Deeper than primes

[doronshadmi]

Show me a line OR a line segment with no points along it.

By your question we can clearly see that you do not distinguish between a buiding-block (endless line) and a complex (a line segment, which is a line AND two points).

 

[doronshadmi]

The evidence doesn't support your conclusion.

evidence? not even in your dreams.

 

[zooterkin]

An endelss line,

You mean just a line?

where only 1-dim is considered (in this case we have a non-local building-block).

You mean if you ignore the points, there aren't any?

 

[doronshadmi]

You mean just a line?


You mean if you ignore the points, there aren't any?

All you have is to get the difference between building-block and complex.

EDIT: Any given single n-dimension is a building-block, any complex is the result of the linkage between more than a single building-block.

 

[zooterkin]

All you have is to get the difference between building-block and complex.

EDIT: Any given single n-dimension is a building-block, any complex is the result of the linkage between more than a single building-block.

As far as I can tell, you have said there are no points (0-dimensional objects) on a line if you only consider 1-dimensional objects.

If that's not what you meant, please clarify what you mean by saying there are no points on a line.

 

[doronshadmi]

As far as I can tell, you have said there are no points (0-dimensional objects) on a line if you only consider 1-dimensional objects.

If that's not what you meant, please clarify what you mean by saying there are no points on a line.

The answer was fully given in http://www.internationalskeptics.com/forums/showpost.php?p=5267276&postcount=6584.

 

[zooterkin]

Please see http://www.internationalskeptics.com/forums/showpost.php?p=5267262&postcount=6583

 

[doronshadmi]

Zooterkin,

The whole problem with the world is that fools and fanatics are always so certain of themselves, because they can't get incompleteness, randomness, redundancy and uncertainty as legitimate properties in addition to certainty.

Do you understand the difference between building-block and complex?

 

[zooterkin]

Zooterkin,

The whole problem with the world is that fools and fanatics are always so certain of themselves, because they can't get incompleteness, randomness, redundancy and uncertainty as legitimate properties in addition to certainty.

Quite.

Do you understand the difference between building-block and complex?

Yes. What relevance does this have to whether there are points on a line?

 

[doronshadmi]

Quite.


Yes. What relevance does this have to whether there are points on a line?

Do you understand that a line segment is a complex?

Do you understand that any given n-dimension is a building-block (independent of any other dimension accept of itself)?

 

[zooterkin]

Do you understand that a line segment is a complex?

A complex what?

Do you understand that any given n-dimension is a building-block (independent of any other dimension accept of itself)?

An n-dimension what?

 

[doronshadmi]

A complex what?



An n-dimension what?

A complex is the result of the linkage between more than a one building-block.

For example:

An endless 1-D (known also as an endless line) is a building-block.

A 0-D (known also as a point) is a building-block.

A line segment (finite or infinitely many) is a complex (it is the result of both 1-D and 0-D).

 

[doronshadmi]

Jsfisher and The Man


You have missed http://www.internationalskeptics.com/forums/showpost.php?p=5264271&postcount=6538.

 

[jsfisher]

Now you do not get the first part of http://www.internationalskeptics.com/forums/showpost.php?p=5267138&postcount=6571 .

No, I got the first part just. As a proof, it fails miserably. It could be called a "proof by assumption", but I'll leave it as an exercise for you to come up with the formal name for that particular fallacy.

Try again. Show that there exists a place along a line that isn't covered by a point.

And while you are at it, what makes something n-dimensional? Your previous evasions were non-responsive to the question. Try again.

 

[jsfisher]

Jsfisher and The Man


You have missed http://www.internationalskeptics.com/forums/showpost.php?p=5264271&postcount=6538.

You shouldn't assume, Doron. Historically, you haven't done very well with your assumptions. This is no exception.

 

[doronshadmi]

Try again. Show that there exists a place along a line that isn't covered by a point.

Try again. Please show exactly (by not missing even a single point) that there are infinitely many distinct points along an endless line (where in your case "endless line" = "line").

If you really understand the meaning of "endless" you have no problem to understand that no matter how many points there are, there is always an uncovered ray beyond them (we get an infinite extrapolation).

The same holds in the opposite direction (which is symmetric to infinite extrapolation), there is an infinite intrapolation between any given segment and a point.

In both cases no proof is needed because both cases are axiomatic.

what makes something n-dimensional?

In order for something to be considered as n-dimensional, it has to be an existing atom, such that it is not made by any other thing that is not itself.

Any non-atomic state is a complex, such that at least two atoms are linked.

A line segment is an example of a complex thing, where 0-D and 1-D are linked

(It is already explained in http://www.internationalskeptics.com/forums/showpost.php?p=5267434&postcount=6592).

 

[doronshadmi]

You shouldn't assume, Doron. Historically, you haven't done very well with your assumptions. This is no exception.

This time please read http://www.math.princeton.edu/~nelson/papers/warn.pdf (http://en.wikipedia.org/wiki/Edward_Nelson)

 

[jsfisher]

This time please read http://www.math.princeton.edu/~nelson/papers/warn.pdf (http://en.wikipedia.org/wiki/Edward_Nelson)

Why? Is there some point you misunderstand it to be making that you think important? Please, give us your critique of the short communication.

 

[zooterkin]

Try again. Please show exactly (by not missing even a single point) that there are infinitely many distinct points along an endless line (where in your case "endless line" = "line").

If you really understand the meaning of "endless" you have no problem to understand that no matter how many points there are, there is always an uncovered ray beyond them.

 

[jsfisher]

Try again. Please show exactly (by not missing even a single point) that there are infinitely many distinct points along an endless line (where in your case "endless line" = "line").

You made the claim in contradiction to standard Mathematics. The responsibility falls to you to show a line isn't covered completely by points.

If you really understand the meaning of "endless" you have no problem to understand that no matter how many points there are, there is always an uncovered ray beyond them (we get an infinite extrapolation).

Were that true, you should have no trouble identifying such a ray.

You keep harping on this endless qualifier, too. Are you saying a line segment is covered completely by points?

The same holds in the opposite direction (which is symmetric to infinite extrapolation), there is an infinite intrapolation between any given segment and a point.

Gibberish.

In both cases no proof is needed because both cases are axiomatic.

More proof by assumption, I see. Upon what set of axioms in Mathematics do you base this bogus claim?

In order for something to be considered as n-dimensional, it has to be an existing atom, such that it is not made by any other thing that is not itself.

You are still evading the question. What property does a circle have that makes it 1-dimensional? What property does a sphere have that makes it 2-dimensional? For what k is a torus k-dimensional? Or, more generally...

What makes something n-dimensional?