- #1
hlin818
- 30
- 0
Homework Statement
a) Let I be a subset of the real line. Prove I is an interval if and only if it contains each point between any two of its points.
b) Let Ia be a collection of intervals on the real line such that the intersection of the collection is nonempty. Show the union of the collection is an interval.
Homework Equations
The Attempt at a Solution
a) An interval is the set (a,b), [a,b], or [a,b). Let I be one of these sets. we want to show that if x and z are in I and x<y<z, then y is in I. Isn't this trivial by how interval is defined?
b) not sure