Deeper than primes

[doronshadmi]

There is nowhere on the line, whether between two other arbitrary points or not, that does not have a point on it.

Given any arbitrary point along a line, it is distinguished from the rest of the points along that line only if there is an arbitrary smaller AND uncovered line between that point and some arbitrary closer point, which is not that point.

EDIT:

Without this simple fact, there is no more than one and only point along the considered line.

This fine reasoning distinguishes between "permanently closer" (not the considered point) and "closest" (the considered point).

 

[doronshadmi]

Mathematics doesn't support this assertion, Doron. In fact, mathematics contradicts it.

Your reasoning (which you like to call Mathematics) is too weak in order to comprehend http://www.internationalskeptics.com/forums/showpost.php?p=7022911&postcount=14741 .

EDIT:

In other words, your reasoning is not fine enough in order to distinguish between "permanently closer" (not the considered point) and "closest" (the considered point).

 

[epix]

"Brilliant" conclusion epix. I clearly write that a circle or a line can't be a point (and this is a exactly the reason of why the smallest line or circle do not exist), but you, by using your twisted reasoning, get exactly the opposite (1=0).

I don't think your writing on the subject has been crystal clear, otherwise The Man, whom I replied to, wouldn't write

Points still aren’t circles, no matter how much you would like them to be or insist that something is lacking because they aren’t.

Doron:

Wrong, by using Cantor's construction method, one enables to explicitly construct the all possible members of P(S), and because of this fact, one enables to define mapping between these explicit members and the same amount of members, taken to from the set of natural numbers, or any other set with different objects.

Furthermore, the mapping exists between no mapping with P(S) members, and a 1-to-1 and onto with P(S) members, and the degree of mapping is chosen according to one's needs (there is no universality about mapping).

Calm down, Doron. Phrases such as "the mapping between no mapping" may suggest that you write these things under duress.
Surely, you can match the members of any finite power set with natural numbers, but the relationship in question is |S| <--> |P(S)| and not N <--> |P(S)|.

Wrong again epix, since all circles have some curvature > 0 AND < ∞ , then:

...then you should realize that the curvature is redundant to the conclusion you list below. If radius is in R and radius is in (0,∞) and radius is an orthogonal vector, you don't need any curvature to obscure the issue.

1) The largest circle does not exist and as a result, the set of all circles can't completely cover an infinitely long straight line, exactly because such an object has exactly 0 curvature, and as a result it is permanently beyond the range of the set of all circles with different curvatures.

If the magnitude of the radius grows unbound in R, then there obviously can't be the largest circle. DUH.
Your conclusion in (1) doesn't make sense, coz for any point X and r: X(-∞,∞)) = |r|(-∞,∞)

2) The smallest circle does not exist and as a result, the set of all circles can't completely cover an infinitely long straight line, exactly because such a collection do not have an object with ∞ curvature, which is exactly a point (the center point is permanently beyond the range of the set of all circles with different curvatures, which are obviously < ∞ curvature).

The center point of those concentric circles is not in the set. Despite your poor definition, the members of the set are points created by the intersection of circumferences and the straight line on which the center point lies.

 

[zooterkin]

Given any arbitrary point along a line, it is distinguished from the rest of the points along that line only if there is an arbitrary smaller AND uncovered line between that point and some arbitrary closer point, which is not that point.

Says who?

 

[doronshadmi]

I don't think your writing on the subject has been crystal clear, otherwise The Man, whom I replied to, wouldn't write

Doron:

Calm down, Doron. Phrases such as "the mapping between no mapping" may suggest that you write these things under duress.
Surely, you can match the members of any finite power set with natural numbers, but the relationship in question is |S| <--> |P(S)| and not N <--> |P(S)|.

You have missed this part:

... , or any other set with different objects.

...then you should realize that the curvature is redundant to the conclusion you list below. If radius is in R and radius is in (0,∞) and radius is an orthogonal vector, you don't need any curvature to obscure the issue.

If the magnitude of the radius grows unbound in R, then there obviously can't be the largest circle. DUH.
Your conclusion in (1) doesn't make sense, coz for any point X and r: X(-∞,∞)) = |r|(-∞,∞)


The center point of those concentric circles is not in the set. Despite your poor definition, the members of the set are points created by the intersection of circumferences and the straight line on which the center point lies.

epix, again your reasoning ignores the fact that there is no pi at diameter=0 or diameter=∞ states (since you like to use radius instead of diameter, then there is no 2pi at diameter=0 or diameter=∞ states).

Once again you are failing to get my argument about the set of all circles (pi or 2pi must exist) with different curvatures.

It is quite fascinating how your friends here and you can't comprehend such simple facts.

EDIT:

Also you ignore the points\line game (circles are not involved), so please look at http://www.internationalskeptics.com/forums/showpost.php?p=7022911&postcount=14741 .

 

[doronshadmi]

Says who?

Do you really need somebody else, but you, in order to say it?

 

[epix]

Good.

In that case there is an uncovered line between any arbitrary closer pair of points, along any given line.

No, it's not good. In this type of contention, you need to define the term "line," coz

The first class of definitions follows Euclid's approach and consists in defining a line as an abstract primitive object whose properties are defined by a set of axioms. Such systems of axioms have been given by Karl von Staudt, David Hilbert, Giuseppe Peano, Mario Pieri and Alessandro Padoa.

The second definition is presently the most commonly used and relies to coordinate geometry introduced by René Descartes. It consists in defining a line in the Euclidean plane as the set of the points whose coordinates satisfy a given linear equation. More generally, a line in a Euclidean space of dimension n is the set of the points whose coordinates satisfy a given set of n−1 independent linear equations.

According to the second definition, there is no such a thing as an uncovered line between two points p and q, where p≠q.

So define the line to your likeness, to your image, so it shall become uncovered.

 

[jsfisher]

Your reasoning (which you like to call Mathematics) is too weak in order to comprehend http://www.internationalskeptics.com/forums/showpost.php?p=7022911&postcount=14741 .

Nonsense. Your post is easily comprehended. It is nonsense.

EDIT:

In other words, your reasoning is not fine enough in order to distinguish between "permanently closer" (not the considered point) and "closest" (the considered point).

Still making up terminology to cover your ignorance, I see.


How's that bijection coming? Ready to retract your bogus claims about power sets, yet?

 

[zooterkin]

Do you really need somebody else, but you, in order to say it?

To remind you, you stated:

Given any arbitrary point along a line, it is distinguished from the rest of the points along that line only if there is an arbitrary smaller AND uncovered line between that point and some arbitrary closer point, which is not that point.

I was asking if that was something you made up yourself, or if you pinched that nonsense from somewhere else.

ETA: How big do you think a point is?

 

[epix]

epix, again your reasoning ignores the fact that there is no pi at diameter=0 or diameter=∞ states (since you like to use radius instead of diameter, then there is no 2pi at diameter=0 or diameter=∞ states).

I don't see how division by zero could affect the fact that you misdefined the set which is particular to your argument. Btw, "diameter = ∞" is a clear sign of you regarding infinity as a number. You should make an attempt to land forward in the 19th century and call a taxi for the trip to the 21st century.

 

[doronshadmi]

No, it's not good. In this type of contention, you need to define the term "line," coz

According to the second definition, there is no such a thing as an uncovered line between two points p and q, where p≠q.

So define the line to your likeness, to your image, so it shall become uncovered.

A line is not a set of points.

As long as you are unable to get this simple fact, you are closed under the concept of point.

Furthermore, without the existence of a line between any arbitrary closer points, no two distinct points exist.

 

[doronshadmi]

I don't see how division by zero could affect the fact that you misdefined the set which is particular to your argument. Btw, "diameter = ∞" is a clear sign of you regarding infinity as a number. You should make an attempt to land forward in the 19th century and call a taxi for the trip to the 21st century.

I am not talking about numbers.

I am talking about the essential difference between a point (pi does not exist) a line (pi does not exist) and a circle (pi exists).

 

[doronshadmi]

Still making up terminology to cover your ignorance, I see.

No jsfisher, from a closed box you can't see.

 

[doronshadmi]

I was asking if that was something you made up yourself, or if you pinched that nonsense from somewhere else.

Again you are seeking me or somebody else in order to determine your reasoning. Can't you do it by yourself?

ETA: How big do you think a point is?

Exactly 0 size.

 

[jsfisher]

No jsfisher, from a closed box you can't see.

Speaking of things that cannot be seen, how are those bijections coming along? Any progress?

 

[doronshadmi]

Speaking of things that cannot be seen, how are those bijections coming along? Any progress?

Any progress to get the following, jsfisher? :

By using Cantor's construction method, one enables to explicitly construct the all possible members of P(S), and because of this fact, one enables to define mapping between these explicit members and the same amount of members, taken to from any other set with different objects.

Furthermore, the mapping exists between no mapping with P(S) members, and a 1-to-1 and onto (bijection) with P(S) members, and the degree of mapping is chosen according to one's needs (there is no universality about mapping).

 

[jsfisher]

Any progress to get the following, jsfisher? :...

We can get to that, but all in good time. Why do you continue with the evasions? Either you can produce the claimed bijections or you cannot. If you cannot, which does appear to be the case, you should retract the claims.

 

[epix]

I am not talking about numbers.

I am talking about the essential difference between a point (pi does not exist) a line (pi does not exist) and a circle (pi exists).

No, you dropped the pants right here:

Once again you are failing to get my argument about the set of all circles (pi or 2pi must exist) with different curvatures.

You simply hold infinity as a point on the real line, otherwise you wouldn't write "diameter = ∞". According to this identity, pi doesn't exist, but the identity doesn't exist in the first place -- ∞ is not a member of any set of numbers.

As far as the circle with radius=0 is concerned, it's called a "degenerate circle."
http://www.sciencedirect.com/scienc...11d65785545c088be65942f276cd187b&searchtype=a
I can't elaborate much further, coz Rule 12 appealing to civility. (Attack the idea, not the circle.)

For such a circle with circumference and area equaling zero -- 2pi*0=0 and pi*0²=0 respectively -- the curvature is not defined due to c = 1/r where r=0 (division by zero). The circle does have a center point though. So pi is present when you compute the circumference and the area, but it is absent when you want to extract it from circumference/diameter (division with zero). The presence and absence of pi w.r.t. the degenerate circle is covered by the following theorem.

Theorem: Now you see it, now you don't.

 

[zooterkin]

Again you are seeking me or somebody else in order to determine your reasoning. Can't you do it by yourself?

What on earth are you talking about this time? You came up with yet more nonsense about lines uncovered by points; what does that have to do with anyone's reasoning, let alone mine?

 

[The Man]

But they are associated with the set of all circles with different curvatures, where these associations can't completely cover an infinitely long straight line, which is intersected by all the circles of this set.

Again we can define any number of sets that include most, some, none or even all but one of the points on your line, just as we can define any number of sets that include all of the points on your line, the simplest one again being just your line.

Exactly the opposite.

For example let us focused on the line segment case:

The existence of any arbitrary pair of points along a line segment is guaranteed by the existence of an uncovered line between them.

Again please identify at what point of your line segment there is not a point?

Without this uncovered line, the pair is merged into a single point.

What “uncovered line”? You have yet to show any point on any line or line segment that is not a point, your line remains covered and no “pair is merged into a single point”. Your assertion fails as usual.