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Deeper than primes

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N is a subset of R,
Wrong. N is a proper subset of R by traditional math.

But it is not relevant exactly as written below the diagram in http://www.internationalskeptics.com/forums/showpost.php?p=7310450&postcount=15777 , which you can't comprehend.

You've been asked several times to identify at least one positive integer which is not a subset of R,
It is not relevant since |R| points can't completely cover a 1-dimensional element.

You simply can't get http://www.internationalskeptics.com/forums/showpost.php?p=7310040&postcount=15773 .
 
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Why would it not be base 10?


I don't think there's any danger of you being accused of using logic.


It does not need any gibberish added, it has more than enough already.

Your 0.000...1 is an unnecessary and meaningless concept. Its value is the same as, well, the value of 1 - 0.999...

Now we can learn that you do not distinguish between, for example, 0.999...[base 11] and 0.999...[base 10].
 
It is not relevant since |R| points can't completely cover a 1-dimensional element.
The members of R are used to define locations in objects whose dimension is greater or equal to 1. Since the set of positive integers is a subset of R, and according to your idea which suggests that the cardinality of R is insufficient for the task, some positive integers must be missing from the set of reals. That means if you let exist positive integers k and k+2, where k is a natural, then there doesn't exist k+1 as a result of

1. (2k+2)/2

not equalling to

2. k+1

In fact, according to your vision of incompleteness and discontinuity of R, (1) doesn't resolve to any integer. So do the OM algebra to prove it. The "traditional" algebra can easily show that

3. (2k+2)/2 = k+1

and that means positive integers cannot be missing from R. So what is the subset of R that is missing some of its membership?

Out of my unbound kindness, I shall provide you with a way to find out. Just recall what David Hilbert once said.
No one shall expel us from the Paradise that Cantor has created.

The Tree of Knowledge grows by a shallow pond. The fruit is no longer within the arm reach though, but that shouldn't stop you . . .

Oops. Lol. You're too heavy, Doron.
 
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The members of R are used to define locations in objects whose dimension is greater or equal to 1. Since the set of positive integers is a subset of R, and according to your idea which suggests that the cardinality of R is insufficient for the task, some positive integers must be missing from the set of reals.
Wrong.

All the points (where each given point is some R member) between some arbitrary pair of R members, are at their locations and yet all these locations together do not have the magnitude of 1-dimensional element, and this is exactly the reason why there are 1-dimensional elements with different lengths, even if the magnitude of all the considered R members is the same.

Once again, you are invited to use the reasoning of traditional math in order to solve the facts above, by using only a set of points.

In fact, according to your vision of incompleteness and discontinuity of R,...
The incompleteness is the inability of |R| points to have the magnitude of 1-dimensional element.

There is continuity that is fulfilled by the magnitude of 1-dimensional element.

Once again, you simply do not get the non-locality of 1-dimensional element, that no collection of local elements has, for example:

1 - 0.999...[base 10] = 0.000...1[base 10] (where "...1" of 0.000...1 expression is the non-locality of the real-line that is
simultaneously < AND = 1, which is a property that no point (locality) along the real-line has).

Please try again.

Start, for example, by providing a logical solution of the fact that line segments have different lengths even if the cardinality of the the set of points (where a point is the smallest existing element) along them is the same, where by your assertion this set of points (notated as R) completely covers these 1-dimensional elements.
 
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The incompleteness is the inability of |R| points to have the magnitude of 1-dimensional element.
What is it that defines magnitude of 1-dimensional element? What is the unit used to measure different magnitudes?

You failed again to set up a collection of math-related arguments to show that if R is missing some of its members, then at least one of the missing members is an element of Z. Your arguments are not a part of mathematical construction; these are just unsubstantiated declaration, like saying that "points lack the ability to match magnitudes of dimensional objects." When you select one element of R, like natural number 666, it means that the element represents a point 666 cubits, fathoms, furlongs, meters, or any length unit away from element 0. A line segment is not made of points; a line segment is defined by points.

(You have been banned from the Paradise till ∞ A.D., coz the damage you've done to the Tree of Knowledge. God tried to fix the felled tree by "let there be . . ." but it didn't work. So he took a bite of that fruit and figured right away how to re-establish the desired vertical order of particular existence.)
 
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A line segment is not made of points; a line segment is defined by points.
Exactly, and because of that reason the magnitude of the points that define a line segment is not the same as the magnitude of a line segment, or of other words: |R| < |1-dimensional element|

This simple fact enables different lengths of 1-dimensional elements, even if along them there are collections with |R| points.

You failed again to set up a collection of math-related arguments to show that if R is missing some of its members,
You still fail not get it. No point is missing, but because a 1-dimensional element is not made of points, a collection of |R| points can't completely cover it.
 
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Exactly, and because of that reason the magnitude of the points that define a line segment is not the same as the magnitude of a line segment, or of other words: |R| < |1-dimensional element|

This simple fact enables different lengths of 1-dimensional elements, even if along them there are collections with |R| points.
That is a classic doronian gibberish skating on a terminology that the Incas abandoned in 87 B.C. for being no good. Points don't have any magnitude
In elementary mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or – as here – simply a vector) is a geometric object that has both a magnitude (or length) and direction.
coz they are 0-dimensional objects.
You can also check what "magnitude" relates to:
http://en.wikipedia.org/wiki/Magnitude_(mathematics)

You make a comparison between magnitude and cardinality to reach some conclusion of yours, which is comparable to the statement that 20 Watts is more than 8 gallons. Cantor had a yardstick called aleph0 to measure sets with, but you haven't come up with anything close to the rational as a substitute. The content of your toolbox wouldn't fix a toilet seat . . .

You still fail not get it. No point is missing, but because a 1-dimensional element is not made of points, a collection of |R| points can't completely cover it.
Missing points is a necessary consequence of your claim, but since you got yourself so deep into the cesspool of phantasmagoric relationships, you can't see it.

I can take any member of R and place it on the line of infinite length with respect to point 0. That means such a line can accommodate all members that qualify by definition to live in R. Just show me a location on such a line where a point cannot be placed x distance units from point zero where x is taken from R.
 
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That is a classic doronian gibberish skating on a terminology that the Incas abandoned in 87 B.C. for being no good. Points don't have any magnitude

coz they are 0-dimensional objects.
You can also check what "magnitude" relates to:
http://en.wikipedia.org/wiki/Magnitude_(mathematics)

The magnitude of a mathematical object is its size: a property by which it can be compared as larger or smaller than other objects of the same kind;

http://en.wikipedia.org/wiki/Magnitude_(mathematics)
In other words epix you are wrong because according to traditional mathematics |R| is a size (or magnitude) of collection of objects (0-dimensional elements, in this case), which is smaller than the size (or magnitude) of a 1-dimensional element, where Dimension is the property "of the same kind" that enables the comparison.

Missing points is a necessary consequence of your claim,
Wrong epix. Missing points is a necessary consequence of your local-only reasoning that simply can't comprehend the non-locality of 1-dimensional element.

Once again, a collection of 0-dimensional elements along a given 1-dimensional element, has a magnitude that is smaller than the magnitude of the given 1-dimensional element.

You can get this reasoning only if you can get the non-locality of 1-dimensional element w.r.t a collection of local elements like 0-dimensional elements, that has |R| size.

Here is more of the nonsense of traditional math, which simply does not get the results of the co-existence of locality with non-locality, exactly because it gets only the local aspect of this co-existence:

In 1890, Peano discovered a densely self-intersecting curve that passes through every point of the unit square. His purpose was to construct a continuous mapping from the unit interval onto the unit square. Peano was motivated by Georg Cantor's earlier counterintuitive result that the infinite number of points in a unit interval is the same cardinality as the infinite number of points in any finite-dimensional manifold, such as the unit square. The problem Peano solved was whether such a mapping could be continuous; i.e., a curve that fills a space.

http://en.wikipedia.org/wiki/Space-filling_curve

EDIT:

Cardinality is an attempt to measure the size of a mathematical object by ignoring its structure (if it has one), such that Cardinality
is only the number of objects that belongs to this mathematical object.

|R| is the cardinality of the real line, where |R| > 0 only if existing mathematical objects are considered.

But since Cardinality is a measurement of size, which ignores the structure of the measured, we are left only with the minimal property that enables some mathematical element to exist, even as an abstract object.

In this case the minimal property of point's existence (under point\line co-existence) is its locality, where the minimal property of line's existence (under point\line co-existence) is its non-locality.

By understanding this abstract mathematical fact we realize that |R| = the number of all points along 1-dimensional element < |1-dimensional element|.
 
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Cardinality is an attempt to measure the size of a mathematical object by ignoring its structure (if it has one), such that Cardinality
is only the number of objects that belongs to this mathematical object.

How convenient for you to just redefine things as you see fit. Why not just stick with its real definition?
 
How convenient for you to just redefine things as you see fit. Why not just stick with its real definition?

In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
http://en.wikipedia.org/wiki/Cardinality

doronshadmi said:
Cardinality is only the number of objects that belongs to this mathematical object.


No, you wrote this:
Cardinality is an attempt to measure the size of a mathematical object by ignoring its structure (if it has one), such that Cardinality
is only the number of objects that belongs to this mathematical object.

You added all sorts of noise and gibberish, but you cannot tell the difference, can you?
 
The Man you have totally failed to get http://www.internationalskeptics.com/forums/showpost.php?p=7294686&postcount=15740 exactly because your reasoning is stuck under the of the commutativity of AND connective, which clearly has no impact on the strict or non-strict output.

Doron everyone got that post and that you have been chasing your own tail for 20 some odd years, except apparently just you. Also everyone here understands that commutative property of the AND connective is what makes the results strictly the same in spite of changes in ordering about the connective.

Once again, only the strict or non-strict input determines the strict or non-strict output.

Nope, strict outputs were given for all your examples.

You can release yourself from the irrelevancy of the commutativity of AND connective on strict or non-strict result at any time.

Evidently you still can’t release yourself from the irrelevancy of your own nonsense any time soon.


Until this moment it appears that you like very much to push your mind into dead end corners, by running after your own tail.

Once again that is still just you for 20 years now by your own accounts.

It just means that you are unable the understand non-strict values like AB superposition.

Oh I understand the principle of superposition quite well. However since you claim your “superposition” does not involve the principle of superposition it is just you that “are unable the understand non-strict values like AB superposition” and just want to call it a “superposition” without, well, superposition.


"AB" is not some strict name of a variable.

You can call it whatever you want Doron, it changes nothing.

"AB" is superposition of variables, which has no clear determination.

Sure it does it has the clear determination that it is not a superposition of anything. Since your “superposition” emphatically and by your own assertion does not involve the principle of superposition.


“A = True” was your own assertion Doron which means that “AB AND A or A AND AB” simply (and strictly) evaluates to “AB”


The output of "AND A or A AND AB input" is indeterminate because AB input is indeterminate, and once again it is clearly seen that the commutativity of AND connective has no impact on the output.

Nope once again since “A = True” “AB AND A or A AND AB” simply (and strictly) evaluates to “AB”





The Man you take "AB" expression as "B AND A" or "A AND B" and totally miss the understanding that "AB" is the indistinguishably of A;B variables under superposition.

Nope. Your claims of …

“A = True
B = False”

Makes them quite distinguishable and your assertions that your “superposition” does not involve the principle of superposition means you are emphatically asserting no superposition of those variables you distinguished yourself.

So you fail again on both fronts and again simply by your own assertions.

‘Please insert more quarters to play again’

It is not funny that you can't comprehend "AB" expression as superposition.

Actually that’s just you again Doron since you’re the one that specifically claims your “superposition” does not involve superposition. When you can actually comprehend your “superposition” actually involving superposition, please let us know.


Again, try to use inputs that are in superposition, in order to realize that the commutativity or the non-commutativity of the logical connective has no impact on strict or non-strict output.

Nope, by your own assertion your inputs are not in superposition as your “superposition” does not involve superposition. When that changes please let us know.

Your failure to understand "AB" superposition input and its impact on the output (where the commutativity or non-commutativity of a given logical connective has no impact on strict or non-strict output), clearly demonstrates the limitation of traditional mathematics only to strict inputs, of the forms (A [logical connective] A), (B [logical connective] B), (A [logical connective] B), (B [logical connective] B), which are closed under F (1,1).

Your deliberate failure to understand that superposition actually involves, well, superposition is why you have been just chasing your tail for 20 some odd years.

Again “the limitation of traditional mathematics only to strict inputs” is just your ridiculous fantasy as is your “superposition” without superposition.

The Man, you are unable to comprehend, for example, "AB" expression as a superposition of variables, and the impact of superposition on the result.

Doron you are simply unwilling to comprehend the impact of your expressed lack of superposition involved in your so called “superposition”.

You still do not comprehend the simultaneity of superposition, which is naturally unordered, because there are no clear values under superposition, that their order may be considered as insignificant, or not.

Doron you still simply do not wish to comprehend that calling something a “superposition” while claiming it does not involve the principle of superposition just makes your assertions, quite deliberately, nonsensical gibberish.

Nope you have simply exposed your lack of understanding of superposition of variables, where "AB" is an example of such superposition, and it is definitely not a name of some variable.

Well who could have guessed, that the name you gave to your own variable in your “superposition” (which does not involve superposition) now “is definitely not a name of some variable”.



ou can't get that exactly because your reasoning is closed under the particular case of F (1,1).

Again stop simply trying to posit aspects of your own failed reasoning onto others.
 
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