Must be future engineers...

[markem]

Originally Posted by QUAZY50

I must not understand this question then. If the answer is zero then they are the same point, making it one point. I would argue the answer, a straight line, is correct to the question you posed, otherwise there are not two points. (I am an electrical engineer, just out of school, but I got the degree lol.)

Am I wrong?

The question is "between two points" which means that you get to pick them. In this case, you pick them to be coincident since that would be the shortest distance (you can also place them infinitely close such that the distance approaches zero).

For "any two points" you do not get to pick the points, merely state that the distance (in 2 and 3 dimensional space but not in higher spaces) is represented by the straight line path between the two points.

The word "any" makes them completely different questions.

[QUAZY50]

Originally Posted by markem

The question is "between two points" which means that you get to pick them. In this case, you pick them to be coincident since that would be the shortest distance (you can also place them infinitely close such that the distance approaches zero).

For "any two points" you do not get to pick the points, merely state that the distance (in 2 and 3 dimensional space but not in higher spaces) is represented by the straight line path between the two points.

The word "any" makes them completely different questions.

Agreed, but then couldn't your straight line be infinitesimally small? This way the length of said line approches zero... Correct?

[markem]

Originally Posted by QUAZY50

Agreed, but then couldn't your straight line be infinitesimally small? This way the length of said line approches zero... Correct?

a point is not a line. basic geometry.

The whole point is to pick on the lack of accuracy in the English language.

[QUAZY50]

Originally Posted by markem

a point is not a line. basic geometry.

The whole point is to pick on the lack of accuracy in the English language.

I understand that.. My point is that if you can place two points infinitesmally close together, you can draw and infinitesmally small line between them... thus making that answer still true. However, if the points are coincident (sharing the same space) then the answer is zero and not a line because the line wouldn't be between them.

No where did I say a line was a point, even though, technically you could argue an infinitesmally small line is a point because a point has no length or diameter, or width or anything.

I completely derailed this thread, sorry.