Deeper than primes

[The Man]

Nope. Again, the continuum is not a collection, the continuum is at least a 1-dim space, and no collection of 0-dim spaces along it reaches it (or "completely covers it" if we are using your jargon).

Again show the point(s) in your "1-dim space" you claim is not covered and can not be covered by (a) point(s)?

 

[doronshadmi]

.000...0001 is impossible. It is an invalid "number" that can not exist according to the use of "..." and the definition of infinity.

First, you write down an infinite number of zeroes (which is impossible in itself), then you finally decide to place a 1. But you can't, because you must instead write infinity more zeroes. Even more impossible. You can never write a 1 because no matter how many infinities-worth of zeros you've written, you must always write infinity more zeroes.

There will never be a 1. There can never be a 1.
When attempting to answer "1 - 0.999... = x", the x has the same chance of having a 1 as a binary number has of having a 2.

Hi ehcks and welcome.

.000...0001 is impossible as long as you get "...0001" as some exact place (or exact location).

But "...0001" is a notation for non-locality, exactly as a 1-dim element can be at-once in more than one location, which is a property that no local 0-dim element like a point has.

 

[ehcks]

Hi ehcks and welcome.

.000...0001 is impossible as long as you get "...0001" as some exact place (or exact location).

But "...0001" is a notation for non-locality, exactly as a 1-dim element can be at-once in more than one location, which is a property that no local 0-dim element like a point has.

Well, ok? A location is designated by a point. A line is designated by the infinitely many points, and so infinitely many locations, that make it up.

 

[doronshadmi]

Again show the point(s) in your "1-dim space" you claim is not covered and can not be covered by (a) point(s)?

Do you see the "...1" of "0.000...1" expression?

It is not covered by points, and it is at-once at the limit point and at some arbitrary point, which is arbitrary closer to the limit point.

No arbitrary point has the property of "...1".

 

[doronshadmi]

Well, ok? A location is designated by a point. A line is designated by the infinitely many points, and so infinitely many locations, that make it up.

EDIT:

A 1-dim element can be at-once in more than one location.

Please show some 0-dim element that has this property.

 

[ehcks]

A 1-dim element can be at-once in more than one location.

Please show some 0-dim element that has this property.

But that's what I just said doesn't happen.

A point has only its own location. A line is infinitely many points and so has infinitely many locations.

 

[doronshadmi]

But that's what I just said doesn't happen.

A point has only its own location. A line is infinitely many points and so has infinitely many locations.

EDIT:

We are talking about infinitely many locations, where each location is different than the rest of locations.

These multiple differences can't exist if only the local property of 0-dim is considered.

 

[ehcks]

EDIT:

We are talking about infinitely many locations, where each location is different than the rest of locations.

These multiple differences can't exist if only 0-dim is considered.

But a line isn't 0-dimensional. A point is 0-dimensional.
A 1-dimensional line is made of infinitely many 0-dimensional points.
A 2-dimensional plane is made of infinitely many 1-dimensional lines.
A 3-dimensional space is made of infinitely many 2-dimensional planes.

A line exists in multiple locations because a location is a point, and a line has infinitely many points.

 

[jsfisher]

http://www.internationalskeptics.com/forums/showpost.php?p=7105665&postcount=15176

Your agreed transfinite system is a joke.

Also you can't comprehend the range between no-mapping and bijection as it found according to one's useful needs between the general form {a,b,c,d,...} and the general form {{},{a},{b},{c},{d},...,{a,b,c,d,...}}.

Doron, it does you no good to substitute one wrongness for a different one. You said that the cardinality of a set and its power set were the same. You said a bijection exists between the members of any set and its power set. These are very wrong things you said. You have been shown simple counter-examples which even a moron could understand. But you willfully don't understand; instead, you hide from your wrongness with topic shifts and insults.

This, however, does nothing to diminish you being completely and utterly wrong about this and most other things.

 

[The Man]

Do you see the "...1" of "0.000...1" expression?

No doubt we all have at this point.

It is not covered by points, and it is at-once at the limit point and at some arbitrary point, which is arbitrary closer to the limit point.

It has been 'covered' by the 'point' that your "expression" is simply a self contradictory notation.

No arbitrary point has the property of "...1".

So your "...1" just isn't a point, is it a line segment then? Perhaps a collection of points in a Neighbourhood either way Doron, geometry’s still got you covered.

 

[epix]

The claim that a line (or a line-segment) is totally covered by points is equivalent to the claim that a line (or a line-segment) is no more than a collection of points.

But there is no such a claim. What you see squirming in the cradle is Claim Doronshadmi -- your daughter conceived under the influence of all-collapsing neural outburst radiation that took five trillion light years to reach the earth.

edit:

Read the definition of line segment.

A line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its end points. Depending on how the line segment is defined, either of the two end points may or may not be part of the line segment.

It just says that there is no location between the end points A and B where a point couldn't be placed. See, the distance between A and B is

|A - B| = c

If you let c in R⁺, then there exists p such as c ≥ p > 0 for which

1. c - p = d1 (d1 in R⁺)

2. c/p = d2 (d2 in R⁺)

So you place the points of division and/or subtraction on the line segment, but you don't reduce the length or divide the segment -- just leave them there -- and repeat the process with different p's that are the members of uncountably infinite set. In each case, there will always be a result to c - p_i and c/p_i. In other words, a line segment is divisible and reducible at any location between A and B, coz it contains every point . . .

 

[doronshadmi]

But a line isn't 0-dimensional. A point is 0-dimensional.
A 1-dimensional line is made of infinitely many 0-dimensional points.
A 2-dimensional plane is made of infinitely many 1-dimensional lines.
A 3-dimensional space is made of infinitely many 2-dimensional planes.

A line exists in multiple locations because a location is a point, and a line has infinitely many points.

A 1-dim element is not made of any amount of collection of 0-dim elements.

The minimal existence of collection of multiple distinct locations is the result of the co-existence of two building-blocks that are not transformed into each other under the co-existence.

A 0-dim element is used as the minimal expression of the local property of this co-existence and a 1-dim element is used as the minimal expression of the non-local property of this co-existence.

By generalization, any given dimension > previous given dimensions, is non-local with respect to them, where the previous given dimensions < a given dimension are local with respect to it, under the co-existence.

Without the co-existence of Locality and non-locality, a collection of previous dimensional degree is collapsed into a single element of the considered previous dimensional degree, and without the previous dimensional degree any current dimensional degree is not measurable, whether this measurement is local (like pi, for example) or non-local (like 3.14...[base 10], for example), where 3.14...[base 10] < pi.

Here is a rigorous diagram of the co-existence of locality and non-locality at the basis of collections of local and non-local number systems (the local property is expressed by vertical lines and the non-local property is expressed by horizontal lines):

In this particular diagram 0 or 1 are local numbers, and 0.111...[base 2] or 0.222...[base 3] are non-local numbers,
such that 0 < 0.111...[base 2] < 0.222...[base 3] < 1, where 0.111...[base 2] < 1 by 0.000...1[base 2] and 0.222...[base 3] < 1 by 0.000...1[base 3].

Also 0.222...[base 3] < 0.000...1[base 2] by (1/3)/(1/2) proportion upon infinitely scale levels ... ad infinitum.

A line exists in multiple locations because a location is a point, and a line has infinitely many points.

A collection of more than one distinct location, is the result of at least the co-existence of 1-dim AND 0-dims.

 

[doronshadmi]

Doron, it does you no good to substitute one wrongness for a different one. You said that the cardinality of a set and its power set were the same. You said a bijection exists between the members of any set and its power set. These are very wrong things you said. You have been shown simple counter-examples which even a moron could understand. But you willfully don't understand; instead, you hide from your wrongness with topic shifts and insults.

This, however, does nothing to diminish you being completely and utterly wrong about this and most other things.

Let us close this subject as follows:

In terms of finite collections, where only the members of S and the members of P(S) are considered |S| < |P(S)|.

This is not the case if S is an infinite set, or the range of possible mappings between the general form {a,b,c,d,...} and the general form {{},{a},{b},{c},{d},...,{a,b,c,d,...}} is considered.

 

[doronshadmi]

No doubt we all have at this point.



It has been 'covered' by the 'point' that your "expression" is simply a self contradictory notation.



So your "...1" just isn't a point, is it a line segment then? Perhaps a collection of points in a Neighbourhood either way Doron, geometry’s still got you covered.

The Man, any collection of more than one element, is the result of Locality/Non-locality co-existence.

Neighbourhood is clearly based on Locality/Non-locality co-existence and not vice versa.

 

[doronshadmi]

It just says that there is no location between the end points A and B where a point couldn't be placed.

Yet no two different points exist at the same location, and only non-locality between them guarantees their distinct locations, no matter what arbitrary scale level is used.

In order to get this simple beauty, you have to grasp the essential difference between smaller and smallest under co-existence.

 

[doronshadmi]

No doubt we all have at this point.

Furthermore, if relation is considered as non-locality and element as locality, then "=" is the non-local aspect and "A" is the local aspect of "A=A" expression.

 

[doronshadmi]

In other words, a line segment is divisible and reducible at any location between A and B, coz it contains every point . . .

Wrong.

No smaller element is reducible into smallest element, along a line segment.

 

[doronshadmi]

So your eaxmples are different orderings of the same set? By all means please show how the ordering is the same in both of your examples.

They are not the same exactly because one case of set S is ordered and the other case of set S is not ordered.

They are the same only if order has no significance.

Again generalize simply doesn’t mean what you apparently would like it to.

Dido.

Ah, so your crap is a direct result of some traumatic “box” experience you had? That makes more sense than anything you have claimed so far

Now we discover that you can't get that the "box" is your experience.

Again there are differences between the letters A and B, but no interval as a result. That you simply want your “interval” to be your “difference” and the opposite of “nothing between” is only your problem.

You simply do not understand the result of the proposition "there is nothing between A and B", and this misunderstanding is some problem of your boxes reasoning.

Again stop simply trying to posit aspects of your own failed reasoning, and I guess traumatic “box” experiences, onto others.

Since you are using only context-dependent reasoning, and can't get cross-contexts reasoning, the traumatic “box” experiences is entirely yours.

Once again you do not understand that it is simply your “proposition”.

Yet your boxes reasoning can't comprehend it.

So far the result has simply been your self contradictory nonsense.

So far your boxes context-dependent reasoning reflects its own self contradictory nonsense, when it is used to comprehend cross-contexts reasoning.

Again stop simply trying to posit aspects of your own failed reasoning, and I guess traumatic “box” experiences, onto others.

Again, your boxes reasoning can't comprehend it.

What? That even makes less sense than you do normally, even just on its own let alone in relation to what was asked.

Since you simply decided not to even try to answer the question, I’ll have to ask it again.

Please show where I claim that smaller and smallest are not in co-existence.

What is “up to” me? To point out the quotation marks around what you said?

Again, please show where I claim that smaller and smallest are not in co-existence.

In both cases there is a set and the remarks were specifically in regard to the membership of those sets. Are your sure you even know where you are looking?

In one case 1 as the considered member, and in the other case there is no member at all.

Again you are unable to show your so called “interval” for the many differences already noted.

Without the interval A and B are actually one and only one thing. You still get interval only in terms of metric space, as some kind of space gap between A and B.

Still you demonstrate your inability to get even just your own notions, by not answering simple and direct questions.

Again, please show where I claim that smaller and smallest are not in co-existence.

Show where I have made such a claim.

Please read and reply about the end of http://www.internationalskeptics.com/forums/showpost.php?p=7138399&postcount=15276 .

 

[epix]

Originally Posted by epix
In other words, a line segment is divisible and reducible at any location between A and B, coz it contains every point . . .

Wrong.

No smaller element is reducible into smallest element, along a line segment.

Read again what I wrote and find any reference to the word "smallest." You commit this atrocity of inventing bogus arguments en masse -- I can see it when you reply to others.

Your claim regarding the relation between a set and its subsets speaks for the presence of extraordinary wrongness that dwells within you and it continues to manifest itself in other venomous forms, as it must.

I think you should recant and cast away the burden of wrongdoing that blinds your eye and darkens your mind. Others did it



so why don't you?

 

[doronshadmi]

Read again what I wrote and find any reference to the word "smallest."

The word "point".