there are 12 distinct named points on a line. How many segments can be named?
Is there a way or formula to know the number of segments can be named in a line with distinct points?
Please help me on this..
Is that the way you think mathematics is done- by plugging numbers into formulas? Where do you think those formulas come from?
Did you consider looking at simple cases? If there are no points, there is the single segment, (-infinity, infinity). If there is a single point, A, there are three segments, (-infinity, infinity), (A, infinity) and (-infinity, A). If there are two points, A and B, with A< B, there 6 segments, (-infinity, infinity), (-infinity, A), (-infinity, B), (A, B), (A, infinity), (B, infinity). Do you see a pattern? With n points you have the intervals from -infinity to each of the n points plus +infinity so n+1 such intervals. Then you have intervals from the "left most point" to each of the other points and to +infinity, n such intervals. That is, you have (n+1)+ (n)+ (n- 1)+ ... + 3+ 2+ 1. Do you know a formula for that? If not, can you work one out?
However, I disagree with Prof. Hals on the definition of line segment. In the Hilbert/Moore system of axiomatic geometry a line segment is defined as:
. The set of which is the union the set of two points with the set of all point between them. (see Moise)
So the answer to your question is .
The concepts of line, ray, half-lines are all different. Those are all what one may call "infinite". A line segment has two endpoints.