic and notionless.

Furthermore, ordering or dragging still have relation to process and therefore to time.

 

[jsfisher]

You the mathematicians hijack words and by force change their straightforward original meaning. This is one of the reasons that your framework is mechanic and notionless.

Somebody owes me a new irony meter.

 

[The Man]

There are sides if they are on the single element that has more than a one location on it. No point has a side but a single location can be used as a side. A side has different relations than a point, with the single element that it is on it, as can be seen at http://www.internationalskeptics.com/forums/showpost.php?p=4731113&postcount=2940 .

In the case of ________ :

If the location in the middle is a point, then the requirement is to be not blue AND not red.

If the location in the middle is a side, then the requirement is to be blue OR red.

Again, it all depends on how you choose to define your red/blue intervals as exemplified before. Simply calling a ‘location’ by a different name (your ‘side’) does not make it any less of a location or point/points.

A single element that has sides on it (it is not made of these sides) is called a non-local element.

Any single element that has no sides is a local element.

A point is the minimal example of a local element.

A line segment is the minimal example of a non-local element.

A line segment is non-local w.r.t the sides along it, but it can be considered as a local element, if it is completely included or excluded w.r.t some given domain.

Ah so now non-locality is not an aspect of your line segment but simply an aspect of the ‘domain’ one chooses to define. You seem to be moving closer to the domain of standard geometry.

A local element is completely included xor excluded w.r.t some given domain xor not included AND not excluded w.r.t to some given domain.

“not included AND not excluded”? So you just do not know where your ‘local’ element is?

Its location w.r.t the non-local element that it is on it (no side is a building-block of the single element that it is no it).

So points (locations) distinguish between your sides. Again, you seem to be moving closer to the domain of standard geometry.

 

[doronshadmi]

Somebody owes me a new irony meter.

Organic Mathematics recovers the damage that you made by your brutal changing of the straightforward and original meaning of many words, for example:

Non-finite, Limit, Process, All (for all), Countable, Complete, Upper bound, Lower bound, Successor, Predecessor, etc …

 

[The Man]

Then call it ordering or what ever you like, except process, because time is involved in any process.

You the mathematicians hijack words and by force change their straightforward original meaning. This is one of the reasons that your framework is mechanic and notionless.

Furthermore, ordering or dragging still have relation to process and therefore to time.

In math the equation 5 * 2 - 3/4 results in 9.25 because of ordering in the processing of the given operations (multiplication and division before addition or subtraction). Please tell us how changes in time might alter that result without changes in ordering.

Somebody owes me a new irony meter.

Organic Mathematics recovers the damage that you made by your brutal changing of the straightforward and original meaning of many words, for example:

Non-finite, Limit, Process, All (for all), Countable, Complete, Upper bound, Lower bound, Successor, Predecessor, etc …

No meter could possibly represent such irony, it is infinite and uncountable.

 

[doronshadmi]

Again, it all depends on how you choose to define your red/blue intervals as exemplified before. Simply calling a ‘location’ by a different name (your ‘side’) does not make it any less of a location or point/points.

It depends on the fact that AND connective is not OR connective (and vice verse).

Ah so now non-locality is not an aspect of your line segment but simply an aspect of the ‘domain’ one chooses to define. You seem to be moving closer to the domain of standard geometry.

It depends if Absolute or Relative views are used, as explicitly shown in
http://www.geocities.com/complementarytheory/OMPT.pdf pages 22 - 24 .

“not included AND not excluded”? So you just do not know where your ‘local’ element is?

[.] = included point

[ ]. = excluded point.

[ . = not included AND not excluded point ( it is exactly on ] )

If the location on ] is a side, then a side is included w.r.t [ ]

So points (locations)

No, location is a point XOR a side.

 

[jsfisher]

Yes, and your inability to get it is the reason of why you don't get my answers about this case.

Ok, if you really consider those three statements equivalent, then it is time to move on. I bet you can't find anyone in this forum that would honestly agree with your position, though.

...I am talking about the immediate predecessor of y...

Fine, we can focus on just that. Why do you assume any real number, Y, must have an immediate predecessor (or immediate successor)?

My claim is this, if y is an immediate successor of some R member, then this member is the immediate predecessor of y.

Since no real number has an immediate successor, your statement is trivially true. IF <proposition that is false> THEN <any proposition whatsoever>.

This claim must be true both in [x,y) or [x,y] cases, since the universal quantifier "for all" is used in both cases.

Umm, did you miss the fact that intervals are not elements of the set of real numbers? And just how do you connect the universal qualifier to this and make it responsible for your claim.

Maybe this will help as a starting point. Here's a half-open interval expressed as an equivalent set:

[latex]$$$ [X, Y) \equiv \{Z : X \le Z < Y\} $$$[/latex]​

Standard Math uses the twisted legend, that any representation method is limited to aleph0

Where'd you get that idea?

...and as a result there is no way to represent the immediate successor or the immediate predecessor of any arbitrary given R member along the real-line.

No, that's wrong. It is not for lack of representation; it is for lack of existence. No real number has an immediate predecessor or immediate successor.

But this twisted legend is collapsed because Standard Math (as you wrote) can't show the immediate successor or the immediate predecessor of any arbitrary given Q member along the real-line, even if there are aleph0 Q members along the real-line.

Yes, rational numbers don't have immediate predecessors or immediate successors, either. Why would you expect otherwise?

We do not need more than that in order to show that the use of the universal quantifier "for all" on a collection of non-finite elements, does not hold.

So, what you are saying is that because the reals (and the rationals) don't have a property they shouldn't have, this proves the universal qualifier doesn't work? Curious.

By the way, the word is qualifier, not quantifier. Also, appending the "for all" to "universal qualifier" is redundant. It weakens your case when you can't even get these simple things correct.

you have failed to get the fact that Cantor explicitly used a way to define the exact member that is not mapped with any member of N, and by using this method, the conclusion and the premise are under a circular reasoning.

Again, you demonstrate you have no understanding of Cantor's second uncountability proof. You have expanded it, though, to show you have no understanding of proof by contradiction nor the term, circular reasoning.

 

[dlorde]

Organic Mathematics recovers the damage that you made by your brutal changing of the straightforward and original meaning of many words, for example:

Non-finite, Limit, Process, All (for all), Countable, Complete, Upper bound, Lower bound, Successor, Predecessor, etc …

Perhaps this is one root of the problem of your sub-optimal relationship with mathematics - that all specialist areas of knowledge must, and do, clearly define the semantics of the words they use, in order to avoid misunderstanding. In the process, the ill-defined everyday semantics of those words necessarily gives way to the more rigorous definitions. If you could bring yourself to accept this, and to define the semantics of your own 'custom' vocabulary, perhaps this discussion would be less frustrating for all.

 

[doronshadmi]

In math the equation 5 * 2 - 3/4 results in 9.25 because of ordering in the processing of the given operations

Wrong.

It depends on the power (hierarchy of arithmetic) and direction of the equation.

Furthermore, there is no universal principle here, because 5 * 2 - 3/4 = 9.25 is nothing but the particular case of serial reasoning, where superposition of identities is ignored.

 

[jsfisher]

Wrong.

It depends on the power (hierarchy of arithmetic) and direction of the equation.

Furthermore, there is no universal principle here, because 5 * 2 - 3/4 = 9.25 is nothing but the particular case of serial reasoning, where superposition of identities is ignored.

Doron, you have seriously lost it. Now, you are just denying things for the sake of contradiction.

 

[doronshadmi]

Doron, you have seriously lost it. Now, you are just denying things for the sake of contradiction.

You did not lose anything, because all you get is serial reasoning.

 

[doronshadmi]

Umm, did you miss the fact that intervals are not elements of the set of real numbers?

No, you are the one who have missed the fact intervals are elements of the set of real numbers (http://www.internationalskeptics.com/forums/showpost.php?p=4732096&postcount=2950 ).

So, what you are saying is that because the reals (and the rationals) don't have a property they shouldn't have, this proves the universal qualifier doesn't work? Curious.

By the way, the word is qualifier, not quantifier. Also, appending the "for all" to "universal qualifier" is redundant. It weakens your case when you can't even get these simple things correct.

I am talking about http://en.wikipedia.org/wiki/Universal_quantification "for all".

"For all" is used on [x,y) or [x,y] (it does not matter) and because it is used, there must be an immediate predecessor to y.

Simple as that.

 

[jsfisher]

No, you are the one who have missed the fact intervals are elements of the set of real numbers (http://www.internationalskeptics.com/forums/showpost.php?p=4732096&postcount=2950 ).

This is just sad, Doron. You don't comprehend your own words. You said:

An interval is an ordered collection of R members

See? You even got it mostly right back in that post. An interval is a collection. It is a collection of real numbers (elements of R, if you prefer); it is not itself a real number.

Why do you make so many simple mistakes like this?

I am talking about http://en.wikipedia.org/wiki/Universal_quantification "for all".

Sure, but why do you continue with that redundancy?

"For all" is used on [x,y) or [x,y] (it does not matter) and because it is used, there must be an immediate predecessor to y.

Simple as that.

Great!

(1) Please show where it is used.
(2) How does its use thereby require an immediate predecessor for Y?

Simple as that.