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## Homework Statement

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?

## Homework Equations

## The Attempt at a Solution

If S1 is a number segment then there must be numbers a and b and S

_{k}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 S

_{k2}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 S

_{k}and S

_{k2}share more than one number in common the common part is a number segment. However if the intersection between S

_{k}and S

_{k2}is unique such that a=c then the common part is not a number segment.

did i do this right?