A student says that a line segment has an infinite number of points. Another student disagrees How?

Question

A student says that a line segment has an infinite number of points. Another student disagrees and says that a line has an infinite number of points. How do you respond?

Answer 1

I would say that the second student is correct. A line segment is just a piece of a line, and ends eventually. Therefore it is impossible for it to have an infinite number of points. A line, on the other hand, never ends, so it can have an infinite number of points.

Answer 2

Both are correct.

Answer 3

Ohh, well when you think about it, that's true, after all, on a line segment, if you take like the billionth decimals and more into account, you can technically say there's an infinite number of points.  

Answer 4

EDIT:

Should have read the question closer.

Both are correct, because for this topic, there is no difference between a line and segment.

EDIT END

The first is confused by the number of points and the number of endpoints. There are an infinite number of points. It doesn't matter how long the segment is, becasue it can always be divided into smaller and smaller segments, and there are an infinite number of points on each, no matter how small they get.

Ignore the Y axis (assume 0) and consider the line from 0 to 1 on the  X axis:

Note that the point 0.1 is on that line.

Note that the point 0.01 is on the line

Note that the point 0.001 is on the line

...

Note that the point 0.00000000000000000000000000001 is on the line,

...

There are an infinite number of points on any segment.

Answer 5

A segment has ending points, as in it will not go on forever like the first student indicated.  It will indeed end when the segment ends.  A line however has no beginning or end, so technically it has an infinite number of point.

Answer 6

At least in theoretical math, lines and segments of lines have an infinite number of points, because you can divide them into smaller line segments an infinite number of times.

If we're defining points to mean end points, then lines have none and continue forever, and line segments each have two.

Rays are really cool. They manage to have just one end point. Trippy!