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