What is a line then?Atla wrote: ↑Thu Oct 17, 2019 6:04 pmErr no, I denied that the line is a set of 0d points.wtf wrote: ↑Thu Oct 17, 2019 5:58 pmYou 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.

## 0d Lines and Circles

### Re: 0d Lines and Circles

### Re: 0d Lines and Circles

So the number line is false?Atla wrote: ↑Thu Oct 17, 2019 5:56 pmThat's plain invalid; you can't jump from 0d to 1d. Obviously.wtf wrote: ↑Thu Oct 17, 2019 5:54 pmActually 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 wrote: ↑Thu Oct 17, 2019 4:39 amEhh.. 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.

### Re: 0d Lines and Circles

### Re: 0d Lines and Circles

What do you mean? A line is a continuous conceptual 1-dimensional object.Eodnhoj7 wrote: ↑Thu Oct 17, 2019 6:09 pmWhat is a line then?Atla wrote: ↑Thu Oct 17, 2019 6:04 pmErr no, I denied that the line is a set of 0d points.wtf wrote: ↑Thu Oct 17, 2019 5:58 pm

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.

### Re: 0d Lines and Circles

The number 1 is a concept of a unit, and the other numbers are derived from this.

What else ffs

### Re: 0d Lines and Circles

Take it up with Euclid. Or any modern mathematician. I can't argue this point with you. Did you miss high school math? The real line is composed of an infinite set of 0-dimensional points. You can make up your own math but you'll be denying all of modern math and science.

### Re: 0d Lines and Circles

You really didn't figure out yet that this is a thousands of years old fallacy?wtf wrote: ↑Thu Oct 17, 2019 6:17 pmTake it up with Euclid. Or any modern mathematician. I can't argue this point with you. Did you miss high school math? The real line is composed of an infinite set of 0-dimensional points. You can make up your own math but you'll be denying all of modern math and science.

### Re: 0d Lines and Circles

So it is a concept of a unit. It is a concept of something we measure.

And units are not composed of units? An orange is not composed of atoms, or one body of organs, or a Russian doll is not composed of further dolls?

### Re: 0d Lines and Circles

### Re: 0d Lines and Circles

No, a unit is something you measure with, not something you measure.

There are no actual units (like oranges and atoms) in the real world.

As I said many times, pretty much your entire 'philosophy' is based on such cognitive illusions.

### Re: 0d Lines and Circles

Atla wrote: ↑Thu Oct 17, 2019 6:27 pmNo, a unit is something you measure with, not something you measure.

So a unit such as a meter is not composed of centimeters or millimeters?

Actually the word unit means "individual or thing that is single or complete" according to a simple dictionary defintion.

There are no actual units (like oranges and atoms) in the real world.

As I said many times, pretty much your entire 'philosophy' is based on such cognitive illusions.

So there are no units in the real world, then there are no measurements kn the real world either then?

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