Deeper than primes

[epix]

Cardinality is exactly a measurement unit of the size (or magnitude) of existence.

"In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {2, 4, 6} contains 3 elements, and therefore A has a cardinality of 3."

"Really? I didn't know that. So like {G, o, d} = 3?"

 

[doronshadmi]

Technically and more specifically it is a “1-dim element” defined by (at least) two “0-dim elements”.



Again a line segment (a “1-dim element”) is defined by two points (“0-dim elements”), the absurdities are again and remain entirely yours.

A line segment is a complex result of the linkage of at least 1-dim element and two 0-dim elements.

Again, you do not undrstand that only 0-dim elements can't define a size > 0.

 

[epix]

Just take to account that that S = 2(a+b+c+d+...) does not have a sum.

We'll get to it. The a, b, c, d, ... line segments are defined by the position of the baselines in the triangle, so we'll see how they look like, despite your claim that a+b doesn't have a sum. If 1+2 have a sum (like 3?) then a+b should have a sum as well.

 

[jsfisher]

A line segment is a complex result of the linkage of at least 1-dim element and two 0-dim elements.

Again, you do not undrstand that only 0-dim elements can't define a size > 0.

Again, you do not understand that stuff you simply make up isn't necessarily true.

 

[The Man]

"In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {2, 4, 6} contains 3 elements, and therefore A has a cardinality of 3."

"Really? I didn't know that. So like {G, o, d} = 3?"

Well a bird (or cardinal) in the hand is worth two in the bush. So since “OM” is “not less than” Hand/Bush “interaction”, giving Doron not just ‘the bird’ but three ‘magnitudes of existence’ in units of ‘the bird’.

 

[doronshadmi]

"In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {2, 4, 6} contains 3 elements, and therefore A has a cardinality of 3."

"Really? I didn't know that. So like {G, o, d} = 3?"

I do not care about the traditional notion of Cardinality because by OM it is extended to measure directly Emptiness (that has no predecessor) Fullness (that has nor successor), and any level between them (that has predecessor AND successor).

 

[doronshadmi]

We'll get to it. The a, b, c, d, ... line segments are defined by the position of the baselines in the triangle, so we'll see how they look like, despite your claim that a+b doesn't have a sum. If 1+2 have a sum (like 3?) then a+b should have a sum as well.

Finitly many positive values have a sum.

Infinitly many positive values do not have a sum.

 

[The Man]

A line segment is a complex result of the linkage of at least 1-dim element and two 0-dim elements.

Again you simply don’t understand that the “linkage” is specifically a line segment being defined by points and that “linkage” is evidently only “complex” for you.

Again, you do not undrstand that only 0-dim elements can't define a size > 0.

Again you, apparently intentionally, do understand that you simply claiming something does not make it a fact and that points can and do define a line segment is a fact.

 

[doronshadmi]

Again, you do not understand that stuff you simply make up isn't necessarily true.

You are invided to provide the proof that an addition of infinitely many 0 sizes is resulted by a size > 0.

 

[doronshadmi]

Again you simply don’t understand that the “linkage” is specifically a line segment being defined by points and that “linkage” is evidently only “complex” for you.

Call it in any name you like, it does not change the fact that any amount 0-dim elements can't be a 1-dim element.

By avoid what you call "linkage", please define two 0-dim elements with different values.

 

[jsfisher]

Call it in any name you like, it does not change the fact that any amount 0-dim elements can't be a 1-dim element.

And yet, Mathematics bends to neither your whim nor your misunderstanding, and lines and line segments continue to consist of nothing but points.

By avoid what you call "linkage", please define two 0-dim elements with different values.

Oh, come on, Doron. Now you are just being silly. The simple mechanism of taking a point's location as a value is sufficient.

 

[The Man]

Call it in any name you like, it does not change the fact that any amount 0-dim elements can't be a 1-dim element.

What name do you think I called you?

Your assertions do not change the fact that two points define a line segment.

By avoid what you call "linkage", please define two 0-dim elements with different values.

Well, since you’re the one claiming points don’t define a line segment, you’ll have to do that.

 

[doronshadmi]

And yet, Mathematics bends to neither your whim nor your misunderstanding, and lines and line segments continue to consist of nothing but points.

Here we go, by jsfisher limited reasoning 1-dim does not exist unless there is a collection of 0-dim elements.

Oh, come on, Doron. Now you are just being silly. The simple mechanism of taking a point's location as a value is sufficient.

It is simple if a 1-dim element is also used by this mechanism.

 

[doronshadmi]

What name do you think I called you?

Your assertions do not change the fact that two points define a line segment.




Well, since you’re the one claiming points don’t define a line segment, you’ll have to do that.

Your definition do not change the fact that at least 1-dim element AND more than one 0-dim element, are involved.

 

[epix]

Finitly many positive values have a sum.

Infinitly many positive values do not have a sum.

If the sum of the positive values diverges then the value of the sum approaches infinity; if the sum converges, then it's value doesn't exceed a certain number called "limit." That limit is considered the value of the summation. It works that way in calculus where integration is basically a summation.

 

[jsfisher]

Here we go, by jsfisher limited reasoning 1-dim does not exist unless there is a collection of 0-dim elements.

If you wish to develop an alternate geometry without points, knock yourself out. I bet you can't, though. You have been unable to define even the simplest of your made-up vocabulary, so it would be impossible for you to build anything more complicated.

It is simple if a 1-dim is also used by this mechanism.

So what? That wasn't the challenge. Can't you follow even your own conversation?

The 5 year olds are giggling loudly now, Doron. Please stop. They really need to focus on their lessons.

 

[epix]

If you wish to develop an alternate geometry without points, knock yourself out.

You know, that Organic Mathematics reminds me Topology -- the other Doron's pointless attempt to modernize math. It just doesn't go anywhere, as many have already found out

 

[epix]

What name do you think I called you?

Your assertions do not change the fact that two points define a line segment.

What name? You know very well what name. Don't make me to remind you.

In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point.

What a ride. LOL.

 

[doronshadmi]

If you wish to develop an alternate geometry without points, knock yourself out.

You still don't get it isn't it jsfisher?

We are not talking here about Geometry, but about Locality and Non-locality as fundamental qualities of any given mathematical branch.

A point is nothing but the minimal geometrical aspect of Locality, and a line is nothing but the minimal geometrical aspect of Non-locality.

By following this fundamental notion a line is not a collection of points, a plane is not a collection of points or lines, a volume is not a collection of planes, lines or points, etc … ad infinitum.

If linked they are resulted by complexities.

 

[jsfisher]

You still don't get it isn't it jsfisher?

I get far more than you can comprehend.

We are not talking here about Geometry, but about Locality and Non-locality as fundamental qualities of any given mathematical branch.

And, yet, you cannot define any of your terminology. The best you can do is misuse established terms.

A point is nothing but the minimal geometrical aspect of Locality, and a line is nothing but the minimal geometrical aspect of Non-locality.

It is amusing to me that, according to you, you are not talking about geometry, but nevertheless here you are talking about geometry.

By following this fundamental notion a line is not a collection of points, a plane is not a collection of points or lines, a volume is not a collection of planes, lines or points, etc … ad infinitum.

Nonsense. You have failed completely to distinguish your line segments from the normal ones. Points do a splendid job of covering your line segments, despite your contradictions and protestations claiming it isn't so.