Re: Is a line segment composed of points?

On Nov 2, 6:30 pm, "Dave L. Renfro" <renfr...@xxxxxxxxx> wrote:
vred...@xxxxxxxxx wrote:
I was told that a line is composed of infinite number
of points. But this doesn't make sense to me. It is
trivial to prove that two line segments of different
length have same number of points on them and as
well as different number of points at the same.
I think it can also be proved that all line segments
are composed of just a single point and multiple
points at the same time.

What did you think when you were finding the point
of intersection for two non-parallel lines in
a first high school (middle school nowadays,
I hear) course in algebra? And what did you
think about graphing lines by plotting some
of the points on the line?

The question of intersection points is already answered in other
thread, saying these points are boundaries of the line segments, but
are not part of any line segment.

Lets take a look at the points used in graphing. Take y = 2x for
example. The line defined by this equation is actually a boundary
between two regions y <= 2x and y >= 2x. The regions exist, but the
line doesn't exist in the 2D space as a standalone object.

Now, what about the paths such as parabolic trajectory of a missile?
Are they boundaries of some thing? Yes these paths are boundaries (or
part of boundary) of some 2D or 3D objects.

- venkat



.

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