Line Segment Can Potentially Be a Circle

[Eodnhoj7]

Question:

If a line segment is infinitely halved thus resulting in a non-zero sized line segment that is equivalent to or less than the infinitely small space between the points that compose the original line segment does this necessitate the line segment as a self-referential process maintained through an infinite process of superpositioning where the infinitely small spaces between points is a process of fractal dimensions within fractal dimensions, as these are infinitely small linear spaces, and this self-referentiality necessitates the line being a circle as each point equidistant from the infinite points manifesting around it, thus a paradox results?

Summary of AI: Potentially yes.

Copy and paste into philosophy ai, on Google, for full analysis.

[wtf]

Question:

If a line segment is infinitely halved thus resulting in a non-zero sized line segment that is equivalent to or less than the infinitely small space between the points that compose the original line segment

Points on a line aren't like bowling balls, lined up one after another. Between ANY two there is a continuum more of them, as many as on the original line.

You can't "infinitely halve" a line and there is no such thing an "infinitely small" line segment. Every line segment that is not a single point of length zero has a positive length, whether it's 1/one million or 1/one zillion. No matter how large a positive integer you put in the denominator, the resulting fraction has length greater than zero.

[Eodnhoj7]

Question:

If a line segment is infinitely halved thus resulting in a non-zero sized line segment that is equivalent to or less than the infinitely small space between the points that compose the original line segment

Points on a line aren't like bowling balls, lined up one after another. Between ANY two there is a continuum more of them, as many as on the original line.

You can't "infinitely halve" a line and there is no such thing an "infinitely small" line segment. Every line segment that is not a single point of length zero has a positive length, whether it's 1/one million or 1/one zillion. No matter how large a positive integer you put in the denominator, the resulting fraction has length greater than zero.

These are abstractions thus the proof is purely mind. You cannot empirically prove or disprove your or my argument.

However,

I am talking about the line segment, not line.

The line segment has infinitely small space between the points (this is the current conception) thus relatively when two consecutive points are chosen within the line segment there is an infinitely small space between points A and B, this space is linear thus can be argued as a line segment.

If there is no infinitely small space between the points through which it is composed then the points are not distinct and cease to exist, thus no points.

The AI claimed that while my argument does not fit in with the current consensus but the argument may be potentially correct.

You can infinitely halve a line as the AI provided an equation to do so. The line will always be finite, but the process of halving occurs regardless.

[wtf]

These are abstractions thus the proof is purely mind. You cannot empirically prove or disprove your or my argument.

Given two real numbers x and y, the number (x + y)/2 is a distinct real number strictly between them. So you are wrong about your idea of points being next to each other.

I am talking about the line segment, not line.

How does that make any difference?

The line segment has infinitely small space between the points (this is the current conception)

No it does not. Nor is it the "current conception." It's your own mistaken conception.

thus relatively when two consecutive points are chosen within the line segment there is an infinitely small space between points A and B, this space is linear thus can be argued as a line segment.

Of course this is nonsense, as I showed. If x and y are the two points, then (x + y)/2 is a third point strictly between them.

If there is no infinitely small space between the points through which it is composed then the points are not distinct and cease to exist, thus no points.

Nonsense. How do you get that? The distance between any two points on a line or a line segment is always greater than zero. If the two points are x and y, the distance between them is |x + y|.

The AI claimed that while my argument does not fit in with the current consensus but the argument may be potentially correct.

You are foolish to believe anything an "AI" says. It's just autocomplete. You might as well take advice from the computer chip in your washing machine.

You can infinitely halve a line as the AI provided an equation to do so. The line will always be finite, but the process of halving occurs regardless.

More nonsense. Curious to see this "equation" though.

[Eodnhoj7]

These are abstractions thus the proof is purely mind. You cannot empirically prove or disprove your or my argument.

Given two real numbers x and y, the number (x + y)/2 is a distinct real number strictly between them. So you are wrong about your idea of points being next to each other.

I am talking about the line segment, not line.

How does that make any difference?

The line segment has infinitely small space between the points (this is the current conception)

No it does not. Nor is it the "current conception." It's your own mistaken conception.

thus relatively when two consecutive points are chosen within the line segment there is an infinitely small space between points A and B, this space is linear thus can be argued as a line segment.

Of course this is nonsense, as I showed. If x and y are the two points, then (x + y)/2 is a third point strictly between them.

If there is no infinitely small space between the points through which it is composed then the points are not distinct and cease to exist, thus no points.

Nonsense. How do you get that? The distance between any two points on a line or a line segment is always greater than zero. If the two points are x and y, the distance between them is |x + y|.

The AI claimed that while my argument does not fit in with the current consensus but the argument may be potentially correct.

You are foolish to believe anything an "AI" says. It's just autocomplete. You might as well take advice from the computer chip in your washing machine.

You can infinitely halve a line as the AI provided an equation to do so. The line will always be finite, but the process of halving occurs regardless.

More nonsense. Curious to see this "equation" though.

Facepalm. A point is paradox. I will address this aspect of the conversation in a new thread focused on this, "The Paradox of the Point and the Foundations of Geometry as Paradoxical".

Anyhow:

If a continuum of points are between points, as there are infinite points in a continuum, than any two points have infinite points between them thus necessitating an infinitely small space between points as points thus infinite line segments within line segments.