Stupid ideas 2: A line is composed of points

[JohnJones]

The typical line definition of mathematics is Mendellsohn’s. This states that a line is composed of an infinite number of points and that between every two points there lies more points.

But this description doesn’t work. If between any two named or positioned points, A and B, there are other points then those other points are unpositioned. Because they are unpositioned then there is no line.

[cheegster]

How are they unpositioned? They are directly between point A and point B.

Also, there is pretty much an active thread on this already, it’s Zeno’s paradox. You should find some satisfying answers there.

[Humpty]

are you by any chance Bill Gaede? (your ideas are very similar to his) if so, i’m sorry to inform you that all your ideas are the result of heavy PTSD and slight insanity.

[fuse]

@Humpty

are you by any chance Bill Gaede? (your ideas are very similar to his) if so, i’m sorry to inform you that all your ideas are the result of heavy PTSD and slight insanity.

…Humpty…that would not necessitate that the ideas are untrue/invalid…

[Only_Humean]

@JohnJones

If between any two named or positioned points, A and B, there are other points then those other points are unpositioned. Because they are unpositioned then there is no line.

If they are unpositioned, how do you know they are between A and B?

[turtle]

@Only_Humean

@JohnJones

If between any two named or positioned points, A and B, there are other points then those other points are unpositioned. Because they are unpositioned then there is no line.

If they are unpositioned, how do you know they are between A and B?

How many neutrinos are there between A and B?

[Only_Humean]

@turtle

@Only_Humean

@JohnJones

If between any two named or positioned points, A and B, there are other points then those other points are unpositioned. Because they are unpositioned then there is no line.

If they are unpositioned, how do you know they are between A and B?

How many neutrinos are there between A and B?

If A and B are physical points, that’s an ill-defined but empirical question which I can’t answer. If they’re conceptual points, then none. You seem to have missed my (conceptual) point.

[jonquil]

@turtle

@Only_Humean

@JohnJones

If between any two named or positioned points, A and B, there are other points then those other points are unpositioned. Because they are unpositioned then there is no line.

If they are unpositioned, how do you know they are between A and B?

How many neutrinos are there between A and B?

All is indeterminate on that level, even A and B.

[Calrid]

It’s not a particularly accepted or even useful definition tbh. But it would suffice until it had to be divided into lines of equal length, then it would be undefinable. An infinite line or set of points does not exist except in concepts such as time.

A line is a closed set of all the points between a and b, practically we can by definition only divide it up mathematically finitely or it would transcend exact definition like pi.

[Humpty]

@Only_Humean

@JohnJones

If between any two named or positioned points, A and B, there are other points then those other points are unpositioned. Because they are unpositioned then there is no line.

If they are unpositioned, how do you know they are between A and B?

BECAUSE THEY DON’T HAVE LETTERS HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA
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[JohnJones]

@cheegster

How are they unpositioned? They are directly between point A and point B.

Also, there is pretty much an active thread on this already, it’s Zeno’s paradox. You should find some satisfying answers there.

They are unpositioned because the only positions given are those of A and B. We don’t know where they fall between A and B.

[JohnJones]

@Only_Humean

@JohnJones

If between any two named or positioned points, A and B, there are other points then those other points are unpositioned. Because they are unpositioned then there is no line.

If they are unpositioned, how do you know they are between A and B?

We know they are between A and B, but because their postions to each other are not specified then they are floating points.

[Humpty]

omgt my parody of him was exactly what he was going to say anyway.

[JohnJones]

@turtle

@Only_Humean

@JohnJones

If between any two named or positioned points, A and B, there are other points then those other points are unpositioned. Because they are unpositioned then there is no line.

If they are unpositioned, how do you know they are between A and B?

How many neutrinos are there between A and B?

Points are not positions.

[fuse]

@JohnJones

They are unpositioned because the only positions given are those of A and B. We don’t know where they fall between A and B.

It doesn’t matter. Because they fall between A and B you confirm that

between every two points there lies more points

[JohnJones]

@jonquil

All is indeterminate on that level, even A and B.

If “everything is indeterminate” on that level, then you cannot specify anything, let alone everything.

[JohnJones]

@Calrid

It’s not a particularly accepted or even useful definition tbh. But it would suffice until it had to be divided into lines of equal length, then it would be undefinable. An infinite line or set of points does not exist except in concepts such as time.

A line is a closed set of all the points between a and b, practically we can by definition only divide it up mathematically finitely or it would transcend exact definition like pi.

If a line is a closed set of all points (and there is no “set of all” - it’s simply “all”) then as all the points are unpositioned (for a set doesn’t order its elements) the idea is a contradiction.

We can give a line a position on it by mathematical construction. But we don’t create a point.

[cheegster]

@JohnJones

@cheegster

How are they unpositioned? They are directly between point A and point B.

Also, there is pretty much an active thread on this already, it’s Zeno’s paradox. You should find some satisfying answers there.

They are unpositioned because the only positions given are those of A and B. We don’t know where they fall between A and B.

A line is the shortest distance between two points. Whether it be conceptual or physically drawn on paper, you can point out any part of where this line travels and call it a ‘point’.

Boom.

[Calrid]

@cheegster

@JohnJones

@cheegster

How are they unpositioned? They are directly between point A and point B.

Also, there is pretty much an active thread on this already, it’s Zeno’s paradox. You should find some satisfying answers there.

They are unpositioned because the only positions given are those of A and B. We don’t know where they fall between A and B.

A line is the shortest distance between two points. Whether it be conceptual or physically drawn on paper, you can point out any part of where this line travels and call it a ‘point’.

Boom.

Only in two dimensions, a line could be further than a curvilinear path in a non euclidean space-time frame, or even simply drawn across the surface of a sphere between two points where travel through the sphere is forbidden by physically breaking the spheres surface. It depends on geometry and its axiomatic form. In Euclidean geometry a circle is related exactly by pi, in non euclidean geometry it could be related by a whole number such as 3.

[north]

what comes first , the line or points ?