0d Lines and Circles

[wtf]

You cannot get one from many zero length points simply because there is an infinite number of them

How do you account for the length of the unit interval then?

By the way I was very impressed by your use of large sized fonts. 1995 was a great year for web design.

[surreptitious57]

How do you account for the length of the unit interval then

The unit interval is composed of zero length points and so it cannot ever be longer than zero
That does not magically change just because there happens to be an infinite number of them

[Eodnhoj7]

How do you account for the length of the unit interval then

The unit interval is composed of zero length points and so it cannot ever be longer than zero
That does not magically change just because there happens to be an infinite number of them

Actually it can be composed of infinite points if there are infinite lines.

The unit interval is a fractal of one line, the unit interval can be composed of further fractals as well.

Wtf is still wrong....

[wtf]

How do you account for the length of the unit interval then

The unit interval is composed of zero length points and so it cannot ever be longer than zero
That does not magically change just because there happens to be an infinite number of them

The unit interval is the interval on the real line between 0 (inclusive or not doesn't matter for us) and 1 (likewise). If you took analytic geometry in high school you know that its length is 1. If not, you can take my word for it. For example the Euclidean distance between the point 0 and the point 1 in the real numbers is |1 - 0| = 1.

But then again don't they teach the real line in first year high school algebra (Algebra I in the US I think) to ninth graders, 14 year olds? Did you miss all this? Genuinely curious as to how someone could deny that the length of the unit interval is 1. Did you just miss high school algebra? No shame in it I suppose but that's the only explanation for your erroneous belief. I know this forum's a bit of an alternate math universe, but still.

It's a bit of a mystery out a one-dimensional line segment of length 1 can be made out of zero-dimensional points each of length zero. But there it is.

[Atla]

Ehh.. Zero times anything is still zero, and the length of the unit is 1. However you simply can't create a 1-dimensional mathematical object from adding 0-dimensional mathematical objects.

The saying that a line is 'composed' of points only means that wherever you look on the line, you can assign a number to it. It doesn't mean that it's literally composed of 0d points.

[Eodnhoj7]

Ehh.. Zero times anything is still zero, and the length of the unit is 1. However you simply can't create a 1-dimensional mathematical object from adding 0-dimensional mathematical objects.

The saying that a line is 'composed' of points only means that wherever you look on the line, you can assign a number to it. It doesn't mean that it's literally composed of 0d points.

It means the line is composed of multiple lines not different than a group of particles form another particle.

The 0d point is formless, it is nothing or void. If you say it exists you are saying multiple forms exist.

[Eodnhoj7]

How do you account for the length of the unit interval then

The unit interval is composed of zero length points and so it cannot ever be longer than zero
That does not magically change just because there happens to be an infinite number of them

The unit interval is the interval on the real line between 0 (inclusive or not doesn't matter for us) and 1 (likewise). If you took analytic geometry in high school you know that its length is 1. If not, you can take my word for it. For example the Euclidean distance between the point 0 and the point 1 in the real numbers is |1 - 0| = 1.

But then again don't they teach the real line in first year high school algebra (Algebra I in the US I think) to ninth graders, 14 year olds? Did you miss all this? Genuinely curious as to how someone could deny that the length of the unit interval is 1. Did you just miss high school algebra? No shame in it I suppose but that's the only explanation for your erroneous belief. I know this forum's a bit of an alternate math universe, but still.

It's a bit of a mystery out a one-dimensional line segment of length 1 can be made out of zero-dimensional points each of length zero. But there it is.

That is your conclusion.."it is a bit of a mystery"? What are you a f"""ing mystic now? That is just saying "our measurements our made up and we only believe them because we built so much on these assumptions". It is a gravity fallacy....mass of information does not necessitate the information is correct.

There is no point 1 on the unit interval as you begin quantifying 0's and equating them to 1. It is a contradiction unless 1=0, which it does, but standard math does not accept it. So according to standard math the 1 is the line itself.

The distance between 0's necessitates any two points as having a length, thus infinite points is to say infinite 1d lines.

The unit interval is thus composed of further number lines as lines in themselves. It is composed of fractals that are lines in themselves and fractions that when viewed individually are whole numbers.

Thus each unit interval shows a progression of positive numbers approaching zero, where each unit interval can be observed as a number line in itself...thus each unit interval is a proof all number lines are approaching zero.

[Atla]

It means the line is composed of...

Here, have a cookie.

[Eodnhoj7]

It means the line is composed of...

Here, have a cookie.

So a line segment, as a unit interval, is not composed of fractals/fractions as 1/2,1/3,1/4...etc?

So 1 is not a "set" of fractions?

What are you a flat earther?

[Atla]

It means the line is composed of...

Here, have a cookie.

So a line segment, as a unit interval, is not composed of fractals/fractions as 1/2,1/3,1/4...etc?

So 1 is not a "set" of fractions?

What are you a flat earther?

You hallucinate too much..

[wtf]

Ehh.. Zero times anything is still zero, and the length of the unit is 1. However you simply can't create a 1-dimensional mathematical object from adding 0-dimensional mathematical objects.

The saying that a line is 'composed' of points only means that wherever you look on the line, you can assign a number to it. It doesn't mean that it's literally composed of 0d points.

Actually that's exactly what it does mean. You can express the unit interval [0,1] as the mathematical union of all its singleton points.

[Atla]

Ehh.. Zero times anything is still zero, and the length of the unit is 1. However you simply can't create a 1-dimensional mathematical object from adding 0-dimensional mathematical objects.

The saying that a line is 'composed' of points only means that wherever you look on the line, you can assign a number to it. It doesn't mean that it's literally composed of 0d points.

Actually that's exactly what it does mean. You can express the unit interval [0,1] as the mathematical union of all its singleton points.

That's plain invalid; you can't jump from 0d to 1d. Obviously.

[wtf]

Ehh.. Zero times anything is still zero, and the length of the unit is 1. However you simply can't create a 1-dimensional mathematical object from adding 0-dimensional mathematical objects.

The saying that a line is 'composed' of points only means that wherever you look on the line, you can assign a number to it. It doesn't mean that it's literally composed of 0d points.

Actually that's exactly what it does mean. You can express the unit interval [0,1] as the mathematical union of all its singleton points.

That's plain invalid; you can't jump from 0d to 1d. Obviously.

You deny that a set is the union of its singleton elements? In other words if I have the set {a,b,c} I can write it as {a} union {b} union {c}. The same goes for infinite sets. You are free to deny that but then you'd have to throw out all of elementary set theory and all of modern math and physical science that's built on top of it.

[Atla]

Actually that's exactly what it does mean. You can express the unit interval [0,1] as the mathematical union of all its singleton points.

That's plain invalid; you can't jump from 0d to 1d. Obviously.

You deny that a set is the union of its singleton elements? In other words if I have the set {a,b,c} I can write it as {a} union {b} union {c}. The same goes for infinite sets. You are free to deny that but then you'd have to throw out all of elementary set theory and all of modern math and physical science that's built on top of it.

Err no, I denied that the line is a set of 0d points.

[Eodnhoj7]

Here, have a cookie.

So a line segment, as a unit interval, is not composed of fractals/fractions as 1/2,1/3,1/4...etc?

So 1 is not a "set" of fractions?

What are you a flat earther?

You hallucinate too much..

So one is not composed of fractions?

So neither is 2 composed of 1+1 or 3 composed of 1+2?