When I was a child I argued with my school teacher, when she draw a circle on table and claimed that there are infinite number of points on it, that in reality there cannot be infinite number of points on a (finite) circle, or else you could never draw a circle.
Today I think that it’s useful to put mathematical concepts in physical context, so, how many points are there between any given points A and B? Divide that distance by plank’s length.
A set doesn’t order its points, but we can. In the set of numbers from one to ten there may be no order, but we still speak of five being more than three.
What do you call the location where two lines cross?
“Infinite” doesn’t mean “like a lot, really a lot, but even more”. It’s more a case of “it doesn’t make sense to talk of limiting things in this aspect”.
In a physical sense, you’re (probably) correct. In a mathematical sense, though, there’s no dimensionality to define the Planck length against. I can have two points at {0, 0, 0} and {0, 0, 1.6×10−35} and still define a million points in a straight line between them, because I’m not dealing in metres. Just co-ordinates.
A set can order its components into sub sets. But yeah we don’t create an actual point we just give a name to something at x distance from a fixed point. In theory none of the points on a line have to be related by distance or anything other than form, depends on the set. We could say that the number of points that are fractions of the whole are equal to the number of points that are whole numbers, theoretically equally infinite, but what would be the point, infinity maths and continuums of 1 to 1 infinites have no practical use except as interesting maths problems. Sets are just ways of boxing up maths into discreet categories of not being a dog and being a cat or mouse. it’s only infinite in your head, which is less useful than infinite on paper where practical limits to reality can be set and approached.
Some philosophy dude.
I think the OPs definition sucks basically as it is not at all necessary to define it as distances from a point as he himself says it is undefinably vague, ie there doesn’t have to be an abstract co-ordinate system,hence the line means little or nothing to anyone.
I have to admit I think the maths guy was trying to sound clever by being vague. Infinity always makes people seem smart because no one really can imagine it, so if you can use it you give the illusion you understood it, even if its limit often seen as something something converges to to be any use definitely, it’s still an undiscovered country and of little use as a destination for real world mathematics.
Yes, and…
But if you do care to call it a point, then it is a floating point because you haven’t positioned it - you can’t reidentify it by a second act of pointing.
Well, in regards to your original post, a line may not necessarily be composed of points, but it is ridiculous to claim that there are no points on a line that is drawn apart from A and B. It’s just a way of constructing things.
i think it’s important to recognize that math is a tool, not an objective description of reality. some of it accurately models reality, but not all of it.
the uses of having a line composed of infinite points instead of finite points is that this line, and all shapes made up of infinite points as well, can be scaled to any level and still be a useful model of reality. if anybody is having trouble understanding what i mean by that, i may be able to explain it. maybe. let me know.
isn’t it annoying when you make a point everyone should agree with by axiom if nothing else. 
Hell yeh, if maths doesn’t reflect reality it’s just mental masturbation (valuable maybe who knows, but it probably only gets pure mathematicians excited, it solves little beyond that) an example is the number axis i, or the imaginary numbers they were pointless when first discovered quite literally because they only applied to a concept not a realised form of science or maths, ie applied maths trumps pure maths in science. 300 years later quantum physics couldn’t exist without them, when they are either the axis of time, a 4th axis, or a relation to x,y,z,at t=i. All geometry and hence all calculus can be modelled from the 4th axis.
Ie 
Genius. Simple and elegant, and it happens to contain all the fundamental rules of maths, this identity makes many mathematicians wet.
Here’s a question, what number can you think of that is the square root of another number when added to +1=0.
Go ahead, you’re right but can you explain why? It’s useful as a definition only if such a definition is deliberately vague. To be useful beyond philosophy it needs exact definition, René Descartes did this with a relation to x and y with a dependant and independent variable from whence calculus rules had come, then someone invited spherical polar co-ordinates and related it to all geometry by pi then someone had the idea that all geometry needed not just 3 dimensions but a relation to more than 3 and i and time or another dimension beyond x,y,z was born.
Lines have no points. They might have positions, but only if they are made.
Possibly in agreement there.
But surely you can make a point on the line, right? The position of the line.
cheegster wtf you silly goose
I don’t even knw why I’m getting involved really.
Yeah I was just gonna say that. The past view posts should have been in the philosophy board of natural science. Specifically mathematics. Are you saying the foundations of mathematics are wrong on some specific conceptions?
“wrong”? no. i wouldn’t use that term. all of simple math - addition, subtraction, multiplication - is completely correct (i’m not interesting in arguing about that, for any of you contrarians out there, it’s pretty obvious why those things are correct). when you get to more abstract concepts is where it starts deviating from reality, but it’s still useful for reality, and i’d even posit that there’s no better way to make math. there’s no way to make it not deviate from reality and still remain as simple and useful as it is.
I would
Such as?
I totally agree. Im still wrestling with the idea to be able to respond to it. To much DEVIATING lol…