Cont: Deeper than primes - Continuation 2

Status
Not open for further replies.
doronshadmi said:
Dear jsfisher,

This is my last post to you on this fine subject.
Click to expand...

Thank you. Too bad you could not define your terms, though.

Fortunately Mathematics is not restricted only to your arbitrary |N| observation.
Click to expand...

I have no such arbitrary observation, nor would Mathematics be restricted by it. Neither your re-definitions nor your straw change the value of 0.999....
 
http://www.internationalskeptics.com/forums/showpost.php?p=10332081&postcount=110 is aimed to those who are interested in the discussed fine subject, which is rigorously defined by the abstract mathematical fact of the strict difference among carnality |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ...

Using ∞ (as currently done among mathematicians) in order to deduce conclusions in terms of infinity is not accurate enough, simply because it does not use the well established mathematical proof of |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... different levels of infinity, where each one of them is defined in no more than one step (no process of more than one step is involved) .
 
Last edited:
doronshadmi said:
http://www.internationalskeptics.com/forums/showpost.php?p=10332081&postcount=110 is aimed to those who are interested in the discussed fine subject, which is rigorously defined by the abstract mathematical fact of the strict difference among carnality |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ...
Click to expand...

You keep using those words, but do not understand what they mean.

Using ∞ (as currently done among mathematicians) in order to deduce conclusions in terms of infinity is not accurate enough...
Click to expand...

No, it is you who do not understand how infinity is used in something like 0.999.... (In fact, it isn't used at all, but that nuance escapes you, doesn't it.) As a result, you make things up in support of your own confusion, and you erect strawmen in attempts to discredit the actual meaning of things.

The things you make up, you cannot ever define, either. That indicates that you, yourself, have no idea what you are saying.

...simply because it does not use the well established mathematical proof of |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... different levels of infinity, where each one of them is defined in no more than one step (no process of more than one step is involved) .
Click to expand...

There's another phrase you misuse and don't understand.
 
What? All the other posters already left Doron? I can understand that; all the talk in the world of being peaceful does not balance the acts of strife and opposition that Doron really commits.

Doron, again. If you are in a discussion, you *MUST* listen to the other side and you *MUST* concede when you are *WRONG*.

If you are unable to do so, then on *any* board on the Internet, people will simply ignore you.

If you look at the preceding weeks, you will find that, with the exception of Apathia, each and everyone, in just about any tone of voice possible, from friendly to arrogant, has asked you the same same thing:

- Define your concepts. Not *show* your concepts, which you keep doing, but *defining* them. Put borders around them, explain why these borders are valid etc.

Whatever you think, whatever you say, if you can not participate in a discussion, then in a few years, when you are gone from the planet, everything you have ever said is just stored and ignored. It won't have mattered that you existed.

To change that, participate, not just direct, and concede when you are wrong.
 
Dear Dessi,

Let's simplify http://www.internationalskeptics.com/forums/showpost.php?p=10334974&postcount=158 as follows:

The serial solution: |1| worker puts |N| stones along an infinite road by speed |N|.

The parallel solution: |N| workers put |N| stones along an infinite road by speed |1|.

So, in both cases the mission is accomplished by one step (|1| worker with speed |N| = |N| workers with speed |1|).

By using one step for each cardinal number of the forms |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... it is clear that no mission of lower cardinality is accomplished if observed from higher cardinality, or in other words, the power of lower cardinality is insignificant in order to reach the power of higher cardinality.
 
Last edited:
doronshadmi said:
Dear Dessi,

Let's simplify http://www.internationalskeptics.com/forums/showpost.php?p=10334974&postcount=158 as follows:

The serial solution: |1| worker puts |N| stones along an infinite road by speed |N|.

The parallel solution: |N| workers put |N| stones along an infinite road by speed |1|.
Click to expand...

Do you know what these two processes have in common with the evaluation of 0.999...? Absolutely nothing. Why do you keep bringing it up?

Do you know what's curious about your so-called solutions (aside from their irrelevance to the infinite series topic)? You so desperately try to make aleph-null behave like an integer, which it isn't, so they are mathematically meaningless.

All that aside, though, why haven't you found a place for aleph-one in any of this? Considering how much mathematics has been ignored to this point, forcing in aleph-one and some of its higher-numbered friends should be easy for you.
 
jsfisher said:
You so desperately try to make aleph-null behave like an integer
Click to expand...
Not even close.

You are simply missing the one step notion, no matter what cardinality>0 (finite or infinite) is used.

As a result
doronshadmi said:
By using one step for each cardinal number of the forms |n>1| < |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... it is clear that no mission of lower cardinality is accomplished if observed from higher cardinality, or in other words, the power of lower cardinality is insignificant in order to reach the power of higher cardinality.
Click to expand...
is not in your scope.

Here is a concrete example (your rhetoric question) that supports my argument about you:
doronshadmi said:
Do you know what these two processes have in common with the evaluation of 0.999...? Absolutely nothing.
Click to expand...
It is clearly seen that you are totally missing the fact that there is one step in both parallel and serial solutions, no matter what cardinality>0 (finite or infinite) is used for a given solution.

Moreover, you are totally missing the fact that a given solution in a given cardinality>0 is not satisfied if observed from higher cardinality (as written in my first quote in this post).

Generally your mathematical universe is the result of no more than one level for each observation (you systematically avoiding observations of lower levels from higher levels, so there is no wonder that my theorem is not in your scope).
 
Last edited:
doronshadmi said:
Not even close.
Click to expand...

Perhaps you don't understand your own posts. Your wrote, among other things, "|N| workers". You are, in fact, using aleph-null as if it were an integer. I am even more than close; I am dead on.
 
Last edited:
doronshadmi said:
Please change "|N| workers" to "|N| integers", and walla, you have no argument.
Click to expand...

No, the same argument remains: Whether workers or integers, you are still trying to use |N| as if it were an integer.

Be that as it may, it still has no relevance to the valuation of 0.999....

(Walla?? Half a city in Washington State?)
 
doronshadmi said:
Wrong, there is a collection of |N| integers, where |N| is not one of them.
Click to expand...

There are infinitely many integers and the cardinality of the set of integers is aleph-null. However, it is incorrect to say the number of integers is aleph-null or anything semantically equivalent, including "|N| integers". As a colloquial convenience, the phrase and its semantic equivalents, "the number of integers is infinite", may be used, but never as a prelude to using 'inifinity' as an ordinary number.

Be that as it may, it is still irrelevant to the valuation of 0.999....
 
Last edited:
doronshadmi said:
Your inabilities are clearly demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=10349404&postcount=208.
Click to expand...

Ah, another Doron-classic massively re-edited post!

One step or a billion (or, dare I say it, infinitely many steps), it is still a process you are chasing. Moreover, whether the steps are performed sequentially or all in parallel, or any combination of the two, it is still the same number of steps. But what of that, either way, you remain fixated on process.

And it still is irrelevant to the valuation of 0.999.... No process, no algorithm, just a simple limit. So simple that only rational numbers are needed. The rest of the reals (and most* of the rationals for that matter) are never needed to establish 0.999... as identical to 1.

The only way for you demonstrate that 0.999... and 1 are not identical is to show that 1 does not satisfy the N/epsilon requirement for the limit of the partial summations corresponding to 0.999....


[SIZE=-1]*"Most" takes a figurative meaning in this parenthetical remark.
[/SIZE]
 
Ah, I see we are back to Doron being snide and insulting again...

I wonder what has happened to the Doron that all of his friends and family said to be a peace-loving person.

Doron, how is communicating with others working out for you? What? Everyone left already?
 
Last edited:
doronshadmi said:
This is another example that supports my argument about your one-level mathematical universe, as very simply addressed in http://www.internationalskeptics.com/forums/showpost.php?p=10349404&postcount=208.
Click to expand...

Doron, you do not get to redefine the meanings of things to conform to your misunderstandings. The valuation of 0.999... stands at 1. Your attempts to distract with irrelevant references to power sets doesn't change that.


(Curious, though. You used to reject Cantor's Theorem. It was just wrong; Cantor was just wrong. Now, you embrace it, even though it lacks utility for your purpose. How flexible of you.)
 
Status
Not open for further replies.

Back
Top Bottom