My question is arose by the three statements:
- An interval could be thought of as a line segment on the number axis according to this book.
- I think it is true that every line segment has two end points.
The points on a line can be put into a one-to-one correspondence with the real numbers.
so the unit interval [0,1] corresponds to a line segment AB on the number axis with its end points corresponding to real numbers 0 and 1 respectively , (0,1) is an interval different from [0,1], so I think it must correspond to a line segment CD on the number axis different from AB, CD must have two end points different from the end points of AB, so what are the real numbers the two end points of CD respectively corresponding to ? Can we name them using some symbolic notations? Is there something wrong with my reasoning here ?