The statement that S is a number segment means that there are numbers a and b and S is the set to which x belongs only in case x is a number between a and b.
Problem 1) If each S1 and S2 is a number segment and there is a number common to S1 and S2 then is the common part a number segment?
The Attempt at a Solution
If S1 is a number segment then there must be numbers a and b and Sk is the set to which the set x belongs only in the case that x is a number between a and b. We assume a and b are not equal. If S2 is a number segment then there are numbers c and d and Sk2 is the set to which x belongs only in the case x is a number between c and d. We assume c and d are not equal. Then if Sk and Sk2 share more than one number in common the common part is a number segment. However if the intersection between Sk and Sk2 is unique such that a=c then the common part is not a number segment.
did i do this right?