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Deeper than primes

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jsfisher said:
It would have been far more direct of you to simply admit you were incapable of providing any definition of incomplete. Your constant evasion, projection, gibberish, and re-reference to previous evasion, projection, gibberish, and re-reference is a colossal waste.
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It would have been far more direct of you to simply admit you were incapable of get definitions that are based on
verbal_symbolic AND visual_spatial skills, exactly as already given in http://www.internationalskeptics.com/forums/showpost.php?p=7617532&postcount=16470 or http://www.internationalskeptics.com/forums/showpost.php?p=7617572&postcount=16472.

As I already said to The Man, I am not going to discuss on that fine subject with you anymore.

I wish you happy life in your limited verbal_symbolic_only realm.
 
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doronshadmi said:
Nothing was actually taken from the shelf, if one picks things in his\her mind.
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There are surely options attached to the word "picking." There are cases where picking something doesn't mean removal of the object. For example, if you think that one item in a collection is unlike any other, you can indicate so by highlighting the item:

1, 3, 5, 7, 8, 9, 11, 13.

The difference between highlighting and removing is in the size of the collection after the action is taken. I'm not sure how you are going to incorporate this into your axioms. It all started with a bunch of question marks raining on your proposition, such as
C is a set.

For all x in C, if all x in C are picked AND no x can be picked twice, then C is infinite.
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http://www.internationalskeptics.com/forums/showpost.php?p=7593948&postcount=16389

where you defined C as a set, but raised your finger not to pick x twice. I think it was The Man who told you not to worry, coz members of a set don't have duplicates and therefore cannot be picked twice. Since The Man must live real life and navigate through it without getting bruised, he interpreted the verb "pick" the normal way - the way which doesn't lead to the starvation. (Parrot drumsticks! Yummy.) But picking/highlighting changes the situation. If you let C = {1, 2, 3} and set your mind on the only even number in C, then

1st pick/highlight: {1, 2, 3}
2nd pick/highlight: {1, 2, 3}

So how does the picking in your mind translate into your axioms? Remember that highlighting doesn't remove items from the set and therefore has something to say to Mr. Incomplete who owns the set, as alleged by the Axioms.

How about coming up with examples of (finite AND incomplete set) and (infinite AND incomplete set) made by those axioms?
 
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doronshadmi said:
It would have been far more direct of you to simply admit you were incapable of get definitions
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Projection.

...that are based on verbal_symbolic AND visual_spatial skills
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Gibberish.

...exactly as already given in http://www.internationalskeptics.com/forums/showpost.php?p=7617532&postcount=16470 or http://www.internationalskeptics.com/forums/showpost.php?p=7617572&postcount=16472.
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Re-reference to previous evasion, projection, gibberish, and re-reference.

As I already said to The Man, I am not going to discuss on that fine subject with you anymore.
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Evasion.

I wish you happy life in your limited verbal_symbolic_only realm.
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More projection and gibberish.

Well done! I think you nailed them all.
 
 
Please look at the Concluding Remarks about "Chapter 7: What is a Definition?", taken from Prof. James Robert Brown book "PHILOSOPHY OF MATHEMATICS - Contemporary Introduction to the World of Proofs and Pictures"

( http://esotericonline.net/docs/libr...rown - Philosophy.of.Mathematics.Jan.2008.pdf )

Concluding Remarks

The official view of definitions has much to recommend it. It clarified an enormous number of confusions and its imposition on working mathematics was a real advance. But it cannot be completely right. Some concepts (polyhedron) have a history and some theories (graph theory) have multiple representations (set-theoretic and pictorial). The official view cannot cope well with either of these. A quite different approach to mathematical definitions is needed. The question in the title – what is a definition? – remains. It is a wide-open problem.
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doronshadmi said:
http://www.internationalskeptics.com/forums/showpost.php?p=7601080&postcount=16418

http://www.internationalskeptics.com/forums/showpost.php?p=7608536&postcount=16434

http://www.internationalskeptics.com/forums/showpost.php?p=7611837&postcount=16443

http://www.internationalskeptics.com/forums/showpost.php?p=7511706&postcount=16304

http://www.internationalskeptics.com/forums/showpost.php?p=7611749&postcount=16440

http://www.internationalskeptics.com/forums/showpost.php?p=7617532&postcount=16470
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I think you misunderstood. I asked for examples involving natural numbers, coz I used them for my example. Remember that you said "that C is a set." In case someone might not be clear on the difference between the complete finite set and the incomplete finite set, I would appeal to the built-in now_you_see_it_now_you_don't skills and supplement my verbal-only explanation with an example using two sets:

Complete Die Set= {1, 2, 3, 4, 5, 6}
Incomplete Die Set = {1, 3, 5, 6}

and then I would go ahead with the lecture . . .

Expected - Observed => |Complete - Incomplete| > 0.

Since everyone is familiar with natural numbers from everyday life appointments with them, they are well-suited for making up an example. So repeat your axioms and then include the examples as suggested.
 
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epix said:
I think you misunderstood. I asked for examples involving natural numbers,
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It does not matter, natural numbers are collection of distinct objects, and any collection of distinct objects (which are actually "hosted" objects) do not have the power of the continuum of the mathematical "host" space.

What I have just wrote is understood only if verbal_symbolic AND visual_spatial skills are used as a one comprehensive framework.
 
doronshadmi said:
It does not matter, natural numbers are collection of distinct objects, and any collection of distinct objects (which are actually "hosted" objects) do not have the power of the continuum of the mathematical "host" space.

What I have just wrote is understood only if verbal_symbolic AND visual_spatial skills are used as a one comprehensive framework.
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Your axioms don't state which set has the power of the continuum and which doesn't. "C is a set" should apply to all kind of sets and that includes N.

Do you believe that the members of R are not distinct? If it was so then the set theorists wouldn't call R set. So why don't you use the continuum as the source for the examples that would accompany the text of your axioms instead of N?

Your progressive hesitation to answer the requested creates an impression of you are having a difficulty to understand the meaning your own constructs.

As far as the "visual_spatial skills" requirement is concerned: You should at least make an attempt to provide an example in the requested frame of perception and show where the insufficiency lies so that those "visual_spatial skills" need to kick in.
 
epix said:
Your axioms don't state which set has the power of the continuum and which doesn't.
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Epix, if your reply to this post will be still closed under collections of distinct objects, I am not going to continue the discussion with you on this fine subject.

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My axioms are expressed by verbal_symbolic skills, but understood only if also visual_spatial skills are also used.

So ,in order to get the incompleteness of collections of distinct objects (whether they are N or R collections) also visual_spatial skills have to be used in order to get the power of the continuum at the level of the "host" space, which is stronger than any collection of "hosted" spaces on it.

In other words, the two following axioms are undersood only if verbal_symbolic AND visual_spatial skills are used as a one comprehensive framework:

Axiom 1:

If (x in C is picked) AND (everything but x, in C is picked) AND (x can't be picked twice), then C is infinite AND incomplete.


Axiom 2:

If (x in C is picked) AND (everything but x, in C is picked) AND (x can be picked twice), then C is finite AND incomplete.

Once again.

Without using verbal_symbolic AND visual_spatial skills as a one comprehensive framework you can't understand that everything in terms of collection (for example, points) can't reach the power of the continuum of non-local object (for example, a line), and you do not understand it exactly because your visual_spatial skills are not used in addition to your verbal_symbolic skills.

Again, you do not comprehend the inability of collections of distinct objects to have to power of the continuum of the "host" mathematical space (for example: there is no homeomorphism between 0 dimensional space and 1 dimensional space), which is naturally non-local w.r.t the "hosted" collection.

The term "host" or "hosted" is used in order to clarify that the "host" space
is not made of the "hosted" spaces (for example: ______ (a 1 dimensional space) is not made of "_ _ _" or "......" (which are sub-objects) on it.)

Again, the axioms above can't be understood without using also visual_spatial skills, expressed, for example, as:

4297878664_e6288d244a_z.jpg


Also please look at http://www.internationalskeptics.com/forums/showpost.php?p=7587585&postcount=16372.
 
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doronshadmi said:
You don't get it do you? ( http://www.internationalskeptics.com/forums/showpost.php?p=7556387&postcount=16359 ).
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Evidently “you just don’t get it”, as exemplified once again below.

doronshadmi said:
By your verbal_symbolic_only reasoning "AB" is defined in terms of "A,B", "A" or "B" (there is no superposition of identities).
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Doron, by your own assertions there is no superposition in your “superposition of identities”.

doronshadmi said:
By your verbal_symbolic_only reasoning 1 dimensional space is completely covered by 0 dimensional spaces.
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Nope, that is your “verbal_symbolic_only reasoning”, so stop simply trying to posit aspects of your own failed reasoning onto others. Again as already explained to you a 1 dimensional space is completely covered by points simply because there is simply no point on that 1 dimensional space that is not, well, a point. Also as already explained to you a 1 dimensional space is completely covered by other 1 dimensional spaces.
 
doronshadmi said:
The Man and jsfisher,

It is about time to put you in my ignore list.

Bye.
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Doron, you’ve been ignoring us along with just about everything having anything to do with mathematics and self-consistency since long before you started this particular thread. Perhaps you should just consider a blog instead of a discussion forum?
 
doronshadmi said:
Epix, if your reply to this post will be still closed under collections of distinct objects, I am not going to continue the discussion with you on this fine subject.

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So this is your current redress, to just discontinue even your poorly veiled simple pretence of discussion with anyone who does not agree with you? Soon you will only have yourself to discuss your nonsense with. Oh wait, since you can not even agree with yourself you won’t even have that. How fortuitous for you that you are already quite accustom to efficiently lying to yourself on such matters.
 
doronshadmi said:
Epix, if your reply to this post will be still closed under collections of distinct objects, I am not going to continue the discussion with you on this fine subject.
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Yes, your post is a collection of distinct objects called "words," but I don't understand how the set Post can be closed under collection of those words. The terminology "closed under" applies to the operations that the members of a set are subjected to. For example, R is closed strictly under addition and multiplication. You should explain what kind of operation the "collection of distinct object" is, otherwise you could be charged with forceful sodomy performed on juveniles. (The set theory is a relatively young field of mathematics.)
 
The Man said:
Doron, you’ve been ignoring us along with just about everything having anything to do with mathematics and self-consistency since long before you started this particular thread. Perhaps you should just consider a blog instead of a discussion forum?
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That Ignore List is actually a subset, coz there are no duplicate nicknames in JREF. So if that subset comes under the influence of those two Doron's axioms, then the promised action taken by him can have an unexpected result, like he can even PM you.
;)
 
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