Deeper than primes - Continuation

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Please look at this quote
Our main point, after all, is that definiteness-about-truth does not follow for free from definiteness-about-objects and that one must say some thing more about it.
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which closes http://arxiv.org/pdf/1312.0670v1.pdf article (also see http://nylogic.org/talks/satisfaction-is-not-absolute), written by Joel David Hamkins (http://jdh.hamkins.org/) and Ruizhi Yang (http://at.yorku.ca/cgi-bin/abstract/cbgg-31).

OM does exactly this, it is not focused only on the considered objects (the localities), but also considers the non-local common ground that enables variety of comparisons, relations etc. among the local objects of a given muitiverse (as explained, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9827757&postcount=3600).
 
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As predicted, doron starts generating other gibberish to avoid dealing with the latest conundrum he found himself in. Not gonna fly, sorry.

So, how about that definition of "set size", doron?
 
laca said:
As predicted, doron starts generating other gibberish to avoid dealing with the latest conundrum he found himself in. Not gonna fly, sorry.
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Fly, no. Flounder, yes.

So, how about that definition of "set size", doron?
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You mean that thing that gave all those crazy results even though he never quite finished it? That thing for which he then started generating other gibberish to avoid dealing with the then latest conundrum he found himself in?

The circle remains unbroken.
;)
 
doronshadmi said:
You are absolutely right, and since this is the case, there is bijection between set x and y.

In terms of comparison if there is a function from a given y member to a given x member, than there is also the inverse function from this given x member to this given y member, so this is not the case that there is no inverse function in y = x^2 expression (as you wrongly claim in http://www.internationalskeptics.com/forums/showpost.php?p=9824635&postcount=3568).
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Wrong and backwards, both.

Let X be the set of positive integers.
Let Y the set of reals.
Let f be a function from X to Y where f(x) = x^2.

Clearly, f is an injection and therefore |X| <= |Y|. Also, clearly, f has no inverse function.
 
doronshadmi said:
Thank you for supporting my claims about verbal_symbolic-only reasoning.
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I was just showing you an easier way to generate gibberish that can get published. It is more coherent and structured than yours as others pointed out so the failure is all yours again.
 
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Wow Doron, your reading comprehension skills are the same as your math skills.

doronshadmi said:
Since Traditional Mathematics does not use a function without an inverse, it is tuned to get only |N|=|N|.
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Little 10 Toes said:
I'm getting tired of your assertions without any proof. Please provide direct proof that "traditional Mathematics does not use a function without an inverse".

<snip garbage>

I always love how you say something about a set isn't equal to itself, start doing some sort of table or graphic and yet never start the set at the same starting point.

I've pointed it out to you before. Yet you continue to make the same mistake.
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realpaladin said:
Doron will fail, because y=x^2 is a function without an inverse.

Or, if you want a more elaborate explanation: http://www.sosmath.com/algebra/invfunc/fnc1.html
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Looky!!! realpaladin has provided a function without an inverse!!!

doronshadmi said:
Little 10 Toes said:
I'm getting tired of your assertions without any proof.
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EDIT:

The non-locality of ____ w.r.t . (___ is at AND beyond the one and only one position of . along it) or the locality of . w.r.t ____ (. is at one and only one given position along ____) is an axiom, which means it does not need any proof.

<SNIP>
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Can you notice that I stated that "Please provide direct proof that 'traditional Mathematics does not use a function without an inverse'."?

You must have since you misquoted me twice. I also noticed you never answered the question. How typical.

doronshadmi said:
realpaladin said:
Doron will fail, because y=x^2 is a function without an inverse.

Or, if you want a more elaborate explanation: http://www.sosmath.com/algebra/invfunc/fnc1.html
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<Full quote used>

Please demonstrate how this function is used as a mapping between members of sets.

Please be aware that I am using a function as a mapping between members of sets, where instead of domain and codomain a non-local common ground is used among the member, as explained in http://www.internationalskeptics.com/forums/showpost.php?p=9823863&postcount=3563 and http://www.internationalskeptics.com/forums/showpost.php?p=9824985&postcount=3569.
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Your claim is that "traditional Mathematics does not use a function without an inverse". realpalidin has shown you a function without an inverse. You are now questioning about mapping functions. A mapping function is still a function. Why are you shifting the goal posts?

Next/Same issue:

Little 10 Toes said:
Your last post does not match anything to what I said. You have decided to invent yet another term that you don't need to use. When you are comparing two sets why aren't you starting with the first element of the sets?
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doronshadmi said:
EDIT:


You have asked about proofs, but axioms do not need proofs.
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Wow doron. Not only did you not read what I said, but you misunderstood it as well. Where did I say proofs? Where did I ask about proofs?
It is not used by verbal_symbolic-only reasoning that understands thing only in terms of locality.

This is not the case with verbal_symbolic AND visual_spatial reasoning which enables to deal with the relations among locality and non-locality, and I did not invent it in this page so this is not another term, but it is an improved explanation of the relations among locality and non-locality, which can be understood only by posters that think in terms of abstract verbal_symbolic AND visual_spatial reasoning.


Take, for example, the following mapping among sets with bounded amount of members:

Code: 
{1,2,3,4,5}
 ↓ ↕ ↕ ↕ ↕ 
  {1,2,3,4}

As you can see, I can start from any place (the first,not the first,last) and get the same result, exactly because the size of sets with bounded amount of members is well-defined.
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Wonderful, but all of your previous examples have been with infinite sets. Why are you using finite sets?

And yes you did create a new term "common ground". You also made, for no reason, a silly little grid.

The same approach (the first, not the first) is used among sets with unbounded amount of members, but since they have no last members, the result is |N| = OR not= |N|, or in other words, unlike in the case of sets with bounded amount of members, in the case of sets with unbounded amount of member (whether it is one and only one set, or not) I do not get the same results by using the first or not the first. In other words the size of sets with unbounded amount of members is not well-defined, for example:


Code: 
{1,2,3,4,5,...}
 ↓ ↕ ↕ ↕ ↕ 
  {1,2,3,4,...}

OR

Code: 
{1,2,3,4...}
 ↕ ↕ ↕ ↕ 
{1,2,3,4,...}
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And you've just done it again. Why are you comparing the exact same set but not using the same elements? Your original un-edited post contained this as the last paragraph
The same approach (the first, not the first) is used among sets with unbounded amount of members, but since they have no last members, the result is |N| = OR not= |N|, or in other words, unlike in the case of sets with bounded amount of members, sets with unbounded amount of member (whether it is one and only one set, or not) do not have well-defined size.
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Lets look at another post:
doronshadmi said:
In addition to my previous post (http://www.internationalskeptics.com/forums/showpost.php?p=9825141&postcount=3574), please look at this comparison, that is done among one and only one set, which is the set of all natural numbers.

Code: 
            |{1,2,3,4,...}|
      ↑ ↑ ↑ ↑ ↕ ↕ ↕ ↕ 
|{...,7,5,3,1,2,4,6,8,...}|

As you can see the set of all natural numbers does not necessarily have a first member (in addition to not having last member), so in this case there are members that have functions without an inverse, which prevent the bijection from N into itself.
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Your purposeful listing of the set is what is causing you problem giving you your "solution". Why didn't you use the set of {..., 25, 20, 15, 10, 5, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, ...,}? It would have made the same amount of sense and would have given you more elements.

And which set of natural numbers are you using? Most people like things in order so the set starts with one. Just because a set starts with something doesn't mean that it's not infinite.

Here is an example of a set with unbounded amount of members, that is compared with itself on the common ground (no domain and codomain are used here):

<more snip using the set of natural numbers starting a 1 and a made up set>


By using the common ground (which its horizontal aspect is distinction, and its vertical aspect is comparison among distinct objects, where both distinction and comparison are non-local w.r.t the given objects) we do not use domain and codomain, because the common ground is the one and only one domain for all comparisons among all the distinct objects.

This common ground is not the Cartesian X/Y grid, as used, for example, by realpaladin in its y=x^2 expression, but it is the common ground of the relations among locality and non-locality (which is not restricted to Geometry or Metric space).

More details about the common ground are given in http://www.internationalskeptics.com/forums/showpost.php?p=9823863&postcount=3563.
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Yes, more details. Didn't have enough time to go back and re-edit any of your posts? And you made up the term "common ground".
 
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Little 10 Toes said:
Most people like things in order so the set starts with one. Just because a set starts with something doesn't mean that it's not infinite.
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Little 10 Toes said:
And you made up the term "common ground".
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Little 10 Toes, here is a simple explanation, which is using abstract visual_spatial AND verbal_symbolic reasoning

I'll use only expressions that are already used by Traditional Mathematics, but I'll give them new interpretations, which lead to new results that are not known (yet) by traditional mathematicians.


The axiom of Existence:

Given the outer "{" and "}", they are exit with respect to the void ("") between them.

From this axiom we deduce that {} is defined in terms existence\void relations.



The axiom of Nonlocality:

Given the outer "{" and "}", they are non-local with respect to the members ("...") between them.

From this axiom we deduce that any amount of existing members ("...") is local with respect to the outer "{" and "}".

{} means that the outer "{" and "}" are undefined in terms nonlocality\locality relations.

Yet {} is defined in terms existence\void relations.



The axiom of Objectivity:

The outer "{" and "}" are the objective aspect of {...} expression.

From this axiom we deduce that ... is the subjective aspect of {...} expression.

{} means that the outer "{" and "}" are undefined in terms objectivity\subjectivity relations.

Yet {} is defined in terms existence\void relations.



The axiom of Universe:

{...} is universe in case that there is one and only one copy for each member.

From this axiom we deduce that multiverse is the case that there is more than one copy for each member.

(B.T.W by using this axiom, we are able to understand the difference between the members of, for example, {1,{1}} universe, such that the first member is not necessarily a member of other members of that universe).


N = {1,2,3,4,...} or in other words, N is a universe.

In this case only |N|=|N| holds.

K = {N,N} = {{1,2,3,4,...}, {1,2,3,4,...}} which means that K is a multiverse (known also as multiset).

In this case |N|=|N| OR |N|¬=|N| hold in case that functions without an inverse are also used.

J = {1,2,3,4}

L = {J,J} = {{1,2,3,4}, {1,2,3,4}}

In this case only |J|=|J| holds in spite of the fact the L is a mutliverse.


It is well-known that multiset is a generalization of set, and so is the case among universe and multiverse, multiverse is a generalization of universe.


But both cases are based on the notion of Nonlocality AND Locality. where Nonlocality is the objective aspect of {...} expression and Locality is the subjective aspect of {...} expression.

Moreover, non-locality is the common ground domain for universe or multivariate , so we do not need to use anymore the terms domain and codomain.
 
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I'd like to focus on the axioms Doron has proffered. For reference, here is his post with only the axioms included; the rest of his text has been omitted so we can concentrate on just the axioms:

doronshadmi said:
..
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Ok, would anyone care to comment on Doron's schema?
 
jsfisher said:
Clearly, f is an injection
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It means that there is a function from some X member to some Y member, for example:

...
X member → Y member
...

In that case it is clear that also the inverse function ← holds, as follows:

...
X member ← Y member
...

Generally if one enables to go from a to b, one also enables to go back (to return) from b to a.

A function without an inverse is simply f(a) that does not return anything.
 
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doronshadmi said:
It means that there is a function from some X member to some Y member, for example:

...
X member → Y member
...

In that case it is clear that also the inverse function ← holds, as follows:

...
X member ← Y member
...

Generally if one enables to go from a to b, one also enables to go back (to return) from b to a.

A function without an inverse is simply f(a) that does not return anything.
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Ok, at least I can understand this (I think), but it is a pretty radical re-definition of inverse.
 
jsfisher said:
Ok, would anyone care to comment on Doron's schema?
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I could give more detailed comments, but the big ones for me are these two:

1. The axioms are not about sets; they are about set notation. We have axioms about what to call the curly brackets, and about what to call what goes inside. Nothing about sets.

2. The axioms just tell us which bits of undefined terminology apply to notation. I don't see anything one could derive from these axioms. Brackets are objective? Ok. Brackets are the universe? Ok. Now what?
 
BenjaminTR said:
Ok, at least I can understand this (I think), but it is a pretty radical re-definition of inverse.
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But think about how much easier it is for Doron to be critical of something if he gets to redefine what it is!
 
BenjaminTR said:
Ok, at least I can understand this (I think), but it is a pretty radical re-definition of inverse.
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It is the simplest conditions of comparison.

One condition enables to go between a and b

The other condition can't go between a and b simply because there is only a.
 
BenjaminTR said:
1. The axioms are not about sets; they are about set notation.
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The axioms provide the fundamental terms that enable sets, or in other words, sets are one of the possible results of these axioms. The notations can be replaced by other notations, but the abstract verbal_symbolic AND visual_spatial reasoning (the notions) remains.

BenjaminTR said:
2. The axioms just tell us which bits of undefined terminology apply to notation.
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It is defined only if one uses his\her abstract verbal_symbolic AND visual_spatial reasoning.

BenjaminTR said:
I don't see anything one could derive from these axioms.
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Only if you ignore what is expressed after the axioms, in post http://67.228.115.45/showpost.php?p=9830197&postcount=3609.
 
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doronshadmi said:
It is the simplest conditions of comparison.

One condition enables to go between a and b

The other condition can't go between a and b simply because there is only a.
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And this is basic ORM (Object Relation Mapping)...

Will there ever be anything original this side of your demise, Doron?

I mean, you give things different words and use convoluted ways of achieving things the rest of humanity already did before you were born...
 
BenjaminTR said:
Ok, at least I can understand this (I think), but it is a pretty radical re-definition of inverse.
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He says nothing more complicated than:

- If there is a result, there is a result and we can shower it with words.

- If there is no result, there is no result and we call it without an inverse.

Or stated more simply:

- If there is a relation between two (or more) entities, we always say there is an inverse, otherwise we say there is no inverse.

Nothing new here.
 
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realpaladin said:
- If there is a relation between two (or more) entities, we always say there is an inverse, otherwise we say there is no inverse.

Nothing new here.
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My claim that f(a) without any result is still considered as a function, and this claim is rejected by traditional mathematicians as "no function at all".

The terms "no function at all" is too strong, and by following such approach, we wrongly conclude that, for example, the following sets have the same amount of members (the same finite cardinality):

Code: 
{1,2,3,4,5}
 ↕ ↕ ↕ ↕ 
{1,2,3,4}

This wrong result is corrected only by the following mapping

Code: 
{1,2,3,4,5}
 ↕ ↕ ↕ ↕ ↓
{1,2,3,4}

where also a function with no inverse ("without any result", in your words) is also used.

(B.T.W the order of the members in the sets above, has no impact on the cardinality of these sets).
 
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doronshadmi said:
My claim that f(a) without any result is still considered as a function, and this claim is rejected by traditional mathematicians as "no function at all".
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No it is not. You are the only one claiming that.

The whole concept of limit (which I tried to have you understand, but which you never could) is based on this.

Actually on the fact that the limit is the *inverse* of 'no function at all'.

Why do you keep making claims about traditional mathematics based on wrong conceptions?

And what does it matter if traditional mathematics is wrong; it produces harmony, beauty and peace, whereas Doronetics, as proven by this thread, only produces bickering, dissent and strife.
 
doronshadmi said:
So you are aware of it and still claim that y = x^2 has no inverse.

Please explain in details how exactly y = x^2 has no inverse.

Again, I am still waiting.
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What has mathematical inverses to do with ORM???

Keep meandering Doron, it only makes you look sillier...
 
Doron, let me help you with the y=x^2 "conundrum"...

If you plot it as a graph (i.e. visualize it) you will get a clue... use your visual reasoning Doron.

Failing that... here is another clue: the root of which integer is a negative?

The detailed proof you ask for is so risibly simple that it is taught to 13-year olds...
 
realpaladin said:
the root of which integer is a negative?
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Your understanding of no inverse function is based on the inability to find a solution for the root of negative integer in the universe of integers.

I am talking about the more fundamental level of comparison between members of sets, and at this fundamental level if there is a function from a to b, there must be also the inverse function from b to a.
 
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realpaladin said:
Or stated more simply:

- If there is a relation between two (or more) entities, we always say there is an inverse, otherwise we say there is no inverse.
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Which means that f(a) without any result (no inverse form b to a, simply because there is no b) is still considered as a function.

realpaladin said:
Nothing new here.
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I agree with you, but traditional mathematicians reject f(a) as a type of function.
 
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Is it fun for you, doron, to show with each post you make just how clueless and incompetent you are?
 
doronshadmi said:
Your understanding of no inverse function is based on the inability to find a solution for the root of negative integer in the universe of integers.

I am talking about the more fundamental level of comparison between members of sets, and at this fundamental level if there is a function from a to b, there must be also the inverse function from b to a.
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Really?

Well, for the current example, it was explicitly stated that f(x) = x^2 was a mapping from the positive integers to the reals. The function is injective.

So, Doron, what pray tell is the inverse function for that? You know, a function that does the reverse mapping from the reals to the positive integers.

You needn't describe the full function. The inverse for 0 will suffice. Remember to check your work. f-1(0) must be in the domain of f and f(f-1(0)) must equal 0.

And remember, too, the context is Mathematics, not the screwy realm of doronetics where you take arbitrary departures from normal meaning.
 
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JSFisher asked you a question. My signature is mine too (ab)use, so, in keeping in spirit with your childishness, neenerneenerneener...
 
doronshadmi said:
Which means that f(a) without any result (no inverse form b to a, simply because there is no b) is still considered as a function.


I agree with you, but traditional mathematicians reject f(a) as a type of function.
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Too funny! Repeating a clear explanation of your own work and then using more complicated and grammarily botched up sentences to do so.
 
doronshadmi said:
Your understanding of no inverse function is based on the inability to find a solution for the root of negative integer in the universe of integers.

I am talking about the more fundamental level of comparison between members of sets, and at this fundamental level if there is a function from a to b, there must be also the inverse function from b to a.
Click to expand...

No Doron the liar, you were not. You were simply saying that in traditional mathematics there were no functions without an inverse.

Both JSFisher and I have given an example (one function, two different examples, both correct in traditional mathematics).

The only proper way to get out of this one is to concede that *your* definition of inverse has nothing to do with the traditional mathematical definition of inverse and hence both can not be compared.
 
jsfisher said:
Well, for the current example, it was explicitly stated that f(x) = x^2 was a mapping from the positive integers to the reals. The function is injective.
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EDIT:

Good, so by using this function please give some explicit example:

Some_positive_integer → some_real.

If you do that, you simply can't avoid some_positive_integer ← some_real.

That is how the fundamental level of comparison works.
 
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doronshadmi said:
EDIT:

Good, so by using this function please give some explicit example:

Some_positive_integer → some_real.

If you do that, you simply can't avoid some_positive_integer ← some_real.

That is how the fundamental level of comparison works.
Click to expand...

Actually, this is all that is needed to convince anyone that you have not even your own work in check.
 
realpaladin said:
The only proper way to get out of this one is to concede that *your* definition of inverse has nothing to do with the traditional mathematical definition of inverse and hence both can not be compared.
Click to expand...

Traditional_mathematical_definition_of_inverse ↔ OM_definition_of_inverse

Well, they are comparable even if they are different.
 
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