Cont: Deeper than primes - Continuation 2

[doronshadmi]

The beginning of my neutral monist view thread can be seen in http://www.sciencechatforum.com/viewtopic.php?f=51&t=27823 .

 

[RickM]

Dear Apathia,

Lately I have found how to use cardinality in order to support OM's view of the linkage among Unity and multiplicity, where this linkage is the head and heart of the mathematician's work.

Is that what this is all about? And I thought it to be more a tale of romance that seemed to be working.

doron….don’t give up now; Cupid’s arrow is within earshot.

 

[doronshadmi]

Is that what this is all about? And I thought it to be more a tale of romance that seemed to be working.

doron….don’t give up now; Cupid’s arrow is within earshot.

It is head AND heart, in case that you have missed it.

Please reply also to the first part of http://www.internationalskeptics.com/forums/showpost.php?p=10365625&postcount=280 (including its links).

Also please reply to http://www.internationalskeptics.com/forums/showpost.php?p=10364025&postcount=277 and http://www.internationalskeptics.com/forums/showpost.php?p=10367441&postcount=281.

Thank you, RickM.

 

[RickM]

Please reply also to the first part of http://www.internationalskeptics.com/forums/showpost.php?p=10365625&postcount=280 (including its links).

Also please reply to http://www.internationalskeptics.com/forums/showpost.php?p=10364025&postcount=277 and http://www.internationalskeptics.com/forums/showpost.php?p=10367441&postcount=281.

Thank you, RickM.

Hi Doron,

Thanks for the offer, but I’m afraid my mathematical achievements if life are limited to two semesters of calculus and two semesters of math department statistics, so I think I’ll leave this one to the experts.

I must admit, though, I’ve been following this thread for a few weeks now with some amusement, but is the storyline ever going to lead to some bedroom activity?

 

[doronshadmi]

I must admit, though, I’ve been following this thread for a few weeks now with some amusement,

Maybe it is the time to reform your amusement by being an active participator and not just passive observer?

 

[realpaladin]

Hi Doron,

Thanks for the offer, but I’m afraid my mathematical achievements if life are limited to two semesters of calculus and two semesters of math department statistics, so I think I’ll leave this one to the experts.

I must admit, though, I’ve been following this thread for a few weeks now with some amusement, but is the storyline ever going to lead to some bedroom activity?

No, this is a story about an eternally frigid virgin; too afraid to commit and trying to keep the attention away from that fact by discussing bedsheet weaves instead.

 

[Belz...]

We know that there are infinitely many levels of infinity

You are seriously out of your depths, here.

 

[doronshadmi]

You are seriously out of your depths, here.

What do you mean, exactly?

 

[realpaladin]

"So this is Christmas, and what have you done? Another year over, a new one just begun..."

Doron, reflect on the fact that you have not managed to keep *any* new poster for more than a few days...

 

[realpaladin]

Awww snap! Doron, seems like you have dawdled too long...

http://www.wired.com/2014/12/mathematicians-make-major-discovery-prime-numbers/

Not only a new major discovery on primes, but also some words like 'infinity'.

You were just too slow, Mr. Shadmi.

 

[doronshadmi]

If we use order and cardinality as significant factors of the mathematical concept of limit, then:

Given two numbers a and b such that a < b and given ordered sets S and K of numbers from a to b (where b is the limit):

1) If |S|=0, then S members can't close the gap between a and b.

2) If |S|>0, then S members can close the gap between a and b, but if K is a proper subset of S such that |K|<|S| AND k₁=s₁=a, then K members can't close the gap between a and b.

According to the definition (2), no amount of K members completely covers S.

 

[jsfisher]

If we use order and cardinality as significant factors of the mathematical concept of limit, then...

Let's not. Let's just leave the well-defined meaning of 'limit' alone.

If you feel compelled to introduce something new and different, start with a new and different definition for it and some new and different name. Then we can see what new and different utility your new and different concept might have.

 

[doronshadmi]

Let's not. Let's just leave the well-defined meaning of 'limit' alone.

http://www.internationalskeptics.com/forums/showpost.php?p=10607099&postcount=291 deals exactly with the failure of the attempt to define a mathematical concept like limit, by simply ignore the linkage among order and cardinality.

There is no need for new definitions here since cardinality and order are well-defined in this case.

So if you have some detailed reply about http://www.internationalskeptics.com/forums/showthread.php?p=10613587#post10613587 content, then please air your view.

Moreover let's be more accurate about (2):

2) If |S|>0, then S members can close the gap between a and b, but if K is a proper subset of S such that |K|<|S| AND k₁=s₁=a AND K and S members are the same from a forward, then K members can't close the gap between a and b.

According to the definition (2), no member of K is b, so no amount of K members completely covers S.

 

[jsfisher]

http://www.internationalskeptics.com/forums/showpost.php?p=10607099&postcount=291 deals exactly with the failure of the attempt to define a mathematical concept like limit

There is no "failure of the attempt to define a mathematical concept like limit." Limit is, in fact, defined very precisely and very completely.

...by simply ignore the linkage among order and cardinality.

The meaning of limit does not depend on any alleged linkage among order and cardinality.

Moreover, whatever linkage you allege to exist you haven't shown. First things first: You would need to define with some mathematical detail what exactly you mean by this linkage to which you refer. History suggests that will never happen.

Meanwhile, the meaning of limit remains unscathed by your onslaught.

 

[doronshadmi]

First things first: You would need to define with some mathematical detail what exactly you mean by this linkage to which you refer.

EDIT:

Here it is:

Given two numbers a and b such that a < b AND given sets S and K of convergent numbers to b, if K is a proper subset of S such that |K|<|S|, then the sum of K members < b.

 

[jsfisher]

Here it is...

You seemed to have left out something. Where is 'limit' anywhere in this?

Remember, you started this current arc with "If we use order and cardinality as significant factors of the mathematical concept of limit..."

You haven't shown at all what that means. Instead, you are just asserting conclusions.

 

[Little 10 Toes]

Here it is:

Given two numbers a and b such that a < b AND given ordered sets S and K of convergent numbers to b, if K is a proper subset of S such that |K|<|S| AND k₁=s₁=a, then the sum of K members < b.

Define convergent numbers please.

 

[doronshadmi]

You seemed to have left out something. Where is 'limit' anywhere in this?

Remember, you started this current arc with "If we use order and cardinality as significant factors of the mathematical concept of limit..."

You haven't shown at all what that means. Instead, you are just asserting conclusions.

b is the limit in the following definition:

Given two numbers a and b such that a < b AND given sets S and K that their members are used as convergent series to b, if K is a proper subset of S such that |K|<|S|, then the sum of K members < b.

 

[doronshadmi]

Define convergent numbers please.

Please see http://www.internationalskeptics.com/forums/showpost.php?p=10614697&postcount=298.

 

[jsfisher]

b is the limit in the following

Is it now? You defined b to be a number and stipulated it to be greater than another number, a. So, it is to be a limit as well....

The limit of what?

You understand, too, don't you, that having b as the limit of something isn't in any way dealing with the definition of 'limit' and its ties (imaginary or otherwise) to order and cardinality.

...definition:

Given two numbers a and b such that a < b AND given sets S and K that their members are used as convergent series to b, if K is a proper subset of S such that |K|<|S|, then the sum of K members < b.

See that part I rendered in bold type? That's a conclusion. You cannot define conclusions; you have to prove them.

But, even it you did, that would get you no where near tying limit to order and cardinality.