Deeper than primes

[doronshadmi]

Whatever.

We are all still in awe, though, because you have perfected a method to construct a power set given the power set as a starting point. Well done!

You miss the simple fact, which is:

Definition 1: A systematic construction method of an infinite set does not omit any member of the considered set.

Definition 1 is equivalent to the existence of the considered infinite set (it is a tautology).

Definition 2: By definition 1, for any systematically constructed infinite set, there is a bijection between its members and the members of any arbitrary infinite proper subset of it.

 

[doronshadmi]

Again that is just your self imposed limitation and once again concentric circles where the center point in not a point on your meets that limitation. Also the first of those circles that intersects your line will do so only at one point (a tangent). The rest will get your pairs. a point of your, well, line. Again please learn some basic geometry.

Even if the set of all circles is defined by consider also the difference of its angle and/or position upon infinitely many dimensional spaces, still this collection does not have the smallest or largest circle, and as a result there is discontinuity between all circles and all points, or between a all circles and and all dimensional spaces.

 

[epix]

You miss the simple fact, which is:

Definition 1: A systematic construction method of an infinite set does not omit any member of the considered set.

The power set of an infinite set is a set that includes an infinite collection of infinite sets as well as an infinite collection of finite sets. It is something that you've proved to be beyond your imagination. Hence your 1-dim. Definition 1.

 

[jsfisher]

You miss the simple fact, which is:

Definition 1: A systematic construction method of an infinite set does not omit any member of the considered set.

Definition 1 is equivalent to the existence of the considered infinite set (it is a tautology).

Definition 2: By definition 1, for any systematically constructed infinite set, there is a bijection between its members and the members of any arbitrary infinite proper subset of it.

No, these are not definitions; and the first is a tautology, and the second neither follows from the first nor is it true. I do note you have shifted the goal posts a bit by sliding in the word, infinite, though.

Be that as it may, it is still trivial to produce as output a set that is provided as input. I continue to be impressed by how loudly you tout this particular feat of yours.

And how is that bijection between {A} and {{}, {A}} coming along? Still nothing? Maybe an even easier example would be in order: How about the set {} and its power set {{}}? What would be a bijection between the members of those two sets?

 

[The Man]

It does not matter.

1) This first circle is omitted from the rest of the circles that get the pairs, so there is a pair of points that does not cover the line, simply becuse there are no two circles with the same curvature in the set of all circles with different curvatures.

"This first circle is omitted from the rest of the circles"? So your set of all circles of different curvatures does not include all circles of different curvatures?

2) Your arbitrary first circle is not the smallest and not the largest circle of the collection of all circles with different curvatures, so nothing was changed by your "tangent trick".

Certainly it is not "the smallest and not the largest circle of the collection of all circles" but as I said it is the first one that intersects your line without being centered on your line. It's no trick but simply a tangent. Again please learn some basic geometry.

In other words, you still have to learn Set theory and Geometry, before you deal with:

http://www.internationalskeptics.com/forums/showpost.php?p=6993998&postcount=14607

http://www.internationalskeptics.com/forums/showpost.php?p=6998970&postcount=14629

or

http://www.internationalskeptics.com/forums/showpost.php?p=6999117&postcount=14631

Nope, that's just you. Please learn some math and geometry then perhaps you can deal with them yourself.

 

[epix]

Even if the set of all circles is defined by consider also the difference of its angle and/or position upon infinitely many dimensional spaces, still this collection does not have the smallest or largest circle, and as a result there is discontinuity between all circles and all points, or between a all circles and and all dimensional spaces.

Doron, the set of all (in the infinite sense) concentric circles can be defined as A|x in R₊ where x is radius. So the set is uncountable. Remember? The diagonal proof? If the set is defined as A|x in Q₊, the set is countable. Just define the vision of yours.

 

[doronshadmi]

"This first circle is omitted from the rest of the circles"? So your set of all circles of different curvatures does not include all circles of different curvatures?

The Man, you still do not know the meaning of: "The set of all circles with different curvatures".

1) Each member of this set has a unique curvature, so if one of the curvatures is used as a tangent, it is not used as one of the centered points, and we get two places along the line, which are not covered by the intersecting points of the circle with the unique curvature that is already used as a tangent.

2) The set of all circles with different curvatures (where pi=circumference/diameter holds) does not have the smallest or the largest circles, so anyway the associated points with the set of all circles with different curvatures, are discontinuous w.r.t the center point (total curvature, where pi=circumference/diameter does not hold) and w.r.t the line (total non-curvature, where pi=circumference/diameter does not hold), or in other words, the set of all these intersecting points, does not completely cover an infinitely long straight line.

 

[jsfisher]

The Man, you still do not know the meaning of: "The set of all circles with different curvatures".

The fact that it is without meaning might be a factor in that. The rule for set membership must be deterministic. This so-called set would need to contain one and only one circle of unit curvature, but which one? The rule doesn't say, so "the set of all circles with different curvatures" is gibberish.

Then again, it is also clear Doron has concocted his own meaning for the term, curvature, but no one is surprised by this.

 

[doronshadmi]

Doron, the set of all (in the infinite sense) concentric circles can be defined as A|x in R₊ where x is radius. So the set is uncountable. Remember?

No, the whole notion of countable\uncountable sets is a mambo jambo wrong reasoning.

Furthermore, let us change our game.

We take a finitely long straight line.

We can locate a point at each end of it, but these two points do not cover that finitely long straight line.

Actually, any additional point between the extreme endpoints is resulted by more lines with end points, etc. ad infinitum, where the points are actually different than each other exactly because, given any scale level, there is an uncovered line between any closer pair of points, along the finitely long line.

 

[doronshadmi]

The rule for set membership must be deterministic. This so-called set would need to contain one and only one circle of unit curvature, but which one?

Simply nonsense.

All is needed is the fact that all circles are different than each other by their curvature, that's all.

 

[jsfisher]

Simply nonsense.

All is needed is the fact that all circles are different than each other by their curvature, that's all.

...except they are not. All unit circles have exactly the same curvature, that being 1.


ETA: How are those bijections coming along? One between {A} and {{},{A}}, and another between {} and {{}}.

 

[ehcks]

I thought all circles had the same curvature. If you measure the tangent of any number of different sized circles at the same arc, the slopes are all equal. Isn't that what curvature means?

 

[jsfisher]

I thought all circles had the same curvature. If you measure the tangent of any number of different sized circles at the same arc, the slopes are all equal. Isn't that what curvature means?

The curvature of a circle is the reciprocal of its radius.

 

[ehcks]

The curvature of a circle is the reciprocal of its radius.

I'm thinking of something else entirely, then. Thanks though.

 

[jsfisher]

I'm thinking of something else entirely, then. Thanks though.

Perhaps you are not. Curvature can also be expressed in terms of not the slope, but the rate of change of the slope.

 

[ehcks]

Perhaps you are not. Curvature can also be expressed in terms of not the slope, but the rate of change of the slope.

That's what I'm trying to say. If you read the change of slope of the tangents by moving around the circle by degrees and not distance, the rate of change of the slope is always the same.

I'm not good at describing this.. That sentence is even hard for me to read.

The change in slope per 1 degree rotation is the same, regardless of the radius?

 

[doronshadmi]

...except they are not. All unit circles have exactly the same curvature, that being 1.

Nonsense again:

----------------------------------------

By the new game (which is no related to circles) any additional point between the extreme endpoints of a given line segment, is resulted by more lines with end points, etc. ad infinitum, where the points are actually different than each other exactly because given any scale level, there is an uncovered line between any closer pair of points (the closest pair of points does not exist exactly becuse there is always an uncovered line between them) along the finitely long line.

 

[jsfisher]

By the new game....

You power of non sequitur continues. The adults were talking about circle curvature.

 

[doronshadmi]

You power of non sequitur continues. The adults were talking about circle curvature.

The adults are wrong about the set of all circles with different curvature degrees because they ignore the difference.

How easy is to be an ignorant adult, isn't its jsfisher?

_________________________________________________

The curvature of the circles has to be compared with a straight line or with a point, in order to distinguish between all circles' different curvatures, but we already know that the adults reasoning is packed within a box.


--------------------------------------------------------


As for the new game, the adults are ignorant about it too.

 

[jsfisher]

The adults are wrong....

You continuing to make stuff up doesn't make the adults wrong.