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Deeper than primes

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doronshadmi said:
Please give some concrete example where I do not answer to some question, along this thread.
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jsfisher asked you:"

Again I ask: Can we expect to see your bijections between the elements of {} and its power set and the elements of {A} and its power set any time soon, or have you given up on this fool's errand?"

A straight answer would be giving the bijections or saying they do not exist. Unless of course you do not understand what a bijection is.
 
doronshadmi said:
The simplest state of awareness is an unbounded awareness, which is stronger than any awareness that is bases no thoughts.

In other words, you are not aware of the simplest state of awareness.
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Talking to yourself again. Probably an old habit.
 
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sympathic said:
jsfisher asked you:"

Again I ask: Can we expect to see your bijections between the elements of {} and its power set and the elements of {A} and its power set any time soon, or have you given up on this fool's errand?"

A straight answer would be giving the bijections or saying they do not exist. Unless of course you do not understand what a bijection is.
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A complete answer was given also in http://www.internationalskeptics.com/forums/showpost.php?p=7069202&postcount=14948 .
 
sympathic said:
Talking to yourself again. Probably an old habit.
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I made some typo mistakes so here it is again:

The simplest state of awareness is an unbounded awareness, which is stronger than any awareness that is based on thoughts.

In other words, you are not aware of the simplest state of awareness, probably an old habit.
 
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doronshadmi said:
A complete answer was given also in http://www.internationalskeptics.com/forums/showpost.php?p=7069202&postcount=14948 .
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Certainly not. Another example of you talking to yourself.

From wikipedia:

In mathematics, a bijection, or a bijective function, is a function f from a set X to a set Y with the property that, for every y in Y, there is exactly one x in X such that f(x) = y. It follows from this definition that no unmapped element exists in either X or Y.
Alternatively, f is bijective if it is a one-to-one correspondence between those sets; i.e., both one-to-one (injective) and onto (surjective).

You provided no such mapping (function). If you wish to communicate to people here you must reply in context to the question. You were asked to give a bijection. You provided none. The fact that you think what you blabbered is a bijection is not relevant - a bijection has a well defined meaning. Failing to comply with that meaning and responding in another direction is an example of you talking to yourself. Nothing prevents from you to do so in an internet thread, in the real world this would be considered a behavioral deficiency. This is probably why you can not/did not undergo any formal education.
 
sympathic said:
From wikipedia:

In mathematics, a bijection, or a bijective function, is a function f from a set X to a set Y with the property that, for every y in Y, there is exactly one x in X such that f(x) = y. It follows from this definition that no unmapped element exists in either X or Y.
Alternatively, f is bijective if it is a one-to-one correspondence between those sets; i.e., both one-to-one (injective) and onto (surjective).
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Again:

I show an explicit construction method of all P(S) members, without missing any one of them, which enables to define a function of one-to-one and onto between all P(S) members and all S members (where S is a proper subset of P(S)) exactly as shown, for example, between N members and the members of the set of even numbers (which is a proper subset of N), or between the members of set Q and set N (where N is a proper subset of set Q).

In general, I show the consistency of Dedekind’s definition of infinite sets on all infinite sets, without exceptional.

jsfisher's and your reasoning is too weak in order to comprehend http://www.internationalskeptics.com/forums/showpost.php?p=7066349&postcount=14908 exactly because you are running in circles inside a closed box and scratch each others back by your weak reasoning.
 
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doronshadmi said:
Again:

I show an explicit construction method of all P(S) members, without missing any one of them, which enables to define a function of one-to-one and onto between all P(S) members and all S members (where S is a proper subset of P(S)) exactly as shown, for example, between N members and the members of the set of even numbers (which is a proper subset of N), or between the members of set Q and set N (where N is a proper subset of set Q).

In general, I show the consistency of Dedekind’s definition of infinite sets on all infinite sets, without exceptional.

jsfisher's and your reasoning is too weak in order to comprehend http://www.internationalskeptics.com/forums/showpost.php?p=7066349&postcount=14908 exactly because you are running in circles inside a closed box and scratch each others back by your weak reasoning.
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Let's take it one step at a time. I'll ask a short question (and I expect a short straight answer). What are the elements of {}?
 
doronshadmi said:
...<gibberish mercifully snipped>...
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Again I ask: Can we expect to see your bijections between the elements of {} and its power set and the elements of {A} and its power set any time soon, or have you given up on this fool's errand?
 
doronshadmi said:
In other words, you do not understand (yet) the following:

http://www.mathacademy.com/pr/prime/articles/cantor_theorem/index.asp is a clear example of Cantor's theorem as a proof by contradiction, which leads to contradiction if one tries to define mapping between an explicit P(S) member and S member, because of the construction rules of the explicit P(S) member (the member of S must be AND can't be a member of the explicit P(S) member, according to the construction rules of the explicit P(S) member, under Cantor's theorem).
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Ah, so RAA is a tautology again is it? When did that change?

Or is there a superposition between RAA being and not being a tautology?
 
This bit of wrongness really needs to be attacked. It is yet one more example of Doron failing miserably to understand simple words and phrases:

doronshadmi said:
http://www.mathacademy.com/pr/prime/articles/cantor_theorem/index.asp is a clear example of Cantor's theorem as a proof by contradiction
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No, it is not. Cantor's Theorem is a theorem. Doron has been corrected on this before, but he appears unable to understand the difference between a theorem and its proof.

...which leads to contradiction if one tries to define mapping between an explicit P(S) member and S member
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Very, very wrong. Even ignoring the use of "explicit" to no benefit, the claim is completely bogus. In the standard proof for Cantor's Theorem a contradiction develops by assuming a bijection exists be all of the members of P(S) and all of the members of S, not just one from each as Doron states.

...because of the construction rules of the explicit P(S) member (the member of S must be AND can't be a member of the explicit P(S) member, according to the construction rules of the explicit P(S) member, under Cantor's theorem).
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And this may well be the core of wrongness. Doron has convinced himself Cantor's Theorem is a construction method for P(S) using some set of bijections that he even admits do not exist.

Doron also continues to be quite proud of himself for is claimed method to build P(S) given P(S).

That pretty much explains what Doron considers achievement.
 
doronshadmi said:
The smallest uncovered line segment exists only in the case of finite amount of segments.
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Nope once again your “uncovered line segment” is your de-facto smallest line segment otherwise it could be covered by still smaller line segments or just points.

doronshadmi said:
You simply demonstrate your inability to get the existence of an infinite amount of ever smaller sub-line segments (which are not completely covered by any possible amount of the smallest elements), exactly because you are forcing a notion taken from finite collections, on infinite collections.
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You again simply demonstrate your inability to get the that it is only the fact that all of your line segments are completely covered by points which guarantees “an infinite amount of ever smaller sub-line segments”.

Again please show some location(s) on any of your “ever smaller sub-line segments” that is not and can not be covered by (a) point(s). It does matter how many times you repeat your “uncovered” nonsense when you can’t show anything is uncovered or define your smallest line segment such that it is uncovered (which would give you a desecrate space). It is your usual self-contradictory problem Doron, you want an “infinite amount of ever smaller sub-line segments” and no “smallest line segment” (a continuous space) but also want there to be some “uncovered line segment” (a desecrate space). So as usual you remain the staunchest opponent of just your own notions.
 
doronshadmi said:
Yet there are smaller line segments between any given amount of points that are located between any arbitrary closer pairs of points, where no one of the smaller line segments is reducible to a point.

Because of this irreducibility, no amount of points completely covers the amount of the irreducible line segments, which exists between them, ad infinitum ...
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Read again the definition of line segment:
In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points.
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This definition is good for any geometric construction in Euclidean space, coz no inconsistencies ever existed. But if you send the definition into the set theory, then a question arises regarding the term "every point" The formal definition using the set theory language simply puts "every point" within the end points a and b and rigourously reminds us about the difference between the open and close intervals. And that's all. The definition deals with location but not with the density of the points -- it doesn't define the term "every point" in this respect.

You are trying to show that the collection of points rules out such point organization where the points are adjacent to each other. In this respect, you and Georg Cantor are right, even though both arguments use a different form of proof. But the definition of line segment doesn't necesarilly mean that all those points within a and b are adjacent. If they are not, then there is a space between them. However, this space can be occupied by another point and when it happens another sub-segment or defined space is created, which can be rented by another point and this repetive process continues infinitely.

You seem to argue that there is a space created in that process that a point cannot occupy, thus screwing up the "full coverage." In other words, there exists a real number r which is not divisible by d, where as d≠0 and r>0. That number r is the length of one of the sub-segments created by the infinite repetitive process that you use all the time. See, additional points in the space created by those end points a and b are created by division and not by addition, even though you add points into the space.

So it comes down for you to prove that there exist r and d, such as

r/d = 0 where d≠0 and r>0

The Wiki definition of the line segment seems to refer to the above and means that there is no sub-space in the space bounded by points a and b that a point couldn't occupy. If you think on contrary, let me know.
 
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The Man said:
Again please show some location(s) on any of your “ever smaller sub-line segments” that is not and can not be covered by (a) point(s). It does matter how many times you repeat your “uncovered” nonsense when you can’t show anything is uncovered or define your smallest line segment such that it is uncovered (which would give you a desecrate space).
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I made an attempt to specify your request here
http://www.internationalskeptics.com/forums/showpost.php?p=7070158&postcount=14974
but I'm not a hundred percent sure that it runs in sync with what you want from Doron.
 
punshhh said:
How long(its measurement) would the 1 Drag be?

I used "unit of movement" to describe the distance between the the original position of the 0 dimensional object and its position after the "1 Drag".
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Why didn't you use "unit of length" instead? For example, 1 meter is the base unit of length in the International System of Units.

How long would 1 Drag be?

Well, this is the same as if you asked what is the temperature of 1 meter. The unit of movement 1 Drag got nothing to do with distances, as much as the unit of inhalation 1 drag got nothing to do with volume. When a moving object comes to rest and then starts to move again, then the process is measured in Drags -- it's a measure of occurrence. For example 10 Drags/s means that an object came to rest and again accelerated ten times in one second.
 
epix said:
I made an attempt to specify your request here
http://www.internationalskeptics.com/forums/showpost.php?p=7070158&postcount=14974
but I'm not a hundred percent sure that it runs in sync with what you want from Doron.
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It is not about what I want from Doron but what Doron wants from Doron, which demonstrably goes against what Doron wants from Doron. However, in my opinion that is purely intentional as contradiction appears to be the only consistency of this “notions”. He often refers to Gödel's incompleteness theorems and I suspect he thinks he’s giving up consistency to get completeness but ends up quite obviously with neither. So it is just a fool’s bargain on his part.
 
The Man said:
He often refers to Gödel's incompleteness theorems and I suspect he thinks he’s giving up consistency to get completeness but ends up quite obviously with neither. So it is just a fool’s bargain on his part.
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His peculiar neural activity seems to be influenced by "external sources," as his various associations help to spot very clever coincidences that would otherwise go unnoticed. Btw, wouldn't you be inspired by the circumstances of some "points" not being accounted for -- the now-you-see-it-now-you-don't kind -- to develop a theorem of incompleteness?

http://www-history.mcs.st-and.ac.uk/Mathematicians/Godel.html

http://www.time.com/time/magazine/article/0,9171,990621,00.html
 
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