Can you plot 1/3 = .3333... on the number line?

How about 1/2 = .4999999....?

- Fri Oct 18, 2019 10:01 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

- Fri Oct 18, 2019 7:02 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

Irrational numbers cannot be marked on a number line as that would make them rational and finite....they would have to be rounded and in a fixed postion. That's silly. Take a square of side 1. Its diagonal has length sqrt(2). That's a fixed, unchanging length of sqrt(2). You could translate the dia...

- Fri Oct 18, 2019 7:21 am
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

Ignore the red, I messed up and forgot you posted in read. Sorry, you are going to have to sort it out...I am using an ipad. It's all red. I never posted in red. YOU posted in red and I had to sort it out. I'll take a look at what you wrote but meanwhile the quote tags are very straightforward on t...

- Fri Oct 18, 2019 5:35 am
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

So points have a distance between them but this distance has no length? That is a contradiction. I said you can call the distance a length if you like. That's exactly what I said. Formally, in the theory of metric spaces, we assign a distance between any two points. If you like, you may informally ...

- Fri Oct 18, 2019 4:45 am
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

I never asked if the points have zero length, I asked if more than one point always constitutes a length No. Two points may have a distance between them. They don't "constitute" a length, that doesn't mean anything. But two points (in a metric space such as the real numbers) always have a distance ...

- Thu Oct 17, 2019 9:10 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

So if a line is length between two points, and a line is composed of infinite points, a line is composed of infinite lengths? A line is composed of infinitely many points, each of which has zero length. Yet a line has nonzero length. This is a mystery, but we have mathematical formalisms to deal wi...

- Thu Oct 17, 2019 8:40 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

Tell me...if two or more points occur....is there a length between them? Yes, this is the fundamental idea of a metric space. Given any two points there's a function, called the metric, that gives the distance (or length) between them. In the real numbers the distance between the points x and y is ...

- Thu Oct 17, 2019 8:23 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

I didn't object to the union operation. To be honest I don't even see what sets have to do with the question of 0d points vs 1d lines. Oh ok. Good point. Perhaps I didn't make the connection clear. In modern math -- again, this is a historically contingent theory made up by humans, and has arguably...

- Thu Oct 17, 2019 7:45 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

Actually, nothing in actual science rests on this fallacy, in case you haven't figured that out either. I agree that the universe keeps on existing and the galaxies keep flying apart and bowling balls keep falling to earth without intervention from people. No theory of physics is required for the u...

- Thu Oct 17, 2019 6:21 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

- Thu Oct 17, 2019 6:17 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

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

- Thu Oct 17, 2019 5:58 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

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 ...

- Thu Oct 17, 2019 5:54 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2979**

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 ...

- Thu Oct 17, 2019 5:51 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Four pointed Triangles, the Case for an Irrational Triangle
- Replies:
**9** - Views:
**207**

- Thu Oct 17, 2019 4:26 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Four pointed Triangles, the Case for an Irrational Triangle
- Replies:
**9** - Views:
**207**

"I understand why you can believe the dot is not meaningful from a traditional stance. However I am not much one for tradition." It's not a dot, it's a mathematical point. It has no internal structure. If you feel otherwise that's your right, but that's not in accordance with usual math. And I'm afr...